This post will be a trip down memory lane. The Bowl Movements were born in December of 2006 as the brainchild of Daniele. The original Movements included Johnebob, T-Bone, JD, and the Big Z. Although I don't remember it this way, according to the USBC, I led the team with a 135 average, and Z was 2nd with a 134. How Z managed to do this is unclear. When he approached the foul line to throw the ball, he looked like a drunk bum stumbling into an alley. Baby Johnny managed a 128, and JD finished the season with a 118. See Canadian, you've got nothing to be ashamed of.

The 2nd season was characterized by turmoil after the loss of Zink. We struggled to find a consistent 4th with a never ending cast of characters who we scraped up out of the gutters of Laramie (Woody, Becker, Timmy, and Jeremiah). On top of that, I sustained a knee injury which kept me out of competition for at least six weeks. JD and JL carried the team that season in every way.

With the 3rd season, we found the Canadian, who has provided a steady and much needed presence occupying the three spot in the lineup. During the first two seasons, we only bowled the 2nd halves. This season, we have bowled both the fall and spring rounds. We have never placed very highly in the league, always in the bottom half. Hopefully this spring will be the emergence of the Bowl Movements as we currently sit in 2nd. After all, we have gone from being enigmas in the league to 10% of the Bernaski rollers actually knowing our names. We have seen at least three teams leave the league. We are now a firm fixture in the Lanes of Laramie and even placed 13th in the City Championships by handicap. We have improved. There is no doubt. In this post, I describe that improvement. I begin with the BIA, the last thirteen weeks of data. Then, I look at the last two years.

The graph to the left shows the progression of our league averages over the last thirteen weeks. The City Championships did not count toward our averages, so those data are left out. At the start of the BIA, JD led the team with a 150 average, but despite a stellar start to the season, he has struggled lately and has dropped to a 145. Johnebob's average has grown from a 149 to a 153 where he has been sitting for many weeks. I have experienced something of a epiphany over this time period, adding ten pins to my average from a 134 to a 144. Geoff bottomed out in the middle of December with a 124 and maxed out toward at the end of January at 129. He currently sits at 127. As a team, our average has grown from 139.75 to 142.25. We have been slowly improving overall.

Over the short term, improvement seems to be slow and steady for the team as whole, but when we look at it over the last three seasons, it is remarkably consistent. First, let's look at bowler averages for the four half seasons of the Bowl Movements's existence.

The graph to the right was mostly culled from data housed in the Great Archives of the USBC. The most recent average is calculated for the first eight weeks of the 2nd half of the Bernaski. Obviously, we don't have much data for Gee-Off, but for the original Movements, we can examine improvement directly. What should be immediately apparent is that Johnebob just keeps getting better. From humble beginnings, he has grown to be a good bowler. For the 2nd half of the season, he has a 160 average, something that would have seemed impossible two years ago. Likewise, JD has added nearly 27 pins to his average since the 07 season, although he has plateaued of late. I started well but declined last spring. I'd like to blame my injury and the adoption of the Green Lady, but let's face it, I had a CRAPPY season. This year, especially lately, I have been going nuts, and I have averaged 157 for the 2nd half. For his first season, Prince Edward Islander is right where he should be, and it should be clear where he is going. Now the part that is truly remarkable.

If we examine the team average for Joe, John, and I, an incredibly steady rate of improvement is evident. Looking at the graph to the left, it may appear that we have been improving rapidly in recent weeks, and we have. However, if we look at the growth of our team average by half season, our rate of improvement is remarkably constant. In fact, our team average has increased 8 to 10 pins for every half season we bowl. This makes me wonder what we would be bowling now if we had bowled the full 06-07 and 07-08 seasons. This should also give Geoff a clear idea of what to expect for the future. As bad as we are at bowling, we are a hell of a lot better than we were two years ago, and we should just keep getting better.

## Saturday, February 28, 2009

## Friday, February 27, 2009

### Are We Improving at Bowling? The Short Term View

Joe, John, and I have been bowling in the Bernaski League for three seasons now. When we started, we stunk. Now, we have a mild B.O. [El Jefe is in his first season and still stinks.] In other words, we are far from being good bowlers, but it’s pretty clear that we have gotten better. We all have our ups and downs, but when viewed from the long term perspective, we have improved. I will look at the long term numbers in another post, but herein I want to focus on the last thirteen weeks, the time period for which we have detailed data.

It is an interesting problem to try to detect improvement in bowling skill over the short term because individually and as a team, our game and series scores fluctuate wildly. The simplest way to try to gauge improvement would be to look for a relationship between time and pin totals for the team. If we are improving, there should be a clear relationship between these two variables. In reality, however, it is not so clear.

The ideal case might involve a team whose average increased a steady one or two pins per week. In that case, we would see a graph that looks like the one above and to the left (click on it to make it bigger). In the real world, however, while the average may slowly creep up like this, there is a huge amount of fluctuation around that average from week to week as shown in the middle graph above (based on fictitious data). In the second case, the improvement signal is swamped by a huge amount of noise, and to even see it would require looking at scores over a long period of time. The graph above and right is identical to the one in the middle except I have expanded it to include 34 weeks of data instead of 13. Notice how the signal becomes immediately apparent when viewed from the long term perspective.

I believe that the latter two graphs are a good description of our bowling improvement. We fluctuate wildly around our average, but our average keeps growing steadily. Here is the evidence for this contention. I looked at the team average for our core bowlers week by week. I left out both of our subs (sorry Becker and Gingy) who have done wonders for us of late. This is shown in the graph below and left. Notice that it looks like we are treading water, that no improvement is evident. In fact, if you fit a regression to this scatter, it would suggest that we are getting worse by approximately 0.14 pins per week as a team. My contention is that if we had data for the entire season, the graph would look a lot like the one above and to the right. In fact, it’s not difficult to demonstrate that this is the case.

The graph above and right shows our team handicap over this same time period. The handicap is calculated using data from the entire season, and over the 13 weeks for which we have data, we have taken 11 pins off of our team handicap (from 287 to 276), an approximate improvement of one pin per week for the whole team. In contrast to week-to-week team averages, the change in handicap tells us how well we have been bowling recently compared to all prior weeks in the season, and it shows clearly that were are improving… one pin at a time.

It is an interesting problem to try to detect improvement in bowling skill over the short term because individually and as a team, our game and series scores fluctuate wildly. The simplest way to try to gauge improvement would be to look for a relationship between time and pin totals for the team. If we are improving, there should be a clear relationship between these two variables. In reality, however, it is not so clear.

The ideal case might involve a team whose average increased a steady one or two pins per week. In that case, we would see a graph that looks like the one above and to the left (click on it to make it bigger). In the real world, however, while the average may slowly creep up like this, there is a huge amount of fluctuation around that average from week to week as shown in the middle graph above (based on fictitious data). In the second case, the improvement signal is swamped by a huge amount of noise, and to even see it would require looking at scores over a long period of time. The graph above and right is identical to the one in the middle except I have expanded it to include 34 weeks of data instead of 13. Notice how the signal becomes immediately apparent when viewed from the long term perspective.

I believe that the latter two graphs are a good description of our bowling improvement. We fluctuate wildly around our average, but our average keeps growing steadily. Here is the evidence for this contention. I looked at the team average for our core bowlers week by week. I left out both of our subs (sorry Becker and Gingy) who have done wonders for us of late. This is shown in the graph below and left. Notice that it looks like we are treading water, that no improvement is evident. In fact, if you fit a regression to this scatter, it would suggest that we are getting worse by approximately 0.14 pins per week as a team. My contention is that if we had data for the entire season, the graph would look a lot like the one above and to the right. In fact, it’s not difficult to demonstrate that this is the case.

The graph above and right shows our team handicap over this same time period. The handicap is calculated using data from the entire season, and over the 13 weeks for which we have data, we have taken 11 pins off of our team handicap (from 287 to 276), an approximate improvement of one pin per week for the whole team. In contrast to week-to-week team averages, the change in handicap tells us how well we have been bowling recently compared to all prior weeks in the season, and it shows clearly that were are improving… one pin at a time.

Labels:
Bowl Movements,
bowling statistics,
improvement

## Thursday, February 26, 2009

### Breakin' Some Eggs...

It has often been said that in order to make an omelette, one needs to break a few eggs. As my rookies season winds down, it is safe to say I've laid my fair share of eggs. Season 1 has not been kind and I have struggled with many of the same issues that NBA rooks experience - the bright lights, the long pro season, and the endless stream of "bowlies" (Laramie Lanes version of "groupies"). Hell, last Tuesday morning I woke up next to some nasty trailer park trashheap in Walden, CO and thought "this is not my beautiful house...that is not my beautiful wife!"

My main issue this year has been consistency. Like many rookies, some nights it is there and some nights it is not. In an effort to improve my consistency (and hide from my schoolbooks), I sought solace at the lanes for a rare Thursday matinee. I found no support from teammates (they have real jobs) so I rolled forward alone. In under two hours, I bowled 10 games. My primary goal was to develop and subsequently hone a new "gyro" ball. The straight-on approach is a bitch goddess - she giveth with one hand and taketh away with the other. As such, I wanted to practice my new style.

Initially, results were not promising. 129...103...88...83 (thank Pinneaus it was not a league night!). The low point of the day came when I broke Lane 15. Things were going so poorly I suspect the automatic-pin-setter-upper took pitty on me and gave up the game. It simply stopped working. The bowling-counter dude quickly ushered me over two lanes to #17, quietly muttering something about "if you didn't suck so bad..." As I found my rhythm on the new planks, I was blinded by a flash of light. "Ah-ha," I thought. "Finally a revelation!" But alas, it was just the bowler-counter dude and his welding-torch-wielding friend trying to summon hot metal to put back together what I had broken.

After six games, the gyro began to take hold. In my last four games, I rolled 130, 144, 160, and 140. I even had three chances at turkies (so elusive). After a few rough Mondays, I am optimistic that I will bounce back with a decent league-night performance. I am less optimistic, however, that I will be welcome back by Lane 15. Having felt the raw power of Canadian (bowling) balls, I suspect it will be reluctant to raise the protective gate the next time I roll.

That's all for now. Cuckoocachoo.

### Rare or Impossible Two Pin Leaves in Bowling

Since I started keeping stats on the pins left standing after the first throw, I have recorded 334 pin configurations. Of these, 110 are unique. It is possible to increase this number to 150 with the current count by making a symmetry assumption: if a particular spare combination has been observed, then the mirror image about the midline is also possible. For example, if a 6-7 leave has been observed, then it is assumed that a 4-10 leave is also possible.

To date, I have observed every possible single pin spare opportunity. There are ten of these. Among the bowlers I have observed, the 5 pin is most likely to be left standing when a score of 9 is received on the first ball. A standing 1 pin is the rarest.

This post concerns two pin leaves. There are 45 theoretically possible combinations of two pins remaining after the first ball. Of these, I have recorded a total of 35 when symmetrical pairs are included. I have divided the ten that I have not yet recorded into two groups, symmetrical and asymmetrical. The symmetrical leaves are symmetrical about the midline. The asymmetrical are not:

Symmetrical leaves not observed: 1-5, 2-3, 8-9, 7-10

Asymmetrical leaves not observed: 1-7, 1-10, 2-6, 2-9, 3-4, 3-8

So here’s the question. Have these not been observed because they are impossible to leave, or because they are rare? One of these is obviously possible because we have all seen it, and it is probably the most famous leave in all of bowling, the 7-10 split. It is apparently not particularly common. Is the same true of the others? My hunch is that all of these are possible but one, the 2-3. It is hard to imagine how this could be accomplished without some crazy pin action. Anyone else care to venture a guess? Has anyone seen a 1-5 or an 8-9?

To date, I have observed every possible single pin spare opportunity. There are ten of these. Among the bowlers I have observed, the 5 pin is most likely to be left standing when a score of 9 is received on the first ball. A standing 1 pin is the rarest.

This post concerns two pin leaves. There are 45 theoretically possible combinations of two pins remaining after the first ball. Of these, I have recorded a total of 35 when symmetrical pairs are included. I have divided the ten that I have not yet recorded into two groups, symmetrical and asymmetrical. The symmetrical leaves are symmetrical about the midline. The asymmetrical are not:

Symmetrical leaves not observed: 1-5, 2-3, 8-9, 7-10

Asymmetrical leaves not observed: 1-7, 1-10, 2-6, 2-9, 3-4, 3-8

So here’s the question. Have these not been observed because they are impossible to leave, or because they are rare? One of these is obviously possible because we have all seen it, and it is probably the most famous leave in all of bowling, the 7-10 split. It is apparently not particularly common. Is the same true of the others? My hunch is that all of these are possible but one, the 2-3. It is hard to imagine how this could be accomplished without some crazy pin action. Anyone else care to venture a guess? Has anyone seen a 1-5 or an 8-9?

Labels:
Bowling,
bowling statistics,
pin statistics,
spares,
Two Pin Leaves

## Wednesday, February 25, 2009

### A Big, Ugly, Greasy Win

We went from having one of our best nights ever, placing 13 out of 66 in the City Championships, to one of our worst nights ever. Still, we pulled out a W, going 3-1 against Overrated. Yes, they bowled poorly, too. As this win is difficult to explain given our prior records, it must be attributed to lane conditions. Lanes 17 and 18 on Monday night were slick, like bowling on Crisco. The ball had no bite. Spin was not causing a lot of action unless the ball was spinning like a dreidel and moving at low velocity. Oily lanes were not only problematic for us but also for the OR boys, as they could not seem to find the pocket either.

The hardwood was so lubricated that balls slipped easy between the pins. It was so slippery out there that the balls would emerge from the chute with glistening lines of lube. If by chance, you foot fouled, you would have found yourself on your back sliding down the lane as if it were a slip and slide. There was so much oil out there that Lou Ferrigno was rolling around on Lane 17 in preparation for the Mr. Olympia competition. Did I mention that the lanes behaved like they were coated with KY Jelly? Yes, it was slick.

While it may seem like I am just making excuses for our poor performance, there is good reason to believe that something was amiss with the lanes against the wall last night. For one, we bowled like shit. This is not necessarily unusual. What is unusual is that the team against which we bowled, bowled even worse. From last week, we dropped a total of 220 pins. On top of that, we had our fewest number of strikes on record, 24 to be exact. This was six fewer than we had ever bowled in a three game set. Yet, we took three of four. We even won a game with a handicapped score of 811 in the first. Our lowest pin total victory prior to this was an 827.

It is worth noting that with the completion of Monday’s bowling, the season is ¾ complete, and we are halfway through the 2nd half of the season. We currently stand in 2nd place with 20 wins, nine fewer than we had for the entirety of the 1st half. The Movements are still poised to finish at the top of the standings in the Bernaski League spring season.

We now have 13 weeks of bowling data. Using prior results, it is possible to estimate the probability that on a given night of bowling we only record 24 strikes. The graph above shows the number of strikes we have rolled as a team for all thirteen weeks, and it should be clear how unusual last night’s strike number is. We had consistently put up between 30 and 43 strikes for twelve consecutive weeks. What is the probability that we would only get 24? It’s at best about 2.4%, so last night, something was different, and it seems like the big puddles of canola oil in the lanes are the obvious culprits. This is even more amazing if you consider that last week we recorded 43 strikes, tying our all time record. But hey, we won, a big, ugly, greasy win.

Lead Off

After an unusual week by his standards, Johnebob came back with a highly consistent performance with three games between 154 and 160. He quickly adapted to Lube Land by throwing a big looping slow curveball. He managed a team leading 470 series, and took every category on the leader board but two. He exceeded his average by almost four pins. He had the high number for strikes with only eight. He rediscovered his spare ball, recording 56.5%. Even though his strike ball looked like it was thrown by a 12 year old, it was effective as he also lead the team in 1st ball average with 8.43.

On Deck

After an unbelievable week, I cooled off substantially. I started slowly with games in the 130’s in the first two but finished well with a 184 in the last. I could not find the pocket all night until the 5th frame of the 3rd game when I started to mimic Johnebob’s pansy throw. I managed to strike four of the last six frames to put up a big number. I took the handicapped pin total and single pin percentage, and came in with a decent 151 average.

In the Hole

The Canadian (who would love to point out that he has been in the USA for almost 10 years and is irked by being referred to as the “Great White Norther”) is still trying to figure out his new throw. He had a rough 1st game, not managing to crest the century mark, but he had a nice 2nd with a 136. He slipped again in the 3rd, but his performance was enough to give us three wins. In fact, he put up his best score in the game we lost, so we can’t blame him. Rookie woes will soon be a thing of the past for the man in the three hole.

Cleanup

JD has been up and down during the 2nd half, but he has been consistently hitting an average in the 130’s as he did last night. He recorded 14 marks including 6 strikes. He struggled a bit with spares, particularly the single pins. The heavy chicken was flying all over the coop last night. If you don’t know what a heavy chicken is, perhaps an instructional post on throwing an H.C. is in order. JD dominated the first frame averaging 15.0 pins (something also done by our leadoff man). Grease seemed to have a serious effect on all the spinners, Daniele included. When the night was over, JD lagged behind after mumbling something about “Ferrigno and lube.”

The hardwood was so lubricated that balls slipped easy between the pins. It was so slippery out there that the balls would emerge from the chute with glistening lines of lube. If by chance, you foot fouled, you would have found yourself on your back sliding down the lane as if it were a slip and slide. There was so much oil out there that Lou Ferrigno was rolling around on Lane 17 in preparation for the Mr. Olympia competition. Did I mention that the lanes behaved like they were coated with KY Jelly? Yes, it was slick.

While it may seem like I am just making excuses for our poor performance, there is good reason to believe that something was amiss with the lanes against the wall last night. For one, we bowled like shit. This is not necessarily unusual. What is unusual is that the team against which we bowled, bowled even worse. From last week, we dropped a total of 220 pins. On top of that, we had our fewest number of strikes on record, 24 to be exact. This was six fewer than we had ever bowled in a three game set. Yet, we took three of four. We even won a game with a handicapped score of 811 in the first. Our lowest pin total victory prior to this was an 827.

It is worth noting that with the completion of Monday’s bowling, the season is ¾ complete, and we are halfway through the 2nd half of the season. We currently stand in 2nd place with 20 wins, nine fewer than we had for the entirety of the 1st half. The Movements are still poised to finish at the top of the standings in the Bernaski League spring season.

We now have 13 weeks of bowling data. Using prior results, it is possible to estimate the probability that on a given night of bowling we only record 24 strikes. The graph above shows the number of strikes we have rolled as a team for all thirteen weeks, and it should be clear how unusual last night’s strike number is. We had consistently put up between 30 and 43 strikes for twelve consecutive weeks. What is the probability that we would only get 24? It’s at best about 2.4%, so last night, something was different, and it seems like the big puddles of canola oil in the lanes are the obvious culprits. This is even more amazing if you consider that last week we recorded 43 strikes, tying our all time record. But hey, we won, a big, ugly, greasy win.

Lead Off

After an unusual week by his standards, Johnebob came back with a highly consistent performance with three games between 154 and 160. He quickly adapted to Lube Land by throwing a big looping slow curveball. He managed a team leading 470 series, and took every category on the leader board but two. He exceeded his average by almost four pins. He had the high number for strikes with only eight. He rediscovered his spare ball, recording 56.5%. Even though his strike ball looked like it was thrown by a 12 year old, it was effective as he also lead the team in 1st ball average with 8.43.

On Deck

After an unbelievable week, I cooled off substantially. I started slowly with games in the 130’s in the first two but finished well with a 184 in the last. I could not find the pocket all night until the 5th frame of the 3rd game when I started to mimic Johnebob’s pansy throw. I managed to strike four of the last six frames to put up a big number. I took the handicapped pin total and single pin percentage, and came in with a decent 151 average.

In the Hole

The Canadian (who would love to point out that he has been in the USA for almost 10 years and is irked by being referred to as the “Great White Norther”) is still trying to figure out his new throw. He had a rough 1st game, not managing to crest the century mark, but he had a nice 2nd with a 136. He slipped again in the 3rd, but his performance was enough to give us three wins. In fact, he put up his best score in the game we lost, so we can’t blame him. Rookie woes will soon be a thing of the past for the man in the three hole.

Cleanup

JD has been up and down during the 2nd half, but he has been consistently hitting an average in the 130’s as he did last night. He recorded 14 marks including 6 strikes. He struggled a bit with spares, particularly the single pins. The heavy chicken was flying all over the coop last night. If you don’t know what a heavy chicken is, perhaps an instructional post on throwing an H.C. is in order. JD dominated the first frame averaging 15.0 pins (something also done by our leadoff man). Grease seemed to have a serious effect on all the spinners, Daniele included. When the night was over, JD lagged behind after mumbling something about “Ferrigno and lube.”

## Tuesday, February 24, 2009

### And the trumpets did sound

As promised, a BM Victory (3-1) and I return to blogging mastery. Let this day live on for all ages as "The Great Return of Joe to the BM Report Day"! Celebrate one and all, may drinks flow from every goblet!

http://www.youtube.com/watch?v=zM9vTeV6lmw

I am now back. The time of lament and disdain for life is over.

I shall blog.

Enjoy this day my loyal fans. You have earned it.

http://www.youtube.com/watch?v=zM9vTeV6lmw

I am now back. The time of lament and disdain for life is over.

I shall blog.

Enjoy this day my loyal fans. You have earned it.

## Saturday, February 21, 2009

### How many spare combinations are possible in bowling? Part I

In this post, I explore the issue of the number of possible spares that exist in bowling. What I mean is how many different combinations of pins can remain after the first ball is thrown. I do not explore whether those spares can actually be picked up. My suspicion is that there are certain spares that are impossible to convert, but this would be very difficult to establish.

[A note: To avoid confusion, I refer to individual pins using numerals. For example “2 pin” refers specifically to the 2 pin. I use words to refer to the number of pins remaining. For example, a “two pin spare” means that two pins remain after the first throw.]

There are two ways to address this question. First obviously there are a finite number of pin combinations that exist. For example, there is only one ten pin spare combination (i.e., the first ball was thrown in the gutter.) There are ten single pin spare possibilities. Any single pin can remain standing after one toss of the ball. Likewise, there are ten nine pin spare possibilities, if any single pin is removed by the first throw. It should be obvious, however, that while some of these spare combinations can exist in theory, in reality they cannot, at least in ten pin bowling. [After playing candlepins last December, it seemed like anything was possible in that crazy game.] For example, it is impossible to pick up only the 5 pin with the first toss. In fact, most nine pin spare combinations are not possible. My hunch is that if a single pin is picked up on the first throw, it will be either the 7 or 10. The remaining eight nine pin spare combinations are likely impossible.

I begin with the total number of pin combinations that can exist in theory. I then turn to the more difficult question of how many of these can actually occur in a game of bowling, but I leave the ultimate solution to that problem for another day [that day has finally arrived]. The first problem is fairly easy to solve. It turns out that there are 1,023 different combinations of pins that can theoretically remain after the first ball is thrown. The table and histogram below show how many possible spares there are given the number of pins remaining after the first throw. Notice that the distribution is nearly normal and symmetrical with one exception. There are no zero pin spare possibilities, but there is one ten pin spare. The greatest number of possible spare combinations is when five pins remain. Of these, there are 252.

Now for the hard part. How many of these can actually exist in the real world? The short answer is, “I don’t know.” Some spares are easy to eliminate. For example, I can’t imagine how a bowler could be left with a nine pin spare opportunity with only the 9 pin missing, or an eight pin spare in which the 7 and 10 have been removed. Others are more difficult. For example, is it possible to leave only the 1, 7, and 10 pins standing? It seems like it might be, but I am fairly certain that I have never seen it (but see here).

So, how should one go about solving this problem? I see two solutions, one empirical and one theoretical. Beginning with the latter, I suppose it would be possible to model or simulate bowling and pin action. If one could do this in a realistic way, it would be possible to simulate literally millions of possible throws and pin strikes to determine the entire range of possible outcomes. My hunch is that it that this system is so complex that it would be difficult to attain this level of realism, yes, even with Nintendo Wii.

The other option, though perhaps much more onerous is to actually record spares observed in the real world. As the sample gets larger, the number of observed spare combinations should asymptotically approach the actual number that can exist, meaning that the number of unique spares observed will begin to plateau. Using statistical methods, it should be possible to estimate with some degree of confidence the total number of combinations that can occur. To get a good estimate, ideally one would observe bowlers of low skill because I suspect that high skill bowlers see relatively few spare combinations compared to those whose first balls are much more erratic.

I have begun collecting this type of data, and I will report on the results in the future. For now, I will share that I have recorded 226 spare combos, and of these 85 are unique.

Here is a related post.

And here's another.

Here's Part II.

[A note: To avoid confusion, I refer to individual pins using numerals. For example “2 pin” refers specifically to the 2 pin. I use words to refer to the number of pins remaining. For example, a “two pin spare” means that two pins remain after the first throw.]

There are two ways to address this question. First obviously there are a finite number of pin combinations that exist. For example, there is only one ten pin spare combination (i.e., the first ball was thrown in the gutter.) There are ten single pin spare possibilities. Any single pin can remain standing after one toss of the ball. Likewise, there are ten nine pin spare possibilities, if any single pin is removed by the first throw. It should be obvious, however, that while some of these spare combinations can exist in theory, in reality they cannot, at least in ten pin bowling. [After playing candlepins last December, it seemed like anything was possible in that crazy game.] For example, it is impossible to pick up only the 5 pin with the first toss. In fact, most nine pin spare combinations are not possible. My hunch is that if a single pin is picked up on the first throw, it will be either the 7 or 10. The remaining eight nine pin spare combinations are likely impossible.

I begin with the total number of pin combinations that can exist in theory. I then turn to the more difficult question of how many of these can actually occur in a game of bowling, but I leave the ultimate solution to that problem for another day [that day has finally arrived]. The first problem is fairly easy to solve. It turns out that there are 1,023 different combinations of pins that can theoretically remain after the first ball is thrown. The table and histogram below show how many possible spares there are given the number of pins remaining after the first throw. Notice that the distribution is nearly normal and symmetrical with one exception. There are no zero pin spare possibilities, but there is one ten pin spare. The greatest number of possible spare combinations is when five pins remain. Of these, there are 252.

Now for the hard part. How many of these can actually exist in the real world? The short answer is, “I don’t know.” Some spares are easy to eliminate. For example, I can’t imagine how a bowler could be left with a nine pin spare opportunity with only the 9 pin missing, or an eight pin spare in which the 7 and 10 have been removed. Others are more difficult. For example, is it possible to leave only the 1, 7, and 10 pins standing? It seems like it might be, but I am fairly certain that I have never seen it (but see here).

So, how should one go about solving this problem? I see two solutions, one empirical and one theoretical. Beginning with the latter, I suppose it would be possible to model or simulate bowling and pin action. If one could do this in a realistic way, it would be possible to simulate literally millions of possible throws and pin strikes to determine the entire range of possible outcomes. My hunch is that it that this system is so complex that it would be difficult to attain this level of realism, yes, even with Nintendo Wii.

The other option, though perhaps much more onerous is to actually record spares observed in the real world. As the sample gets larger, the number of observed spare combinations should asymptotically approach the actual number that can exist, meaning that the number of unique spares observed will begin to plateau. Using statistical methods, it should be possible to estimate with some degree of confidence the total number of combinations that can occur. To get a good estimate, ideally one would observe bowlers of low skill because I suspect that high skill bowlers see relatively few spare combinations compared to those whose first balls are much more erratic.

I have begun collecting this type of data, and I will report on the results in the future. For now, I will share that I have recorded 226 spare combos, and of these 85 are unique.

Here is a related post.

And here's another.

Here's Part II.

## Thursday, February 19, 2009

## Wednesday, February 18, 2009

### City Classic Update

I stopped by the Lanes of Laramie today to see how we stand in the City Classic. First, apparently we bowled in the "City Championships," not the "Classic". Second, despite our valiant efforts, we will probably not place. To date, 24 teams have bowled. By handicapped pin total, we currently rank 6th. By scratch pin total, we are 22nd. What does this mean? Well, first we should be proud of ourselves that we aren't the worst bowling team in Laramie. There are at least two who are worse. The first place team, whose name I can't remember (something like Laramie Lanes CTG), has a handicapped pin total of 2,916. We came in at 2,859 using the tournament handicapping system. In order to get 2,916, we would have needed to bowl 86 pins above average per game as a team. This should give you an idea of the magnitude of the challenge. If a 90% handicapping system had been in play, we would have come in at 2,970. In other words, the 80% handicap is what fucked us over, but I suppose we should be thankful that a handicapping system was in play at all.

I was told on Monday night that roughly 1 in 8 teams place, and that 54 teams were competing. So, at least six teams should be paid. Normally, this would mean that the top three scratch and handicap teams will earn winnings. We do not fall in either group. If a team appears both in the top three handicap and scratch groups, they will only be paid once. So, there is an outside chance that we could squeak in there. Of course, there are still at least 30 teams left to bowl, so our chances of even remaining in the top 10 are minimal.

We should be proud of ourselves. I feel very confident that we will finish in the top 20-30%, and I would be surprised if any team exceeded their averages to the extent that we did. Our dream of having the name "Bowl Movements" engraved in the City Championship plaque for eternity will have to wait for another day.

I was told on Monday night that roughly 1 in 8 teams place, and that 54 teams were competing. So, at least six teams should be paid. Normally, this would mean that the top three scratch and handicap teams will earn winnings. We do not fall in either group. If a team appears both in the top three handicap and scratch groups, they will only be paid once. So, there is an outside chance that we could squeak in there. Of course, there are still at least 30 teams left to bowl, so our chances of even remaining in the top 10 are minimal.

We should be proud of ourselves. I feel very confident that we will finish in the top 20-30%, and I would be surprised if any team exceeded their averages to the extent that we did. Our dream of having the name "Bowl Movements" engraved in the City Championship plaque for eternity will have to wait for another day.

## Tuesday, February 17, 2009

### Rising to the Occasion

Last night was the 62nd Annual City Classic bowling tournament of Laramie. We walked into the Laramie Lanes like four cavemen in a Circuit City. We had no idea what was going on, why we were there, or what we were supposed to do. The Lanes were abuzz with people. Laptops were strewn across tables. Cash was being exchanged in large sums. The best bowlers in the city were milling about. We were out of place, sporting our meager averages and BM jerseys.

On top of this, JD was fighting off a nasty rhinovirus that took hold of him a day before. He was sick and tired and had no interest in bowling, but he came out for the sake of the team. If he had not, we could not have rolled.

As I handed my $21 entry fee to Troy Baker, I felt like I was flushing it down the toilet. After all, there were 54 teams entered in this citywide battle of balls. The 80% handicapping system put us at an even greater disadvantage. How could the Movements possibly compete?

With a brisk tide flowing against us, we rolled. In fact, we had our best night ever, some might say. We definitely rose to the occasion, one shining moment at a time. Was it enough to take the city championship? I doubt it. Will we place? Maybe.

Here’s the scoop. In all, we recorded 1,893 pins. The was our 2nd best of all time. On the 5th of January, we got 1,938 with Rory subbing for Gee-off. Of course, relative to our handicap, this was the most dominating performance we have put forth. Using our standard league handicap (276), this equates to 2,721 pins. On Jan. 5, we got 2,712 handicapped. We averaged 157.8 per bowler per game. As a team, we tied our record for strikes (43) and single pin’s (17), and we set new team records for handicapped series (2,721), marks (81), single pin % (68%), and accuracy (46.8%).

Ok, now the bad news. Handicaps were standardized to 240 using an 80% deduction. (Take your average, subtract it from 240, and multiply by 0.8. Eliminate the decimal.) I recalculated our handicaps and those of Lazer Wash based on a prior post. The bad news is that if Lazer Wash bowled their averages, we would have to bowl 48 PINS ABOVE OUR AVERAGE PER GAME just to keep up.

Ok. Now for the good news. Because of the weird averages used last night, and the fact that I ate a whole tub of steroids before leaving my house, I put up 50 pins over my average per game, effectively eliminating the Lazer Wash advantage. But I was not alone. Everyone crested their averages. In fact, as a team, WE BOWLED 72 PINS OVER AVERAGE PER GAME.

Is this enough to put us in the money? I don’t know, but we gave it one hell of a shot.

On top of this, JD was fighting off a nasty rhinovirus that took hold of him a day before. He was sick and tired and had no interest in bowling, but he came out for the sake of the team. If he had not, we could not have rolled.

As I handed my $21 entry fee to Troy Baker, I felt like I was flushing it down the toilet. After all, there were 54 teams entered in this citywide battle of balls. The 80% handicapping system put us at an even greater disadvantage. How could the Movements possibly compete?

With a brisk tide flowing against us, we rolled. In fact, we had our best night ever, some might say. We definitely rose to the occasion, one shining moment at a time. Was it enough to take the city championship? I doubt it. Will we place? Maybe.

Here’s the scoop. In all, we recorded 1,893 pins. The was our 2nd best of all time. On the 5th of January, we got 1,938 with Rory subbing for Gee-off. Of course, relative to our handicap, this was the most dominating performance we have put forth. Using our standard league handicap (276), this equates to 2,721 pins. On Jan. 5, we got 2,712 handicapped. We averaged 157.8 per bowler per game. As a team, we tied our record for strikes (43) and single pin’s (17), and we set new team records for handicapped series (2,721), marks (81), single pin % (68%), and accuracy (46.8%).

Ok, now the bad news. Handicaps were standardized to 240 using an 80% deduction. (Take your average, subtract it from 240, and multiply by 0.8. Eliminate the decimal.) I recalculated our handicaps and those of Lazer Wash based on a prior post. The bad news is that if Lazer Wash bowled their averages, we would have to bowl 48 PINS ABOVE OUR AVERAGE PER GAME just to keep up.

Ok. Now for the good news. Because of the weird averages used last night, and the fact that I ate a whole tub of steroids before leaving my house, I put up 50 pins over my average per game, effectively eliminating the Lazer Wash advantage. But I was not alone. Everyone crested their averages. In fact, as a team, WE BOWLED 72 PINS OVER AVERAGE PER GAME.

Is this enough to put us in the money? I don’t know, but we gave it one hell of a shot.

## Monday, February 16, 2009

### The Bowler's Prayer

Pinnius, God of Bowling, to thee I pray. On this [insert day of league] night, please bless my two balls. Let the first find the pocket and the second, what remains. Let the grease of the lanes not harm my throw. Oh, Pinnius, in your great bowling alley in the sky, please see to it that my teammates don’t fuck up again. As you gaze down upon us across your nacho cheese-stained polo bowling jersey, I ask only that you prohibit splits, well not “only” since I’ve already asked for some stuff, and I’m about to ask for some more stuff, but it sounded good. God of Bowling, I trust that as you guzzle heavenly bowling juice from your golden pitcher, and as your holy and rotund belly fills with said juice, and as you find yourself eternally in a perfectly divine state hovering between drunk and buzzed, you will forgive my lexical imperfections. For I am just a lowly servant doing your work once a week. Pinnius, if you finally see me worthy, for I have accepted you as my only Bowling God and Savior, let me score over 200. Have I not earned your devotion in return? I mean, come on, big fat stupid bowling god. Give me a fucking break already. What do I have to do? I started throwing a spin as you commanded in your Third Commandment of Bowling. I bought my own ball, and even some stupid ugly bowling shoes. I love you Pinnius, and yet you refuse to love me back. Gods are supposed to reward their subjects for Pinnius’s sake, you fucking son of a bitch, Pinnius. Fuck you. You’re just gonna fuck me over again this week, aren’t you? Sincerely, your humble servant, [insert your name].

## Saturday, February 14, 2009

### Bowling 200: All Your Questions Answered

In this post, I pose and answer some basic questions about various ways to reach a bowling score of 200. What does it take?

If my memory serves me correctly, the Bowl Movements have reached the 200 mark four times in league competition. Johnebob has achieved this feat three times, and JD did it once. I have done it once but not during league. Geoff has bowled as high as 169 in league, and I have topped out at 192. If you are like us, 200 represents the promised land. It means you have arrived as a decent bowler. Hitting 200 regularly means you are a good bowler.

What is the minimum number of strikes that can be bowled to reach 200?

In order to have a 200 game, you must have strikes. A game with 10 spares won’t do it, not even a game with ten spares and one strike. It is possible to reach 200 with only two strikes, but they must be back to back. To pull off a two strike 200 game requires bowling a spare on the remaining 8 frames, and seven of those must be nine-spares with the last an eight spare. It’s much easier to do with 5 or more strikes.

How many strikes guarantee a 200 game?

This one might surprise you. The answer is eleven. It is possible to have ten strikes and not bowl 200. It would be an extremely unusual result, but it is possible. In order to do this, three of those strikes would have to occur in the 10th frame, and the remaining two frames would have to be left open with three or fewer pins. I have a hard time imagining this actually occurring, but it is possible. Get 11, and you're home.

How many frames can be left open and still reach 200?

No doubt you have been in this position. You step up to the first frame thinking this is going to be the game when you reach 200, but you leave it open. Is a 200 game still possible? Yes. For most 200 games, zero to one frames are left open. Nonetheless, it is possible to reach 200 with four open frames. To achieve this, all of your strikes must be consecutive. In the 200 game below, six consecutive strikes are followed by four open frames. It is also possible to leave the first four frames open and strike frames 5 through 10. In this case, it is possible to reach 200 with a score of X,4,- in the 10th.

When should I give up on 200?

You probably know that if you are sitting on a 120 in the 9th frame, you can give up on reaching the deuce, but should you have given up on it in the 8th? Not necessarily. Here are some simple rules to remember if you are wondering if 200 is still possible. 1) The maximum score you can receive on any frame is 30. You can always multiply the number of frames remaining by 30 to determine how many more pins are possible. 2) If you are sitting on a spare, again multiply the remaining frames by 30 and add 10. If you are sitting on a strike, multiply the remaining frames by 30 and add 20. If you are sitting on two strikes, add 30. This is the score you will receive if you strike out.

The table to the left shows the minimum score you must have by frame to keep 200 within the realm of possibility depending on what happened in the prior frame(s). The first thing to notice is that no matter what happens in the first three frames, 200 is still possible, but by end of the fourth frame, you must have at least a score of 20.

If you left the 9th open, you must have at least 170. If you spared the 9th, you need at least 160. You can still reach 200 with 150 in the 9th if you struck it. If you struck 8 and 9, you can have a 140 in the 9th and still reach the deuce. All of these scores are minima meaning that if you have any of these, you must strike out to reach 200. If you want to reach 200, try to keep your scores above these.

Easier said than done, I know.

If my memory serves me correctly, the Bowl Movements have reached the 200 mark four times in league competition. Johnebob has achieved this feat three times, and JD did it once. I have done it once but not during league. Geoff has bowled as high as 169 in league, and I have topped out at 192. If you are like us, 200 represents the promised land. It means you have arrived as a decent bowler. Hitting 200 regularly means you are a good bowler.

What is the minimum number of strikes that can be bowled to reach 200?

In order to have a 200 game, you must have strikes. A game with 10 spares won’t do it, not even a game with ten spares and one strike. It is possible to reach 200 with only two strikes, but they must be back to back. To pull off a two strike 200 game requires bowling a spare on the remaining 8 frames, and seven of those must be nine-spares with the last an eight spare. It’s much easier to do with 5 or more strikes.

How many strikes guarantee a 200 game?

This one might surprise you. The answer is eleven. It is possible to have ten strikes and not bowl 200. It would be an extremely unusual result, but it is possible. In order to do this, three of those strikes would have to occur in the 10th frame, and the remaining two frames would have to be left open with three or fewer pins. I have a hard time imagining this actually occurring, but it is possible. Get 11, and you're home.

How many frames can be left open and still reach 200?

No doubt you have been in this position. You step up to the first frame thinking this is going to be the game when you reach 200, but you leave it open. Is a 200 game still possible? Yes. For most 200 games, zero to one frames are left open. Nonetheless, it is possible to reach 200 with four open frames. To achieve this, all of your strikes must be consecutive. In the 200 game below, six consecutive strikes are followed by four open frames. It is also possible to leave the first four frames open and strike frames 5 through 10. In this case, it is possible to reach 200 with a score of X,4,- in the 10th.

When should I give up on 200?

You probably know that if you are sitting on a 120 in the 9th frame, you can give up on reaching the deuce, but should you have given up on it in the 8th? Not necessarily. Here are some simple rules to remember if you are wondering if 200 is still possible. 1) The maximum score you can receive on any frame is 30. You can always multiply the number of frames remaining by 30 to determine how many more pins are possible. 2) If you are sitting on a spare, again multiply the remaining frames by 30 and add 10. If you are sitting on a strike, multiply the remaining frames by 30 and add 20. If you are sitting on two strikes, add 30. This is the score you will receive if you strike out.

The table to the left shows the minimum score you must have by frame to keep 200 within the realm of possibility depending on what happened in the prior frame(s). The first thing to notice is that no matter what happens in the first three frames, 200 is still possible, but by end of the fourth frame, you must have at least a score of 20.

If you left the 9th open, you must have at least 170. If you spared the 9th, you need at least 160. You can still reach 200 with 150 in the 9th if you struck it. If you struck 8 and 9, you can have a 140 in the 9th and still reach the deuce. All of these scores are minima meaning that if you have any of these, you must strike out to reach 200. If you want to reach 200, try to keep your scores above these.

Easier said than done, I know.

## Thursday, February 12, 2009

### Dear Dick's Sporting Goods,

You have needs, and so do we. In these trying economic times, you need to maintain your revenue and profit. You need to sell more sporting goods, but people aren’t exactly in a shopping mood. You would like to increase your market share of bowling equipment, and we can provide this.

We need a canoe, a fishing canoe. You have these. You see, our plan was to earn enough money through our bowling league to buy a canoe, but we have been hampered but one small problem. We are bad bowlers, but why should that be a detriment?

We envision a symbiotic relationship between our humble bowling team, the Bowl Movements, and your humble company. Consider this. The endorsement of athletes by sporting goods companies is a long standing tradition, but it is a bit tiresome, isn’t it? In this economic climate, do people really want to listen to hyper-wealthy prima donna athletes peddling shoes and golf balls? Does paying $10 million a year to Tiger really translate to a profit in the sales of the Sasquatch and Nike One golf balls? I imagine it does otherwise it wouldn’t be done, but that’s beside the point.

Most of us know that if I buy a pair of Nike Zoom Lebron VI shoes that I will not suddenly have the ability to go strong to hole and posterize somebody’s face when I jam it through the rim. So, why should I buy LeBron’s shoes? To feel good that I wear the same shoes as King James? That trick might work on the kids, but after age 30, it won’t fly. Plus, in a recession, kids don’t have much money. You need to market to middle-aged weekend warriors. What is the best way to do this?

You need to sponsor the everyday man to be your spokesperson. We are that man. We are handsome and well spoken dudes who work for a living. We have improved the quality of our life by bowling on Monday nights. Of the ten teams that bowl in our league, there are only three that bowl more poorly than we do.

Imagine this commercial for bowling goods. We are decked out in our retro red and black jerseys with Dick’s Sporting Goods patches on the sleeves. A single pin spare awaits a bowling ball; the lonely five pin sits on the center board. A Movement rolls, and the ball brushes by, missing the pin by a hair. Repeat missed spare after missed spare in high speed. Why does this sell bowling balls? Obviously one might blame the ball purchased at Dick’s Sporting Goods. No! That’s the old way of thinking. How many guys sitting on their couch will grin and think, “I can relate to that.” The next time they need to buy a bowling ball, they will think Dick’s Sporting Goods.

Here’s what we need. We want four patches to attach to our jerseys, and $500 to cover the remaining cost of our canoe and accessories. To recoup your investments, you’ll only have to sell an extra 20 bowling balls. That sounds like an easy decision to me. What do you think? How do you like the sound of the following phrase, “The Dick’s Bowl Movements?” It rolls right off the tongue, doesn’t it?

What’s that? You’re not interested? Don’t make me write to the Sports Authority.

## Wednesday, February 11, 2009

### That Didn’t Go According to Plan

I planned a Rocky III type performance for Monday night, but if I’m not mistaken, Rocky won that fight, didn’t he? Maybe we were trying to mimic his first fight with Clubber Lang. We took only one of four for the third week in row. We have clearly hit our slump. The Bowl Movements aren’t moving. It seems like a constipation joke should follow here, but I’m not in much of a joking mood.

So, we’ve gone 3-9 over the last three weeks. On top of that, JD promised a vow of silence until we have a winning or even 2-2 night. He will have to deliver, silence that is. Now is the winter of our discontent. The pins aren’t falling like they used to.

While it’s easy to focus on the bad, I’ll point out a few good things. We bowled above average for the 8th straight week, and our pin totals climbed for two weeks in a row. On Monday night, we recorded 1,747, or an average of 145.6 per roller per game for the team. It’s hard to complain about that. On another night, this could have brought a 2-2 result or even a 3-1. I put up my first 500 series ever with a 519. Johnny found his strike throw, picking up 13 and tying the record in that category. Gee-off dramatically changed his throw, and although he struggled a bit, it should pay dividends as he starts to master it. Joe continued at a decent clip in the spare realm picking up 40%.

Here’s a brief note about the demoralizing loss in Game 3. We put up 872 handicapped pins. We lost by five. In the 10th frame with the 3rd bowler bowling his 2nd ball and ten pin standing, the only way the Lounge could win would be by accomplishing at least the following: pickup the spare, and strike the bonus ball. The final bowler needed at least strike-strike-six. If any of these things did not happen, we would have won. But they pulled it off. So, we lost with an 872. Is an 872 loss common?

We now have 44 games in our database. For scores between 850 and 875, we have lost 5 of 9 games. What is striking is that if our score exceeds 875, our chances of victory increase dramatically. We have won 12 of 14 games between 875 and 900, or 85.7%. The highest losing score we have on record was an average of 879.3 on December 15. The next highest was an 876. So, a loss with an 872 is a bit unlucky but not particularly unusual.

Lead Off

The Johnebob from Monday was not the Johnebob we know. He struggled with spares all night long, but he found his strike ball tying the record with 13. Because of his first ball prowess, he still averaged over 150 pins. He took the strike category and had the 2nd highest series with a 454.

On Deck

The Green Lady was behaving as I had my best week ever. A 519 series brings me half way to the 700 club if I can ever break the 200 mark in league. The best news of the night for me was a 60% pickup percentage, far and away my best ever, but still a long way from UJ’s record of 71.6%. This performance should finally bring my handicap under 70. Let’s hope I keep it there.

In the Hole

Gee-off abandoned the overhand reverse spin ball for an underhand heater. Whipping it around 18 mph was a new look for the Maritimer, but it may take a week or two to figure out how to control Captain Midnight at high velocity. G-Spot kept alive his hot streak on single pins, leading the team in that category with JD and picking up 50%.

Clean Up

Papa D averaged a hearty 135.3 pins, definitely respectable but well below his average. His strike ball has faded a bit lately, only recording five on Monday. He picked up 60% of his single pins and 40% of his spares overall. This week, he was the first to crest the 10,000 pin mark for the season, something he would like to attribute to superb bowling skills, but is more so due to his perfect attendance record.

So, we’ve gone 3-9 over the last three weeks. On top of that, JD promised a vow of silence until we have a winning or even 2-2 night. He will have to deliver, silence that is. Now is the winter of our discontent. The pins aren’t falling like they used to.

While it’s easy to focus on the bad, I’ll point out a few good things. We bowled above average for the 8th straight week, and our pin totals climbed for two weeks in a row. On Monday night, we recorded 1,747, or an average of 145.6 per roller per game for the team. It’s hard to complain about that. On another night, this could have brought a 2-2 result or even a 3-1. I put up my first 500 series ever with a 519. Johnny found his strike throw, picking up 13 and tying the record in that category. Gee-off dramatically changed his throw, and although he struggled a bit, it should pay dividends as he starts to master it. Joe continued at a decent clip in the spare realm picking up 40%.

Here’s a brief note about the demoralizing loss in Game 3. We put up 872 handicapped pins. We lost by five. In the 10th frame with the 3rd bowler bowling his 2nd ball and ten pin standing, the only way the Lounge could win would be by accomplishing at least the following: pickup the spare, and strike the bonus ball. The final bowler needed at least strike-strike-six. If any of these things did not happen, we would have won. But they pulled it off. So, we lost with an 872. Is an 872 loss common?

We now have 44 games in our database. For scores between 850 and 875, we have lost 5 of 9 games. What is striking is that if our score exceeds 875, our chances of victory increase dramatically. We have won 12 of 14 games between 875 and 900, or 85.7%. The highest losing score we have on record was an average of 879.3 on December 15. The next highest was an 876. So, a loss with an 872 is a bit unlucky but not particularly unusual.

Lead Off

The Johnebob from Monday was not the Johnebob we know. He struggled with spares all night long, but he found his strike ball tying the record with 13. Because of his first ball prowess, he still averaged over 150 pins. He took the strike category and had the 2nd highest series with a 454.

On Deck

The Green Lady was behaving as I had my best week ever. A 519 series brings me half way to the 700 club if I can ever break the 200 mark in league. The best news of the night for me was a 60% pickup percentage, far and away my best ever, but still a long way from UJ’s record of 71.6%. This performance should finally bring my handicap under 70. Let’s hope I keep it there.

In the Hole

Gee-off abandoned the overhand reverse spin ball for an underhand heater. Whipping it around 18 mph was a new look for the Maritimer, but it may take a week or two to figure out how to control Captain Midnight at high velocity. G-Spot kept alive his hot streak on single pins, leading the team in that category with JD and picking up 50%.

Clean Up

Papa D averaged a hearty 135.3 pins, definitely respectable but well below his average. His strike ball has faded a bit lately, only recording five on Monday. He picked up 60% of his single pins and 40% of his spares overall. This week, he was the first to crest the 10,000 pin mark for the season, something he would like to attribute to superb bowling skills, but is more so due to his perfect attendance record.

## Monday, February 9, 2009

### Action speaks louder than words..

I realize all of you love my posts. You find them witty, funny, and written so well you feel a pulitzer is in order. Alas, I have bad news. We have not bowled well of late. In lue of our recent back-to-back 1-3 weeks I am taking a vow of blog silence. You will not hear from me again until we win (or go 2-2). That is, after all, our objective. I begin BM report blog silence now. My fans lament this day.

Of Note: I will be starting a "Check the Vow" blog. It will be a weekly update for you on how my vow of BM report blog silence is going.

### Preview: Laramie Lanes Lounge

We have come full circle. The first ever BM Report was written on December 2, 2008. The prior night, we bowled Laramie Lanes Lounge. We were victorious, winning three of four games. In those days, we were floundering in the bottom half of the league. Today things have changed. Tonight, we will win again.

The Loungers find themselves in 1st place due to our recent slump. We are two games back. They have five team members, only four of whom I can recall. Bryan the Republican, Devin Altitude, Derek Lounge, and Double Calf Bird.

We can take these guys, and we will. If we take three, we will be tied for 1st place. If we take four, we will have sole possession of the lead.

Here is our strategy. We'll call it Rocky III. Early in the first game, we are going to struggle. They will do well. They will make good progress on erasing our handicapped pin lead. Around Frame 5 or 6, we will start to bring it. We'll start to land body blows and the occasional jab to the jaw. We'll take Game 1, but it will be close. Game 2 will be a full on brawl. It will be back and forth, blow for blow. We'll need to cinch down on the nut sack to pull this one out out, but we will take Round 2. In Round 3, Clubber Lounge will be pissed after giving away the first two rounds. Their anger will only lead to irrelevant sloppiness because there will be nothing they can do to stop the runaway BM freight train. We will be throwing southpaw hooks like mad, and they will crumble. At the end of the bout, we'll moan the name "Adrian" in a slurry punch drunk Italian ghetto accent before we go to the Ranger to get drunk.

## Saturday, February 7, 2009

### Chances of Bowling a Perfect Game

Have you ever wondered what are your chances of bowling a perfect game? A perfect game consists of 12 consecutive strikes totaling to a score of 300. It is actually a remarkably simple thing to estimate. For the Bowl Movements, a perfect game is nearly impossible at our current skill level. Since we have seen this happen at the Lanes at least three times, though, for "non-developing" bowlers it is not that uncommon.

First, I'll give you the calculation. I'll explain it later if you really want to know how its derived. In order to know your chances of rolling 12 straight strikes, you only have to know one thing, your strike probability. In a single game, you have between 10 and 12 opportunities for strikes depending upon what happens in the 10th frame. To calculate your strike probability, take the number of strikes you receive divided by the number of opportunities you have to bowl a strike. The larger your sample, the better. To get a really good idea of your strike probability, I recommend you have at least 30-50 frames. Once you have this number, raise it to the 12th power. This is the probability that you will roll 12 strikes in a row. You can multiply it by 100 if you want to convert it to a percentage, i.e., a 25% chance.The graph above shows the relationship between strike probability and perfect game probability. In brief, unless you strike >50% of your frames, perfect games will be extremely rare, generally occurring less than once in a thousand games. This aptly describes our game. My strike probability is 0.2368, or approximately one strike per 3.8 frames. This corresponds to a perfect game probability of 0.000000113, or one perfect game in every 9 million attempts. In comparison, PBA Bowler Walter Ray Williams had a strike percentage of 66.35% for the 2007-08 season (the best ever in PBA competition). This corresponds to a perfect game probability of 0.0072 (0.72%), or one in every 137 games.

The calculation is a simple case of binomial probability. Think of it like tossing a coin. When you toss a coin, the probability of getting heads is 50%. The probability of getting heads followed by another heads is .5 x .5 = 0.25. The probability of getting three heads in a row is .5 x .5 x .5, or 12.5%. The probability of getting 12 heads in a row is .5 to the 12th power, or 0.024%. It's very unlikely. (Go ahead and try it if you don't believe me, and you have a lot of time.) Calculating the likelihood of a perfect game is identical. Just replace heads and tails with strike and non-strike. If you know the probability of a strike, the probability of 12 in a row is that probability raised to the 12th.

I do wonder if another factor must be considered. I think bowlers, like any other sports folk are prone to hot streaks. If you find yourself "in the zone," and your motion is consistent, you may be able to temporarily elevate your strike probability. My hunch is that this is what perfect games are all about. So, this calculation may be somewhat of an underestimate.

First, I'll give you the calculation. I'll explain it later if you really want to know how its derived. In order to know your chances of rolling 12 straight strikes, you only have to know one thing, your strike probability. In a single game, you have between 10 and 12 opportunities for strikes depending upon what happens in the 10th frame. To calculate your strike probability, take the number of strikes you receive divided by the number of opportunities you have to bowl a strike. The larger your sample, the better. To get a really good idea of your strike probability, I recommend you have at least 30-50 frames. Once you have this number, raise it to the 12th power. This is the probability that you will roll 12 strikes in a row. You can multiply it by 100 if you want to convert it to a percentage, i.e., a 25% chance.The graph above shows the relationship between strike probability and perfect game probability. In brief, unless you strike >50% of your frames, perfect games will be extremely rare, generally occurring less than once in a thousand games. This aptly describes our game. My strike probability is 0.2368, or approximately one strike per 3.8 frames. This corresponds to a perfect game probability of 0.000000113, or one perfect game in every 9 million attempts. In comparison, PBA Bowler Walter Ray Williams had a strike percentage of 66.35% for the 2007-08 season (the best ever in PBA competition). This corresponds to a perfect game probability of 0.0072 (0.72%), or one in every 137 games.

The calculation is a simple case of binomial probability. Think of it like tossing a coin. When you toss a coin, the probability of getting heads is 50%. The probability of getting heads followed by another heads is .5 x .5 = 0.25. The probability of getting three heads in a row is .5 x .5 x .5, or 12.5%. The probability of getting 12 heads in a row is .5 to the 12th power, or 0.024%. It's very unlikely. (Go ahead and try it if you don't believe me, and you have a lot of time.) Calculating the likelihood of a perfect game is identical. Just replace heads and tails with strike and non-strike. If you know the probability of a strike, the probability of 12 in a row is that probability raised to the 12th.

I do wonder if another factor must be considered. I think bowlers, like any other sports folk are prone to hot streaks. If you find yourself "in the zone," and your motion is consistent, you may be able to temporarily elevate your strike probability. My hunch is that this is what perfect games are all about. So, this calculation may be somewhat of an underestimate.

## Thursday, February 5, 2009

### Bowling Scoring and Statistics Spreadsheet

Note: I have since created a new version of the spreadsheet, which you can find here.

Are you looking for a way to quantify your bowling game, or way to track your progress or regress? Do you want to know how often you pick up single pin spares or your strike percentage? Would you like to be able to quantify these stats for your whole bowling team from week to week? Well, you have found the right place. Our bowling spreadsheet is the Bowl Movements’s gift to the world. We use it to create our box scores (Here’s an example). You can have it free of charge. For absolutely nothing. Yes, we are nice people. In return, you should read our blog more often and tell your friends about it. That's all we ask.

How does it work?

The Bowl Movements bowling statistics spreadsheet is a remarkably simple thing. It is currently set up for teams with four bowlers who play a three game series. If you want to use it to track the stats of a single bowler, you can do this, too. All you have to do is enter bowler initials and frame by frame ball scores (and handicap if you have one), and the spreadsheet does the rest. It calculates the score for the game, and automatically provides a suite of statistics:

- Marks: The total number of strikes and spares received
- Strikes: The total number of strikes
- Strike Opps: Strike opportunities, or the number of chances you had to roll a strike. This varies between 10 and 12 depending what happened in the 10th frame. This stat is used to calculate Strike%.
- Strike%: This is the percent of strike balls you throw. It is calculated as strikes/(strike opps)x100
- Spares: The total number of spares
- Spare Opps: Spare opportunities, or the number of chances you had to convert a spare. This varies between 0 and 10 depending upon how many strikes you received. This stat is used to calculate Pickup%.
- Pickup%: The percent of spares you picked up. It is calculated as spares/(Spare Opps)x100
- Opens: The total number of open frames
- Single Pin: The number of single pin spares you picked up.
- Single Pin Opps: The number of opportunities you had to pick up single pin spares (i.e., you received a nine on the first ball).
- SP%:The percent of single pin spares you converted: (Single pin)/(Single Pin Opps)x100.
- 1st ball average: This is the average score you received on the first ball of each frame. For the significance of this stat, see here.
- Accuracy: This stat attempts to capture your overall accuracy. It varies from 0 to 100%. For a detailed explanation of its derivation and significance see here.

- Series: The sum of your scores for all three games.
- Average: Your average score for the three game series
- Handicapped pin total: If you bowl in a handicapped league, enter your handicap, and the spread sheet will calculate your handicapped pin total for the series.

To get the spreadsheet, just click here.

[Addendum: I have since updated the sheet to fix a bug. I also added a blank sheet for a three man and five man team due to requests. The link for the updated spreadsheet is the same.]

A FEW NOTES ON THE USE OF THE SPREADSHEET

1. This is an Excel spreadsheet, version Office 1997-2003.

2. Make sure you use a capital “X” for strikes. Depress Caps Lock when entering scores.

3. To record a spare, use backslash “\”.

4. To record a gutter ball or a throw in which no pins were recorded, just leave the cell blank. DO NOT ENTER A DASH “-“.

5. If you want to use it for multiple nights of bowling, just copy the worksheet as many times as you like.

Labels:
Bowling,
bowling spreadsheet,
bowling statistics

## Wednesday, February 4, 2009

### A night captured in song (kind of)

Play this, open two windows for viewing, sing in my appropriate lyric changes, kick back and know we bowled well, the other team bowled great, and we will NEVER Surrender.

http://www.youtube.com/watch?v=mHl4OmRpq8M

Note to league: No retreat, no surrender. Back off our 16-8. -The Movements.

Thanks to Corey Hart for the rockin tune and most of the lyrics.

http://www.youtube.com/watch?v=mHl4OmRpq8M

*Just a little higher score is all we're asking for**Cause just a little more time could allow better scores**Just a little uncertainty can make bowlers frown**And nobody wants to bowl with you now**And nobody wants to show you how (to bowl)**So if you're lost and on your own**You can never surrender**And if your lanes won't lead to home**You can never surrender**And when the night is cold and dark**You can bowl, you can bowl strikes**Cause no-one can take away your right**To strike and never surrender**With a little more beer you can get things down**Without the little Ceasar's pie that has conquered some**And nobody wants to bowl with you now**And nobody wants you show how (to bowl)**So if you're lost and on your own**You can never surrender**And if your lanes won't lead to home**You can never surrender**And when the night is cold and dark**You can bowl, you can bowl strikes**Cause no-one can take away your right**To strike and never surrender, to never surrender**(Play air sax here and rock out)*Note to league: No retreat, no surrender. Back off our 16-8. -The Movements.

Thanks to Corey Hart for the rockin tune and most of the lyrics.

## Tuesday, February 3, 2009

### It’s not fun to be pummeled

Last week, we sat atop the league at 14-2. We looked down upon the competition from our mighty perch. They cowered before us. We faced PBR, poised to leave the league in our dust. Last week, we were humbled. This week, we were pummeled. The team named after No. 2 sat in the No.2 position, positioned in Lane 11, going head to head against the team named Team 2. Too many two’s to ponder, me thinks. In the first game, we were thrown to the ground like a piece of cheap garbage as we sat hopelessly and watched the deuces put up three scores over 220, totaling a game of 1011. In the 2nd, we were kicked and beaten with nightsticks as they put up a 965. We felt like Rodney King. Somehow, bruised and battered, we managed to win the third with an 884, a score barely enough to garner one win out of four chances. We have now dropped to 16-8 and likely sit in third place in the league. It was a rough night, but given the circumstances, the outcome was largely out of our hands.

While we could focus on the 382 strikes rolled by the team formerly known as Jeffrey’s Bistro, I would rather focus on our high points, and there are a few good things to acknowledge. While no new records were set for the third week in a row, there are three nice things to point out. First, I tied my records for strikes (13) and strike percentage (38.2%), but I required a 10th frame turkey in Game 3 to do so. We all picked up more than 50% of our single pin spare chances, and as a team recorded 61.5%. Finally, JD for the first time broke the 50% mark on pickup percentage, converting 51.9% of his spare tries. We knocked down more pins than last week and bowled above average for the 7th consecutive week.

Two interesting and related statistical notes. Johnebob put up remarkably consistent game scores of 157, 157, and 156, which begs the question of whether anyone during the BIA has ever come close to this level of consistency? To answer this question, I looked at the difference between the minimum and maximum game scores for a three game series, and the person to come closest was Johnebob himself from last week when he rolled 147, 157, and 152, a total range of 10. This week, one mere pin separated his minimum and maximum scores. Who had the greatest difference in game scores? Daniele, of course, who rolled 111, 150, and 193 on the 5th of January, a range of 82 pins.

The 2nd stat of week concerns my ridiculous series: 180, 116, 190. Don’t ask about the 2nd game. I have no idea. This begs the question of the largest consecutive game score drop and rise. Has anyone ever dropped 64 pins in consecutive games or gained 74? Yes. Who? JD, of course. In one day of bowling, Daniele did both on 12/15 with the series 108, 182, 116. This corresponded to a consecutive game pin increase of 74, which I tied, and a consecutive game score decline of 66, two better than my feat from last night. Other than that, my performance from last night was the most inconsistent on record. So much for my “Mr. Consistency” title.

Lead Off

The Hawkeye had an unusual night by his standards, and by that I mean that he only picked up 40% of his spares. Regardless, he had a 470 series, eclipsing his average once again. He recorded 11 strikes on his way to the most consistent series ever. His average keeps climbing slowly and steadily like the itsy bitsy spider. The Iowan has been bringing it week after week. He took two categories on the leader board: Game 2 and first ball average. It seems impossible to keep him off of there.

On Deck

I predicted a 223 in Game 2. I was only off by 107 pins. Ouch. At least I redeemed myself with a 180 in the first and 190 in the last. I got the majority chunk of the leader board. In the 8th frame of 3rd game, I asked the Green Lady about the view from the pocket down there at the other end of the alley. She responded with a weak seven. That bitch. Other than Game 2, she served me well. I had a weird week. A 500 series was only 14 pins away, and there were about 12 opportunities to get them. I didn’t. I’ll do it next week, and that’s a guarantee.

In the Hole

I think I cursed the Canuck on the 1st January when I wrote that his average would soon reach the 130 mark. He got close, but this week his average took a hit, dropping a single pin. In brief, the Expo had a high game of 128 and did not drop below the century mark. It was a bit of a struggle, but he did take two categories on the leader board, single pin spares and single pin percentage. He went 5 for 7, or 71.4%. For the sake of the Oiler, I think we should bring some Labatt’s, maple syrup, and beaver pelts to the Lanes next week.

Clean Up

Luca’s papa had a decent week, averaging nearly 141 pins. This was a good six pins below his average, but it’s hard to complain about anyone averaging over 140. Two years ago, if we had bowled this high, we would have considered going pro. We gotta give some props to Joe, Jr. for taking both spares and pickup percentage on the leader board. Spares have been his nemesis lately, but last night, he busted the .500 mark and took the category. It was a good night in that everyone picked up at least two categories.

While we could focus on the 382 strikes rolled by the team formerly known as Jeffrey’s Bistro, I would rather focus on our high points, and there are a few good things to acknowledge. While no new records were set for the third week in a row, there are three nice things to point out. First, I tied my records for strikes (13) and strike percentage (38.2%), but I required a 10th frame turkey in Game 3 to do so. We all picked up more than 50% of our single pin spare chances, and as a team recorded 61.5%. Finally, JD for the first time broke the 50% mark on pickup percentage, converting 51.9% of his spare tries. We knocked down more pins than last week and bowled above average for the 7th consecutive week.

Two interesting and related statistical notes. Johnebob put up remarkably consistent game scores of 157, 157, and 156, which begs the question of whether anyone during the BIA has ever come close to this level of consistency? To answer this question, I looked at the difference between the minimum and maximum game scores for a three game series, and the person to come closest was Johnebob himself from last week when he rolled 147, 157, and 152, a total range of 10. This week, one mere pin separated his minimum and maximum scores. Who had the greatest difference in game scores? Daniele, of course, who rolled 111, 150, and 193 on the 5th of January, a range of 82 pins.

The 2nd stat of week concerns my ridiculous series: 180, 116, 190. Don’t ask about the 2nd game. I have no idea. This begs the question of the largest consecutive game score drop and rise. Has anyone ever dropped 64 pins in consecutive games or gained 74? Yes. Who? JD, of course. In one day of bowling, Daniele did both on 12/15 with the series 108, 182, 116. This corresponded to a consecutive game pin increase of 74, which I tied, and a consecutive game score decline of 66, two better than my feat from last night. Other than that, my performance from last night was the most inconsistent on record. So much for my “Mr. Consistency” title.

Lead Off

The Hawkeye had an unusual night by his standards, and by that I mean that he only picked up 40% of his spares. Regardless, he had a 470 series, eclipsing his average once again. He recorded 11 strikes on his way to the most consistent series ever. His average keeps climbing slowly and steadily like the itsy bitsy spider. The Iowan has been bringing it week after week. He took two categories on the leader board: Game 2 and first ball average. It seems impossible to keep him off of there.

On Deck

I predicted a 223 in Game 2. I was only off by 107 pins. Ouch. At least I redeemed myself with a 180 in the first and 190 in the last. I got the majority chunk of the leader board. In the 8th frame of 3rd game, I asked the Green Lady about the view from the pocket down there at the other end of the alley. She responded with a weak seven. That bitch. Other than Game 2, she served me well. I had a weird week. A 500 series was only 14 pins away, and there were about 12 opportunities to get them. I didn’t. I’ll do it next week, and that’s a guarantee.

In the Hole

I think I cursed the Canuck on the 1st January when I wrote that his average would soon reach the 130 mark. He got close, but this week his average took a hit, dropping a single pin. In brief, the Expo had a high game of 128 and did not drop below the century mark. It was a bit of a struggle, but he did take two categories on the leader board, single pin spares and single pin percentage. He went 5 for 7, or 71.4%. For the sake of the Oiler, I think we should bring some Labatt’s, maple syrup, and beaver pelts to the Lanes next week.

Clean Up

Luca’s papa had a decent week, averaging nearly 141 pins. This was a good six pins below his average, but it’s hard to complain about anyone averaging over 140. Two years ago, if we had bowled this high, we would have considered going pro. We gotta give some props to Joe, Jr. for taking both spares and pickup percentage on the leader board. Spares have been his nemesis lately, but last night, he busted the .500 mark and took the category. It was a good night in that everyone picked up at least two categories.

## Monday, February 2, 2009

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