Saturday, April 25, 2009

The Turkey Hunter

It’s turkey season in Wyoming, and Johnebob has a permit. Whether he actually makes it out to stalk the wiliest of gobbling prey is dependent upon the fickle spring weather of the Equality State. Rain, snow, or sun, though, we must ask whether Johnebob is up to the task. Which of the Bowl Movements it the most likely to bag a turkey when given the opportunity?

In this post, I look at our team strike stats. In some ways, they are predictable. In other ways, not so much. I began keeping track of our feeble attempts to bowl on December 1, 2008. Since that time, I have painstakingly recorded 252 games of bowling by hand. Johnebob and JD rolled 63. Jefe and I got 60, and Becker and Gingy, 3 each. Excluding subs, our strike totals are:

John: 204 3.24 per game
Todd 193 3.22 per game
Joe: 155 2.46 per game
Geoff: 103 1.72 per game

The key to big game scores is stringing together the X’s. So, the raw number of strikes is not as important as a bowler’s ability to put them up consecutively. The following graphs show the frequency of singles, doubles, turkeys, etc. by bowler during the BIA. Johnebob leads the team in singles with 113. I am the king of the double with 34. John dominates turkeys with 11. John and Joe both have two four-baggers, and I have the only five in a row from the BIA. El Jefe is still looking for his first turkey in league.

But the question at hand is not who has the most turkeys, but who is the best turkey hunter? Given an opportunity to bag a turkey, who most often steps up to the occasion? Here’s how I solved this problem. If a bowler got two strikes in a row, how often did they pick up at least the third? The best turkey hunter is… Johnebob. He picks up a turkey approximately one out of every three tries. Daniele is second best with a 24.1% conversion rate. While Daniele is definitely the best and most prolific chicken choker on the team, Geoff and I are clearly the best turkey chokers.

Good luck with your turkey, Johnny. You are the right man for the job.

Wednesday, April 22, 2009

How many idiots does it take to drink seven pitchers of bowling juice?

Here's the setting. We arrive early to the lanes, circa one hour prior to the final night of league bowling. We do this to get a bit of a head start on our companion activity to bowling, the guzzling of bowling juice. We bowl our first game. We put up 652 pins, or a 931 with the handicap figured in. It was a big game. We beat Team Breakfast even though they also had a 900+ game. The 2nd game comes to a close, and we do even better, a 657 (937 hdcp).

Here's the funny part. After two games, we had our best start to a night of bowling ever. We were sitting on 1,309 pins. Let me put this into perspective. Three weeks prior, we had 1,629 for the entire night. The best we had ever done up to this point was 1,223 pins through the first two. Yet, on Monday night we were on pace to have our best night of bowling EVER on the last night of the season no less. We were averaging a beefy 163.6 pins per bowler per game.

But there was another record on our mind- the record for pitchers consumed. We were just polishing off our 5th jug of bowling juice, and the record was six. We decided to go for it. Seven pitchers of bowling juice went down as easily as our 3rd game score. How did we do in the third game? We got a grand total of 512 pins, or an average of 128 pins per bowler. It was ugly, but it was fun.

By the end of the night, we had won three games despite our Bacchanalian behavior. There were other good things, too. First, we finished the 2nd half six games above .500, and it was just enough to give us a .500 record for the whole season. We finished 64-64 amazingly. Also, on Jan. 8, I laid out some goals for the team. To be honest, I started to doubt we could ever accomplish them. On Monday night, we picked up another. We got 50% of our spares as a team. In all, we were 46 for 92. Everyone but myself got more than 50% of our spares, and this was the first time the Canadian had done so. What is even more impressive is that we did this despite putting up 13 splits. JD really came on with his spare ball, despite bowling with a brand new and undrilled Hammer Raw Acid.

It was a nice way to end the season, although my body is telling me that I am too old to go on such binges. If we are ever going to inspire young bowlers with our slogan, "Don't you want to grow up to be a Bowl Movement?", maybe a bit more moderation is in order.

Monday, April 20, 2009

The Great Ball Transplant

In about three hours, we have our final week of league bowling. Bernaski has been a regular Monday night occupation for the last 32 weeks. It has been an interesting season. As we end this season and begin thinking about the next, we are on the verge of another great transition. Three of us are retooling, replacing our current balls with new ones. This puts us in the unique position of being able to directly assess the effect of a new bowling ball, but there's more.

Here is how I see our evolution. We each began using house balls. Then, we got our own balls. Three of us have them custom drilled. JD got a hand-me-down. Then, we started throwing spin. First Joe, then John, and finally me. Geoff is still throwing a straighty. With each step, our games have seemed to improve slowly and steadily. I must admit, my average took a serious hit in year 2 due to injury and the new ball, but I recovered this year.

Anyway, here's where it gets interesting. All four us are currently bowling with what are essentially custom house balls. The Green Lady might be one notch above house, but it is basically a plastic house ball with a pancake core. Now, three of us are upgrading in a serious way.

Joe: His current ball is Qubica 14 lbs house ball that used to be housed at his uncle's bowling alley. He has on hand a 15 lbs Hammer Raw Acid. He has been waiting for over a week for it to be drilled.

John: Currently he rolls a Brunswich Axis 14 lbs'er. He claims he's seen one in the rack at the lanes. He is replacing the blue beauty with 15 lbs of Brunswick Twisted Fury.

Todd: I am having an affair with the Green Lady, a 13 lbs Columbia 300 Scout Reactive. In the mail is a 14 lbs Brunswick Smash Zone.

In every case, the old ball has little break, and the new ball has a ton. So, there should be a noticeable difference in score. We all expect a lot more strikes. We'll see if that actually happens. Does equipment really matter? I want the answer to be yes, but we will find out soon.

So will our new balls help us perform better? I can't speak for Joe and John, but my balls are fine. It's not like I need a new ball or anything. I just thought it would be cool to have one.

Thursday, April 16, 2009

The Incredible Sulk

We are not good bowlers. This fact has been well established. The stats, graphs, and posts on this blog attest to our poor skills at this simple game. Yet, sometimes it seems like our success or lack thereof from week to week is not related to our skill or performance but instead to how our opponents bowl. This week was an excellent example. We did not bowl well, but our performance wasn't awful either.

In sum, we got 1,694 pins. This was 16 pins below our team average. It equates to an average of 141.7 pins per bowler per game, not too shabby by our standards. On top of that, we set a team record in Game 1 with 671 pins, or an average of 167.5. This was a big game for us. Handicapped, it was a 948, our 3rd highest game on record. Nonetheless, we lost. The Mighty Hulks were indeed mighty, beating us by 21 pins in that game. This sad outcome portended the rest of the night: zero wins in four opportunities.

Here are a few interesting tidbits as we head into our last week of Bernaski competition. If we lose all four, we finish at .500 for the second half of the season. So, it would be nice to get at least one. For the entire season (fall and spring), our current record is 61-62, so in fact, we have a chance of finishing above .500 for the whole season. For the 3rd worst team in the league, this would be a major accomplisment. In order to do so, we would need at least three wins. We'd have to do it against Double Calf Bird and his cronies.

On the good side, I finally broke through the 200 ceiling with an odd game in the 1st. With respect to this season, it took me 91 tries to get there. If you add to that the last two seasons, in all, it probably came after 160 games or so. It was nice to get that monkey off my back.

Speaking of 200 games, here's a little Bowl Movements trivia. In the BIA, do we have more games over 200 or under 100? I was surprised to discover the answer. In fact, it is a trick question. We have the same number of each, five. Johnebob has four 200+ games during the BIA and as least as many prior to it. I have one. Geoff has four sub-100 games, and Joe has one.

One more thought before I end this incredible sulk. We have plateaued lately. We knocked eleven pins off our team handicap between December 1 and February 16. In the subsequent eight weeks, our handicap has stagnated. It currently sits at a 277. Here's how I see it. We have all settled into our routines and our throws. It is time for some new tricks.

Here's what we need for the off season. Geoff needs to work on a spin. JD needs to master his new bowling ball. We should get a first glimpse of its effects next week. Johnebob and I need to upgrade our equipment. If so, I see another 20-40 pins off the handicap next year. Would it be possible to get it to a 150? We would have to get our team average up to a 177 or 178. It seems like a lofty goal, but I think we could it.

In Season IV, we should make our move from being the chumps of the league to being a mid-tier team.

Friday, April 10, 2009

How many spare combinations are possible in bowling? Part II

In a prior post, I explored the question of how many possible spare combinations exist in bowling, or how many different combinations of pins can remain standing after one throw of the ball. In that post, I answered that question theoretically meaning that there are a finite number of pin combinations that can exist, 1,023 to be exact, but some of them cannot be achieved in reality. For example, it is not possible to remove only the 1 pin with the first ball. In this post, I look at the question empirically.

Over the last few months, I have been recording leaves, or the pins left standing after the first ball is thrown. In all, I have recorded 774 leaves, many of which are repeated. In fact, of these, only 155 are unique. Every week of our league, I record approximately another 70 leaves. Early on in the process, many new spare combinations were recorded. As the database grew, however, unique spares became increasingly rare. Now, I will record maybe 1-5 new leaves for every 70 added to the database.

Given enough time and a large enough sample, I could in theory observe all possible spare combinations, but to be honest, I don't really want to. This would require an absolutely enormous sample, and I don't want to keep doing this for the rest of my life. Instead, it is possible to use observed trends to estimate the number of possible spares with some degree of precision.

First, I'll give you the answer. If you want to know how I solved this problem, I will explain below. In short, my best estimate is that there are between 269 and 297 different spare combinations that can exist. My best estimate is 283. Therefore of the 1023 spare combinations that can exist in theory, only about 1/4 of them can exist in reality.

To answer this question, I begin with a symmetry assumption: If a particular leave has been observed to be possible, then its mirror image is also possible. For example, if a 9-10 leave has been observed, then a 7-8 pin leave is also assumed to be possible even if it has not been observed. So, the first step in the process is to create a series of mirror image spares using the observed set of leaves. This increases the sample to 1,548 leaves, of which 187 are unique.

There are some interesting patterns in this dataset. The figures above show the frequency distribution of observed spares relative to the number of pins left standing. The greatest diversity of spare combinations observed is for three pin leaves. Of these, I have observed 48. I have observed 45 combinations with four pins remaining and 39 with two. This differs dramatically from the theoretical leaves. In theory, five pin leaves have the greatest diversity with 252 possible combinations, but in actuality, I have only observed 28 different five pin combinations. When viewed as the ratio of observed:possible leaves, there is a very clear pattern. All 10 single pin spare leaves that are possible have been observed. Of two pin leaves, 39 of 45 or 86.7% have been observed. This ratio slowly declines to seven pin leaves, of which only 2 of the 120 possible have been observed. the ratio climbs to ten pin leaves, of which only one is possible (a gutterball), and it has unfortunately been observed. I pulled off this feat twice last week. Ugh.

Here's how I solved for the total number possible. There is clear relationship between sample size and diversity. As shown above, as you observe more leaves, the sample of unique pin combinations grows. This curve is increasing asymptotically, which means that there is a finite number of spare combinations that exist. The curve is approaching that number. At first, it approaches quickly, but as the sample grows, the rate of increase declines. The reason is simple. Early on, you observe a lot of very common leaves and some rare ones. Once you have observed the most common leaves, only rare ones remain. There are likely some pin combinations that are exceedingly rare, combinations that only occur say 1 in every 10,000 frames. To observe these, you need a huge sample size, and I don't have the time or interest in waiting around for them to happen.

So, the solution to the problem is to use regression. I sought an asymptotic function that could be fit to the curve shown above. I found one here. This function describes the behavior of an electrical circuit component called a limiter, but it also seems to describe the relationship between sample size and diversity in bowling spares incredibly well. The fit is quite amazing. Anyway, it is possible to solve for the values of the coefficients that best fit the observed curves, and one of these is the asymptote, or the total number of possible spares. I use a very simple procedure. First, I randomize the list of spares. Then, I fit this function to the curve (like the one shown above) and solve for the asymptote. I repeat this process over and over again. Each time I do this, I get slightly different estimates. Then, I take those estimates and create a 95% confidence interval for the total number of spares that can exist. When I do this, I get a range between 269 and 297 with a mean of 283.

To give you an idea of how long it would take to observe all possible spares, it is a fairly simple question to answer using this regression model. According to this model, if I had a sample of 20,000 observed spares, of these approximately 263 would be unique. If I recorded another 20,000, I would observe four new unique pin combinations. This is why I am happy to stop here. Maybe somebody more insane than myself can pick up the torch.

Wednesday, April 8, 2009

The End is Near

It seems hard to believe but the season is soon to come to a close. Two weeks remain, and we sit somewhere between 4th and 2nd place depending on this week's outcomes. We went 3-1. We did so despite bowling below average. It was an interesting week in that everyone put up a 400 series, something we have not done in a long time, but we all barely broke 400, so our overall performance was not terrific.

Still, we won. It seems like how well we bowl has very little to do with the outcome in terms of wins and losses, and in fact the stats bear this out. I don't have the time or energy lately to demonstrate such a contention, as I have so often done in the past. I hope to be able to do so soon, but for now I have a lot of other responsibilities that have pulled me away from the BM Report.

I will note one thing about this week's bowling. It was a nice week in that everyone got a piece of the leaderboard, something you can check out if I ever get the box score posted. It has been a good season, and I suggest we go out with a bang. By this, I mean that we should bowl really well, really poorly, our at least try to set a new record for pitchers consumed. That would require seven, or 2.333 per game. We can do it. I know we can.

Monday, April 6, 2009

Getting Lazered in the Eye

In case you were wondering if the BM Report had perished, not at all. Three of the Movements spent the week in Cody, Wyo, and I did not have the opportunity to report on last Monday's match. At the outset, let me just say that we got our collective ass kicked by Lazer Wash. It was like getting lasered in the eye, and I'm not talking about Lasik surgery. I mean it was like they took some high powered He-Ne lasers, and pointed them right into our eyeballs.

We bowled poorly. Forget all that stuff I wrote about improving at bowling. We seem to be sliding. Here's the good, the bad, and the ugly. The Good- Over the previous five weeks of bowling, we had only broken the 30 strikes mark one time. This is something we had done regularly in prior weeks. Last week, we got 33.

The Bad- We lost three of four games and had our worst week on record as a team recording only 1,629 pins. JD made a run for the record books trying to beat Geoff's low game record of 88, but he failed in the last frame, instead only managing to tie it.

The Ugly- For each of the 18 weeks of the BIA, we have more marks than open frames. On Monday, we had 61 of each.

The Weird- Another statistical oddity of the night was that we recorded our worst win and loss, or maybe our worst win and best loss. In Game 2, we had a very nice 899 game (handicapped) and lost because they recorded something in the 1,000's. In the third game we rode Daniele's 88 all the way to victory with a 796. Prior to this, our lowest win was an 811.

We stunk it up.