Saturday, January 31, 2009

Attn: Pelican International

I’m sure you have heard that the Bowl Movements’s goal this season is to earn enough money through bowling to buy a canoe to be used as a fishing vessel during the off season. This lucky canoe will cruise the waters of Wyoming in search of trout. It should be obvious given our chosen recreational activities that we are middle aged men of leisure. How is the canoe quest coming along? Well, we have 44 wins at $9 a pop, and ¼ of our earnings will go to the Canadian who is not part of Canoe Quest 2009.

Our goals have been hampered by one small hiccup. We are not good at bowling. In fact, we have nearly as many losses as we have wins, 40 to be precise. While there is a remote possibility that we will eventually win enough games to purchase our dream boat, chances are we won’t have enough to even pay the sales tax. This is why I’m writing. I have a proposition.

The Pelican Bayou 160 is a fine boat. Check her out over there on the left. She’s a looker. “Ideal for hunting and fishing and boasting a 950 lb maximum carrying capacity, this multi-functional sportsman's square back canoe also comes in handy for a quiet ride on the lake!” She’s 16’3” in length. She’s got a built-in motor mount. Three molded bench seats. She even comes with rod holders. What more could a man want in a fishing canoe? Well, a kegerator, but I know that’s still in the pipeline.

Here’s the proposition. It is time that Pelican International got in the business of sports sponsorship. The Bowl Movements are currently without a sponsor, unlike many of the teams in our league. We roll against Laramie Lazer Wash, ASAP Sprinklers, Prairie Rose Cafe, and others. These teams show up to the Laramie Lanes weekly and advertise their sponsors on the scoreboard and in some cases on their jerseys. We need a sponsor, Pelican Canoes, and you are the obvious choice.

What’s it going to cost? Well, first we’ll need four patches to affix to our right sleeves. Then, we’ll need a canoe, a Bayou 160 would be perfect. The sooner you can get the canoe in the mail, the better.

What do you get in return? Every week for the 30 weeks of the season, you will have the name of your company proudly displayed on the shoulders of four handsome and charismatic men who bowl poorly. In the off season, we will pull trout after trout over the gunnels of your boat. Everyone who sees this will attribute our fishing success not to our amazing ability to tempt fish with shiny objects but to the vessel in which we float across the water. No doubt when folks see our fishing prowess and shoulder patches, your revenues and profit will double, or more likely quadruple.

When we get our boat in the mail, we will be able to use our earnings to truly pimp our ride. We will now be able to buy all of the necessary accoutrements, like life jackets, oars, a trolling motor, and 20 cases of beer.

So, Pelican Canoes, I’ll be waiting for the patches and the boat. I’ll be checking my mailbox daily. I can’t wait. What’s that? You aren’t interested? Don’t make me write to Old Town.

Friday, January 30, 2009

The Great BM Simulator, v. 1.0

Herein, I explore a little fantasy bowling using something I fondly call BM Sim v. 1.0. It dawned on me the other day that I could simulate our bowling, essentially creating a pretend version of the Bernaski League. We have enough data that I know our tendencies, so I could simulate games by our team. To do so would allow a number of interesting things. For example, it would be much easier to calculate probabilities of certain things occurring, like a 200 game, or even the probability of someone breaking Geoff’s amazing low game record of 88. Not only that, it would allow us to answer some “what if” type questions, like what if we picked up 75% of our single pin spares? How would this affect our scores and team averages?
The simulation is very simple. It is based on two sets of probabilities (shown above). The score for the first ball of every frame is determined by the relative frequencies of our first ball scores. We have 960 frames to our credit, so these probabilities are very robust. If a strike is not received, a second ball is thrown. The likelihood of a spare is determined by our observed pickup percentages given a particular first ball throw. If a spare is not received, the simulation chooses a random number of pins from zero to the number remaining. The 10th frame is a little more complex, but it basically works the same way.

Using just this information, it is possible to simulate games. Now bear in mind that the current simulation recreates an average bowler from our team; we’ll call him Big BM. It would be possible to simulate individual bowlers, like Johnebob or G-Spot, but it would be nice to have a little more data to do so. Nonetheless, the predicted game scores for Big BM are remarkably accurate. I began by simulating 20,000 games and examining their distribution to examine three things: 1) Do the resulting game scores fall within similar ranges to ours? 2) Is the average game score similar to ours? 3) Is the distribution of scores similar to ours? The short answer is yes.

The histogram above shows the distribution of 20,000 simulated games by Big BM. The scores should look eerily familiar. The simulated games have an average of 146.0. Over 96 games, we have actually averaged 146.9. The minimum and maximum observed game scores in the simulation are 64 and 246 compared to 88 and 213. This difference can be attributed to a much larger sample in the simulation. Most striking is the similarity between the distribution of actual and simulated game scores (above right). What all of this means is that we can be boiled down to numbers, and that the computer can replicate our bowling perfectly.

Now on to the interesting part. What is the probability of Big BM rolling a 200 game in any given game? It is approximately 2.3%. Bear in mind that if we were to simulate Johnny, it would probably be higher and for the Canadian, it would definitely be lower, but for the team as a whole, it is 2.3%. What about a 220? It’s about .42%, or 1 in 235 games. A 250? Very low. In 20,000 games, no scores over 250 were observed. The chances of a perfect game, while possible in the simulation, are extremely low. It can be fairly easily calculated. Given our observed strike probability of 26.7%, the chance of a perfect game is 0.000013%, meaning that at our current skill level, we should have a perfect game in every 7,733,484 tries. If we don’t improve, it would take us about 645,000 more weeks in league to achieve this, sometime around the year AD 14401 assuming we bowl every week.

What about the likelihood of someone bowling 88 or lower? This did occur in the simulation a few times. It’s 0.19%. It should occur about once every 534 games, so Geoff’s record might be around for a while. My suspicion is that if we were to simulate Canadian Bacon or myself, the probability would be a bit higher. Needless to say, though, with a little bit of improvement, our days of bowling the occasional sub-100 game should be over. Notice in the distribution above that very few games have sub-100 scores, only 1.5%.

To beleaguer this a bit more, I will do two simple analyses. First, I ask how improving our pickup percentage would affect our likelihood of rolling 200 or higher. It turns out that 200 games are not particularly sensitive to pickup percentage. As a team, we have picked up 40.7% of our spares. If we were to increase this to 50%, it would only increase the likelihood of 200 games to about 3.7%. In fact, if we picked up 75% of our spares, a 200 game would still be fairly unlikely, only 7.3%. I should note that this would be a dramatic improvement over our current state. Such games would occur every 13 or 14 games, but picking up more spares doesn’t get us much closer.

Strikes are a different story altogether. We currently record strikes on 26.7% of frames. If we could increase this to 40%, the probability of a 200 game would increase to approximately 10%. If we struck every other frame (50%), the probability is huge, about 27.4%. In this case, we could expect on average a 200 game from at least one bowler a game.

The simulation is capable of performing many other analyses, but I’ll save that for another day. I see the next round of simulation involving individual bowlers, but I’ll wait until I have four or five more weeks of data to make virtual Joey D.

Thursday, January 29, 2009

It was supposed to be an exhibition!

After several days of lament, I can now write of the bad night of team bowling. 14-2, a great record, perhaps to good.

We walked in there with our American flag shorts, our Uncle Sam hat, James Brown "Livin in America" playin in the backgroud. The fight was supposed to be an exhibition, a beating for us to dole out as we pleased. A night where the opposition just caves in. However, like Apollo Creed in Rocky IV we were simply not up to task. Sure, we looked good, all really for another 4-0 week. But alas, the mental edge had shifted sides.

As Apollo danced around, he looked like he had it in control. After all, what do Russians know of boxing? Drago was an unknown commodity in 1985. I know, Yevgeny Gerblackitov was a great boxer in the 1920's when he beat the American champ, ole' two tooth (pronounced toof) Wilson, in the 1927 Worlds Fair exhibition fight, but other than that, nothing. I digress.

Rocky eventually threw in the towel when he saw the beating of Apollo was to much. We, however, had no Rocky to throw a towel. All we had was cold frothy beer, which by itself is not capable of throwing in the towel. It was only able to tatse good and mildly kill the pain of the 1-3 beating we were getting. If we were Apollo that night, then team PBR was Drago, and they kicked our asses. Drago's trainer stated:"Whatever he hit's, he destroys!" Well, you could say PBR hit and destroyed many more pins then we did.

But know this, the next time we meet up we will play the role of Rocky, beat them down and maybe, just maybe, point out the futility of an American-Russian cold war in the process.

Wednesday, January 28, 2009

Bowling Haiku I

The pin called seven
Will not drop on a strike ball
As if super glued

Tuesday, January 27, 2009

PBR: Pathetic Bowling Report

In the past, when the Bowl Movements went toe to toe against the team known as PBR, more pins were garnered by handicap than by actual bowling. It was not exactly a display of bowling skills. Last night’s matchup promised to be different. The Movements sat atop the league at 14-2. The Beer Boys were 9th at 2-14. It looked to be a good night for us. It is a rare occasion when the handicapping system works in our favor, but last night we had the advantage. We have been hot. Unstoppable. Last night, we were stopped dead in our tracks, only picking up one of four games. Maybe it’s because PBR by some miracle became tea-totalers. Whatever the cause, this sad defeat probably will result in a drop to 2nd place behind Laramie Lanes Lounge. We’ll see…

For the second week in a row, no records were set, individual or team. It was a strange night all around. Our scores dropped from game to game. We took the first with an 882 but followed this up with an 848 and an 812. PBR did not roll particularly well either, so we can only blame ourselves. No bowler put up double digit strikes, and we tied our low for strikes with 30. We tied our 2nd worst night ever for marks with 35. We left 56 frames open. Instead of this night highlighting our steadily improving skills, it was business as usual with two crappy bowling teams bowling crappily.

Two interesting notes. One involving the team and one about myself. First, if you have been wondering if our 2nd half success is due to luck or skill, we have largely earned it. The graph on the left shows the total number of pins recorded for the team since the start of the BIA (green line) in comparison to the number we would have received if we had bowled our averages (purple). The large rise and dip in average correspond to subbing by Becker and Gingy, respectively. Since January 5, we have bowled well above average. With the sole exception of last night, we have put up between 79 and 168 pins over our team average, with a mean 124.6. Last night, we actually bowled above average as well but only by a single pin.

Regarding my game last night, I had one extremely unusual result (above right). I converted more single pin spares (n=6) than anyone, but I continue to struggle with this aspect of my game. In fact, Daniele had a much higher single pin pickup percentage (66.7% vs. my 46.2%). What was unusual was that I had 13 single pin spare attempts. This is far and above any other night by any other roller. The closest was Joe who had ten chances on January 12. Of the 13, I left seven untouched. I guess my first ball was regularly finding the pocket, but the 10th pin refused to fall.

Lead Off
To be honest, I’m running out words for the first sentence of Johnebob’s recap. Let’s try this. John is the best Bowl Movement in the world. Uncle Johnny had a bit of an off night by his standards, but he still had the high series for the team with a 456. This was a single pin off his average. He was consistent, putting up scores in the 140’s and 150’s, but lacked any huge numbers as he is known to do. Johnny led the team in nine categories: Game 2, Pins, Average, Marks, Mark %, Spares, Fewest Opens, Pickup %, and Accuracy. Regarding Pickup%, we should probably rename this category “John” because he owns it.

On Deck
I’m tired of writing about myself in the 3rd person, so I’m abandoning it. I started slowly with two games in 130’s, but finished strongly with a 180 in the 3rd. I took four categories on the leader board: Game 3, handicapped pins, single pin spares, and 1st ball average. On the good side, I put up 9 pins over my average with a 150. On the bad side, of 13 single pin tries, I only converted six. With one more spare, I would have hit a 50% pickup rate, but this number seems almost unreachable of late.

In the Hole
Geoff had a rough night, averaging a buck twenty-one, despite putting up two consecutive games in the 130’s. Rather than reliving the woulda-coulda-shoulda’s, I’ll just give the rook a few words of encouragement. Bacon, we need you to rediscover that pre-bowl form on a league night. You hold the oldest individual record of 733 handicapped pins from December 3. On that day, you rolled huge, and obviously it’s a tough record to beat. You may have the team low average, but you have a huge upside. When you thrive, we thrive. So bring it next week.

JD had very strong starts in Games 1 and 2, but failed to hit the deuce. He took Game 1 with a 189 and had a solid 144 in the second. The 3rd game? Well, look it up if you really want to know. Daddy D took his fair share of the leader board with four categories: Game 1, strikes, strike %, and single pin %. He put up a nice average of 147.3, a full 1/3 of a pin above his league average of 147. Dan-Yelly is definitely out of the slump, a good thing. He had a strange night, starting strong and declining slowly over the night, more or less a microcosm of the team. We were inconsistent.

Sunday, January 25, 2009

Do you like bowling and quantitative analysis? I didn't think so.

Bowling is a sport often enjoyed by folks with simple pleasures, like bowling. It is my impression, though unfortunately I have not quantified it, that the literacy rate at bowling alleys is similar to that of pre-Dynastic Egypt. My point is not to be a bowling elitist, but only to note that my obsession with the analysis of bowling scores is not common. This probably explains a few things about me. It explains why my calculator and pens often fall out of my pocket protector when I’m going after the 7 pin, thus tripping the foot fault indicator. It explains why when I step up to bowl, I commonly hear electronic “beep-beep-boop-boop” sounds and things like “the probability of picking up this split is 21.94%” spoken in a robot voice by my teammates as they guzzle bowling juice. It may also explain why I can’t seem to roll a 200 game in league, despite having some 200 chances to do so. But hey, I can tell you exactly the likelihood that I will do just that next week (1.96%), and I could do the same for you.

For it is my impression that while I am often the butt of nerd jokes, people like having a nerd to tell them how their bowling game is coming along. Parenthetically, I am an unapologetic nerd. There are only a few bowling statistics that most people can use to describe their game: average, handicap, series, etc. These are nice general summaries of one’s proficiency at the game, but I think knowing a bit more can be helpful. Wouldn’t it be nice to know that you throw a very good strike ball, but that for some reason, you struggle with spares? Aside from this, there is another point to my madness.

Quantitative analysis has traditionally been applied to certain niches, primarily the scientific realm. Descriptive statistics in sports, especially baseball, has a long tradition as well. Major league baseball teams now hire statisticians to help them evaluate prospects and the likelihood of reaching the Series. Ken Pomeroy has made a second career for himself by analyzing the statistics of college basketball. Nate Silver rose to stardom from nowhere with his detailed analyses of political polls and by almost perfectly predicting the outcome of the 2008 elections. Quantitative analysis is experiencing something of a renaissance. It is Revenge of the Nerds playing out in real life, but unfortunately real life lacks Bugger, Ogre, Gilbert, Lamar, and Louis.

My dorky obsession with the performance of the Bowl Movements and the general properties of bowling scores will not change the world. It will not result in fame. It will not land me a career with the PBA nor ESPN 8, but that is not the point. I like crunching numbers, and I enjoy the irony of this endeavor. Is it not the least bit ironic to apply mildly sophisticated analytical methods to the performance of a crappy bowling team in Laramie, Wyoming? This amuses me. If nothing else, this endeavor will shed a little light where there was none before. Prior to keeping track of my performance, I had no idea how consistent my performances have been. Who knew that I regularly throw between 8 and 13 strikes over a three game set, or that I only pick up 39.3% of my spare opportunities? Knowing this hasn’t really changed my game, but I feel like I understand my skills or lack thereof a little better.

So, I will continue to roll right through the beep-beep-boop-boop’s and continue to play with my data. They say that playing with your data can cause hairy palms and blindness, but it has brought a small chunk of the world into clearer focus. So bring on your nerd jokes.

Saturday, January 24, 2009

Bowling All Spares

In this post, I explore the total range of scores that can be received if a bowler receives a spare on every frame. When a spare is received, the pin total of the next toss is added to the frame with the spare. The answer depends upon the values of the first balls thrown, and there are a huge number of possible games. I’ll begin with the minimum and maximum.

The minimum bowling score possible in a game with 10 spares is 100. This is achieved by throwing gutter ball-spare on every frame with a gutter ball thrown for the 3rd ball in the 10th. In this game, a score of 10 would occur in every frame. The maximum possible score depends on whether you allow a strike for the 3rd ball in the 10th. I’ll assume that the score of the bonus ball is a nine. In this case, the maximum is 190. This is achieved by throwing 9-spare on every frame with 9-spare-9 in the 10th. This would equate to 10 consecutive frame scores of 19. So, a game comprised of nothing but spares can produced a score ranging from 100 to 190. If a strike is allowed for the bonus ball in the 10th, the maximum score is 191.

Neither of these outcomes is particularly likely because they would require a degree of consistency that is probably not attainable. For the minimum, it is hard to imagine how someone could consistently alternate between gutter balls and knocking down all ten pins. The maximum score is perhaps a bit more likely, but it makes you wonder how someone could consistently pick up single pin spares but not record a strike. So what are the most likely game scores in games comprised of all spares?

To answer this question, I performed two simple simulations. In each, I simulated 5,000 games. In the first simulation, a random number of pins (0 to 9) was given for the 1st ball in all frames and the 3rd ball in the 10th. The results are shown in the histogram above. The average score comes in at 145, and 95% of the scores would range between 127 and 163. This simulation probably is not a very good reflection of reality because the likelihood of picking up spares correlates with the 1st ball pin score (see here). For example, it is much easier to pick up a single pin spare than one involving seven pins left standing after the first throw.

In the second simulation, I changed only the range of the random numbers plugged into the 1st ball throws to vary between 6 and 9. In this version, the average score is 175, and 95% of scores fall between 168 and 182. This is probably closer to reality for the typical scores received in actual games involving nothing but spares.

Wednesday, January 21, 2009

The Sub, The Snub, and The Simian

Call it a renewed sense of purpose, if you will. The Movements, once a cupcake team, now dominate even the league's best. A 4-0 beating of the second place team made this team of young upstarts 14-2 in the young second half. We are so good, we even get intimidated by the thought of us walking in there on Monday nights.

It was, well, great to have Joey G. rollin the way he was. He was TCB'in (Takin Care of Business). Sheer domination from our sub, much like Becker provided. Much appreciated.

No Surovell, no problem. Is an Inauguration that was televised on every network worth missing league? An obvious nay. Rumor has it the good Dr. held up a sign at the Inauguration that read, "Hey Barak, come fly on my UFO!" The votes have not been counted yet, but Dr. Political may have been voted off in favor of our new, calm, cool, and collect super sub. (Stay tuned)

As our token math dork, Todd was missed. Geoff looked like a proto-simian doing Chinese arithmatic. There were tears of pain from Geoff as he tired to write down something, something that resembled anything, on that piece of paper. There were several primal hoots and hollers from Geoff, and at one point he looked to be throwing feces in frustration. Nobody really knows what in the hell he did write. Maybe it was some proto-simian language he speaks. By the end of the night, the paper looked as if a gang of zoo gorillas broke in and went to town on it! Of note: For whatever reason, he was craving Bananas at nights end.

Sunday, January 18, 2009

Practice (Does Not) Make Perfect

Well into this past Friday evening, around the time that you begin to realize that it is in fact early morning, I found myself in an unfamiliar place with unfamiliar folks. Laramie Lanes. Classmates. No uniforms. No Movements. Eighty's hair metal. WTF? It was like some kind of weird dream - like the one where you forget to put on your pants before leaving the house.
To change it up a little this past weekend, a group of my non-bowling friends and I opted to go bowling for "fun." Now that I am in a highly competitive league, the word F-U-N has been dropped from my vocabulary (only to be replaced by a different one-syllable F-U word). There is no F-U-N in the Bernaski - only business. Fortified by a stomach full of baby carrots and Odell's IPA (a recipe for a potentially messy Movement), I prepared to take care of business.
Among our group of seven, I figured I was in good shape to walk away a winner. A motley collection of folks, there was nary a bowler among them. The lone exception was J-Gig, the Movement's supersub. Although teammates and dear friends, we sometimes find ourselves locked in mortal combat in a struggle to be the second-crappiest Movement. What he lacks in experience, Gingergoo makes up for in raw talent. As such, I figured he'd be my only competition.
It turns out that I severely underestimated my fellow rollers. Each of the two games we played was a highly competitive affair in which the ladies prevailed. For us guys, it was like we put our wallets together and hired some crazed troupe of bowling dominatrixes to punish us our gutterballin' ways. A sort of Crique de Soleil bowling beatdown if you will. Simply put, they owned us. The triple threat of bowling vixens posted top 5 finishes each game and in the end, Willa Mullen walked away with back to back victories - a resounding testament to why there are no women rollers in the Bernaski. I am not sure we'd put up much competition.
In the end, I chalk my poor finish up to a lack of food, excessive liquid, and the fact that I left the captain at home in the trunk of my car (like a bad scene from the Sopranos). Bowling is apparently something I should not participate in on a whim. What started as an extra practice roll ended as a strike to my confidence. Each ball the ladies threw was like a little kick to my stomach until I realized that I badly needed a Movement. Laramie Lazer Wash beware. This coming Monday, I'll be ready and am bringing the high pressure washer to clean out the gutters...

Saturday, January 17, 2009

Super Deluxe Lazer Wash Preview

If you are so lucky to bring your car, or more likely your truck, to Laramie Lazer Wash, you will be greeted by an old man who will offer to put your money in the bill sucker upper for you. You will feel obliged to allow him this courtesy. He will then wash your headlights with a mop. This is customer service at its best, Wyoming style. This mysterious old man of Laramie Lazer Wash is truly a hero, but what is more mysterious is that he does not bowl on the bowling team that carries the name of his business.

On Monday, we face the back to back to back to back to back to back league champions, Laramie Lazer Wash. They consist of Troy "The Briefcase" Baker, Brett "Zero Cap" Baker, Cody "The Kid Wonder" Caldwell, Dell "The Godfather" Sol, and Rod "The Bear" DeBruin. They are a tour de force in the League of Bernaski, but this week, they find themselves in an uncomfortable and unfamiliar setting, sitting in 2nd place behind the best bowling team in the world, the Bowl Movements.

I will be sadly vacating the two spot this week. I will miss what has been dubbed by the international press, "The Battle for Gem City". In my place will be the Gingasaurus Rex, who comes in with an "impressive" 115 average and 94 handicap. The Lazer Wash advantange will be stretched to new heights, so the Movements will have to roll with heart and gut and gusto and passion and a bit of good fortune, too.

Ginges Khan has a lot of downside but sitting on that beefy handicap, he also has a lot of upside. Here is what I want to see upon my return. I want to be wiped from the record book. To do this, someone has to put up better than a 189 in Game 2 and more than 13 strikes for the night. I want the record thought to be unbeatable, Geoff's low game of 88, to be beaten. Gingy seems like the man to do it. I want to see at least two wins over the Dominators of Bernaski, so we hold our position at the top of the league. I want the Movements to step up to the plate. I know it will be hard when your hearts will be aching for me, but you can do it.

Thursday, January 15, 2009

Special Delivery

Riddle me this ---It is round, it is cheesy, it is pepperoni laden, it is made with all organic crust, and it was intended to throw us off our bowling game. What is it?
“It”, is a yummy Little Caesar’s pizza pie given to us by our bowling adversaries on Monday night. The pizza was an ill-fated attempt to throw us off our game and tilt the odds in their favor.
Now, sure, it has been said the quickest way to a man’s heart is through his stomach, and pizza ranks number one in the United States for delivered food, posting a whopping 162,000 tons per year. (followed closely by Chinese take-out and Meals on Wheels). So the logic for the opposing team to befriend us with pizza seems valid. Alas, it did not go to plan. Instead, we ate free pie, and posted a 3-1 victory for the night.
So, on an evening where the Little Caesar’s team thought they were going to distract us, the opposite occurred. It turns out Little Caesar’s heard a knock on their door and within 2 hours of placing the pizza in front of us, we in turn hand delivered one extra-large beatdown.

Wednesday, January 14, 2009

Presidential Bowling

As I will miss my first league night of the season next Monday to attend the inauguration of the 44th president of the United States, I thought it would be fitting to honor Barack Obama with a brief history of presidential bowling. After all, one of the least effective moments of the otherwise impressive campaign was his visit to the Pleasant Valley Lanes in Altoona, PA on March 29, 2008. Obama rolled his way to a 37, a score that can be obtained by most folks while bowling blindfolded. Unfortunately, he was trying to impress the blue collar voters of the Keystone State. Obama went on to lose Pennsylvania to Hillary in the primary. His poor performance at bowling is rumored to have been the cause. Obama was not the first president to try his luck at bowling, nor the first to embarrass himself in the process. I begin with the 33rd president of the United States, the man from the Show Me State, Harry S. Truman because it was under Truman that the bowling alley was first installed at the White House, but the history of presidential bowling can be traced back at least to Abe Lincoln’s days in the U.S. House of representatives as reported in the June 13, 1928 Washington Post.

33. Harry S. Truman - The story of the White House bowling begins with Harry Truman searching the basement of the West Wing in 1947. He discovered a long narrow storage area and felt that it would be a good space for a bowling lane. Truman was not a big fan of bowling himself, but he felt that it might be useful for the recreation of White House staff and a way to maintain morale. An aide to the President, Major General Harry Vaughn determined that it would cost roughly $7500 to install a lane in the space, but found a manufacturer willing to do it for the paltry sum of $5000 given the proposed location. To fund the alley, Vaughn raised funds from Truman’s friends, mostly folks from Kansas City, and the lanes (two of them) were presented to the president on the occasion of his 63rd birthday on May 8, 1947. Truman reportedly rolled a 7 on the first ball thrown in the White House, but apparently did not bowl much again.

34. Dwight D. Eisenhower- The bowling habits of the WWII general turned president remain unclear. According to the Jan. 17, 1953 edition of the Washington Post, three days prior to his inauguration, Eisenhower’s intent was to remove the bowling alley because representatives of the president elect were “appalled by the lack of space in the White House Executive Office.” The same story reports that the White House bowling league, consisting of eight teams of “policemen (who have three teams), chauffeurs, stenographers, mimeographers, and others,” would be displaced. Clearly the Eisenhower administration did not have their priorities correctly prioritized. In 1955, the lanes were moved to the Executive Office Building, where they remain today. The location of the original bowling alley is now occupied by the Situation Room.

35. John F. Kennedy – Little is known of the bowling habits of JFK. According to the July 21, 1970 Washington Post, “President John F. Kennedy and his family rarely used the lanes, preferring other sports.”

36. Lyndon B. Johnson- The Texan who took over the Oval Office after the 1963 assassination of John Kennedy was an occasional bowler, but Lady Bird Johnson was apparently the first member of the first family to regularly take up the sport. She was serious enough to have her own custom drilled bowling ball. This photo shows her bowling with her son-in-law, Patrick Nugent. According to the Post on March 26, 1966, she preferred to swim, but the heated pool of the White House wreaked havoc on her hair, not good when one has a busy public life. She reportedly bowled three to four times a week and was happy with a score of 130 or higher.

37. Richard M. Nixon- The Nixon administration marked the Golden Age of Presidential Bowling and the Dark Age of the Presidency. Richard Milhous Nixon was an avid bowler. Nixon bowled frequently, both in the Executive Office Building and at the bowling alley at Camp David, a two lane facility. Nixon preferred bowling to golf because it could be done quickly in the gaps in his schedule. According to the Washington Post’s July 21, 1970 edition, Nixon’s average was a closely guarded state secret but purportedly was in the range of 165-200.

38. Gerald Ford- With Nixon’s resignation and the decline of the American presidency, presidential bowling declined as well. Not much is known of the bowling habits of presidents 38 through 40. Either Gerald Ford felt it was best to not emulate the habits of his former Commander-in-Chief, or the press lost interest in covering the benign habits of the Executives. I can’t imagine why.

39. Jimmy Carter
– According to one website, bowling is one of Carter’s favorite sports. Other than that, good ol’ Jimmy’s bowling habits are a mystery.

40. Ronald Reagan – Like his predecessor, it is unknown whether Ronald Reagan enjoyed to roll balls toward pins. I was able to find a gem of a photo of the Gipper at the lanes with his first wife, Jane Wyman.

41. George H. W. Bush – The first of the Bushes was not much of a bowler. He was an avid sportsmen, but apparently bowling was not one of his favorites. Bush Sr. was the first president to perform a bowling faux pas. On April 11, 1984 while campaigning as Vice President, Bush visited a bowling alley in Milwaukee and fell onto his knees trying to pick up a single pin spare. This moment has been forever enshrined in the annals of YouTube:

42. William Jefferson Clinton – According to Dick Evans, Slick Willy was an "avid junior bowler" with a 160 average and apparently used the White House lanes quite a bit. By 1994, his average was down to 140.

43. George W. Bush – I wouldn’t be surprised if the Dubya is a decent bowler, but it is difficult to know. Here is some video of the 43rd president chucking a turkey at some bottles of Coke. I was able to glean two other bits of bowling trivia on the shrub. In October of 2000, while campaigning in Hopkinsville, Kentucky, he visited the Ebonite factory and was presented with a red, white, and blue bowling ball. He also made a campaign stop at the Leda Lanes in Nashua New Hampshire to try his hand at candlepins, as shown in the picture here.

44. Barack Obama – In addition to his 37, Obama has talked on numerous occasions of pulling an “Eisenhower”. The president elect’s love of basketball is no secret, and I applaud his hoops habit. Unfortunately, B Ob’s loves to “joke” about replacing the Presidential Bowling Alley with a basketball court. What would this say to the bowlers of America, Mr. Obama, especially the bowlers like yourself, who lack skill, the very bowlers who maintain this blog. Listen, Mr. New President, I’m a big fan, but you’re the president. You can have your hoop dream and work on your bowling game. When you're president, you can have all the recreation facilities you want. Don’t replace one hardwood with another. And by the way, if you are looking to create the Department of Bowling and are looking for a Secretary of Bowling, give me a call.

A word of advice to bowling presidents: When you do bowl, take off your tie and have a beer.

Tuesday, January 13, 2009

Pizza Pizza

Despite their peace offering of pizza pie, we owed Little Caesars something. In the first half of the season, in the Battle of the Basements, they gave us one of our worst beat downs of 2008. They used their victory over the Movements as a springboard to the top half of the leader board. Week after week, we watched them climb in the standings while we fell. In Wyoming, we believe in prairie justice. When somebody wrongs you, you wrong them back. Filled with the national food of his homeland, graciously delivered by the Pizza Men, Daniele carried us to a 3-1 victory over the Diminutive Emperors. The Bowl Movements now stand 10-2 in the 2nd half, hanging somewhere between 1st and 2nd place. In the 2nd half of the Bernaski League, there is only one team that can prevail, and that team might be (with a hell of a lot of luck) the Bowl Movements.

How did we do it? We did it by being remarkably average. Over the previous six weeks, we averaged 1,759 pins per series as a team. Last night, we recorded 1,768. What should be noted, though, is that we have been generally bowling over our averages since the start of the BIA (Bowling Information Age). If we were to bowl our current averages, we would put up 1,701 pins in a three game series. So, we bowled above average from the long term perspective, but average when seen in comparison to the last seven weeks.

Only one team record was set this week. We recorded our highest pin total for the 1st game, a 613. Handicapped, it was a dominating 894, six pins shy of 9’er. We also tied our record of 17 single pin spares. As the night went on, our pin totals declined game by game, likely attributable to five pitchers of bowling juice, mostly distributed among three bowlers. In the 2nd, we recorded an 864. In the 3rd, an 853. This was good enough to take games 1,2, and the pin total. We lost the third game by approximately 20 pins. We can take most of the credit for our 3-1 victory, but we must give a little credit to the Little Caesars who struggled in the presence of greatness. In the Battle of the Bowling Shirts, it was orange on black versus red on black. Red was the victor.

Tonight’s BM Report Stat of the Week has to concern our cleanup man, the Italian Scallion, JD. As has been thoroughly documented, though perhaps not thoroughly enough, Daniele was in a slump, a bad slump. He began the BIA easily leading the team in average with a 150. Then, his game began to slide, so much that he was erased from the record books. He bottomed out in mid-December with back to back 381 series, but since that time, he has been resurrected. Over the last two weeks, he has been over 450 and last night led the team with a 474. I will not declare the slump over because doing so would only doom it to return. Let’s just say that he has put a nice dent in it.

#1 just keeps on ticking. Everything seems to be working for Juan Pablo. He split the leaderboard with JD picking up nine highs of the night including Game 3, in which he recorded a 174. He also led the team in marks, mark%, spares, fewest opens, pickup%, single pin%, and accuracy. Johnebob is the undisputed king of the 2nd ball. He converted 60% of his spare opportunities, and nobody else even came close. Uncle John tied two of his prior spare records with 15 overall and 6 of the single pin variety.

On Deck
It seemed like an off night for the #2 man, which is a good thing because it was remarkably average. He averaged 140.7 pins, only 1/3 of a pin below his current average of 141. T-Bone bottomed out with a 132 in Game 3 and topped out with a 154 in Game 2. Overall it was a relatively consistent night but consistently mediocre. Xander struggled mightily in picking up spares, collecting only 36.4% of his chances and did not get a single yellow rectangle on the leaderboard.

In the Hole
There were concerns about the Maple Leaf, who returned to bowling after almost a full month without touching the hardwood. His skin was stained with the melanin of the Belizean sun. Both factors would suggest an off night for the rookie, but he had a solid night. The RCMP averaged 135.3 pins on the night, a full 8.3 over his average. He carried us through the 2nd game with a solid 160, and dominated the 3rd frame with an 18.7 average.

JD rediscovered the record board this week by leading the team in Game 1 and setting a new record with a 191. He was tops in series, average, handicapped pins, strikes, strike%, and 1st ball average. He averaged 158 pins a game, while recording 11 strikes and a 1st ball average of 8.5. Seeing the return of our cleanup man to his standard form was a welcome sight, and his Qubica Bowland Buster House Ball has earned the title of "Ball of the Week". Good on ya' J-Dog.

Monday, January 12, 2009

One Ball Wonders

In this post, I explore the relationship between the score achieved on the first ball and the resulting frame score. Generally speaking, it would be expected that a higher pin count on the 1st toss would lead to higher frame scores for obvious reasons. 1) You knock down more pins; 2) You increase the likelihood of achieving a mark; 3) If you get a mark, you have additional chances to enhance your frame score.

I begin with a histogram of first ball scores. It may be somewhat surprising given our relatively low skill level at bowling that the most common first ball outcome for our team is a strike. Strikes account for 27.2% of first balls thrown. Obviously, this does not mean that we strike most frames. If framed in terms strike vs. non-strike, we have not recorded strikes on approximately 73% of first balls. The distribution is highly left-skewed and thankfully first ball scores of 0-4 in total account for less than 4% of attempts. Scores of 5-10 are increasingly common in our database, again with strike being the most common, and therefore, the most likely of any possible outcome. Maybe we aren’t as bad at bowling as we thought.

How does the likelihood of picking up a mark change as a function of the first ball score? Although we don’t have a lot of data for first ball scores less than five, generally speaking, a small pin total after one throw means a low likelihood of picking up a spare. For us, it’s less than 20%. In our current database, with first ball pin totals of five or greater, the probability of picking up a spare increases steadily from approximately 25% for a 5 pin first ball to approximately 50% for a 9 pin first throw. It appears that we may be slightly better at picking up spares when three pins remain than when two are left. This slight discrepancy could be due to a small sample size, but I expect that this reversal is due to split effects, that the most common and difficult splits to pick up involve two pins. Of course, all ten pin first tosses are marks, so the 100% mark frequency for a 10 pin first toss is meaningless.

The score received on the first ball determines the minimum and maximum score possible for a frame. The minimum score possible for a frame is the first ball score (i.e., it is impossible to receive less than an eight for a frame if the first ball is an eight). The maximum score is constant for first balls of 0 through 9; it is 20 if a spare is picked up followed by a strike. For a first ball of 10, the maximum score is 30 if two strikes follow. In the scatter plot above, the area in yellow shows the total possible range of frame scores than can be achieved given a certain first ball score. The gray dots show our actual frame scores for 720 frames.

Given the considerations above, it should be no surprise that higher first ball scores lead to higher frame scores, although for our team, this effect does not appear until a 1st toss score of five. The graph above shows the average frame score for our team as a function of the first ball score. When less than five pins are recorded, we generally average less than 10 pins per frame with a mean outcome around eight. For all first throws above four, our average frame scores are above ten and increase steadily. For five pin first balls, we average a score of 10.3. For nine pins, our average frame score is 13.5. For strikes recorded on the first throw, there is a huge jump, and we average 21.4 pins per frame.

So what does all of this mean? Well, this story has no moral, except that I obviously have too much time on my hands. If I had to conclude something, I guess I was surprised that our most common first ball outcome is a strike. I would have guessed that we throw more nine balls. I suppose the most obvious conclusion is that success begets success. Do well on the first throw and good things tend to follow.

Saturday, January 10, 2009

Two New Bowling Statistics

Among our many hundreds of readers (i.e., ones of readers) is the guru of college basketball statistics, Ken Pomeroy, who apparently became obsessed with picking up single pin spares after I sent him a copy of our bowling score/statistics spreadsheet, which I use to create our box scores. Evidently , this obsession was not leading to higher scores. To give him something else to worry about, he started keeping track of first ball average pin count. He also wanted a way to distinguish between a high score attributed to skill from one resulting from luck. In honor of Ken, I have now added this statistic to our scores and a second one as well, a stat I call accuracy.

1st Ball Average
If you are throwing a consistent first ball, you should be regularly hitting the pocket. If your ball is a regular citizen of Pocketville, you should have consistently high pin counts for that throw, usually 8's, 9's, or 10's. Having a high 1st ball average should generally lead to higher scores because you are getting a lot of strikes, or you are leaving yourself in a good position to pick up spares (unless you pull a Game 1 Daniele from last week and find yourself getting splits every other frame). Therefore, there should be a correlation between 1st ball average and game score, and in fact, there is. According to Ken, "If you are averaging in the upper 8's then you would consistently have games in the high 100's," and from our sample of 72 games, this generally appears to be true. If you have a high first ball average but a low game score, this means that you are not taking advantage of the situation into which you have put yourself (imagine 10 open frames with 9's on the first ball). For our games, we have gone as high as 9.3 (JL's 213 game) and as low as 6.1 for a ten frame first ball average.


In thinking about what it means to really be "on" when bowling, I developed the accuracy stat. When you feel like you have good control over your ball, your first ball is always near the pocket, and your spare ball is hitting its mark, no matter which pin or pins you have left standing. So, a good night simply means picking up a lot of marks. Of course, strikes lead to higher scores than spares, so both types of marks should not be treated equivalently. So, a really good night means picking up a lot of strikes, and cleaning up the garbage when you are left with a spare opportunity. The accuracy stat is based on this idea. It is very similar to our mark% stat, which simply gauges the percent of frames marked, but it gives strikes a greater weight. It is calculated as: (strikes*1.56+spares)/18.72. It varies between 0 and 1, and for simplicity, I present it as a percentage. This stat has some intuitively satsifying properties. A game with zero marks equates to 0% accuracy. A perfect game with 12 strikes is 100% accurate. A game with 10 spares is approximately 53% accurate. This statistic correlates very well with game score. Generally speaking, to get a score above 150, you want to have an accuracy above 50%. For our 72 games, we have gone as high as 73.7% (Joe's 192) and as low as 10.7%. Here's the interesting part.

There are many ways to get your accuracy above 50%:

0 strikes, 10 spares
1 strike, >7 spares
2 strikes, >6 spares
3 strikes, >4 spares
4 strikes, >3 spares
5 strikes, >1 spare
>5 strikes

If you bowled games with exactly these numbers, they would all be considered to be roughly equivalent in terms of "accuracy" and would result in similar game scores.

Of course, we don't need any more bowling stats, but it does give us a way to spread the wealth on the leaderboard, and when I add these to the record books, Joe will have some representation once again, only to be quickly erased by Johnebob.

Thursday, January 8, 2009

Bowl Goals II

I laid out three goals for the team on December 12. By January 5th, they were accomplished:

1. Roll a 200 game. Accomplished by Johnebob on 1/5/09 with a 213.

2. Get one bowler to a 50% pickup percentage for one series. Johnebob has managed this three times, each time going above 60% (12/15, 12/29, 1/5). I barely eked out a 50% on 12/15, and Joe and Geoff have gotten close. Rory did it on his first try.

3. Record 1,800 pins as a team. On 1/5, we smashed this goal with 1,938.

Accordingly, it is time to set some new goals within reach. Here they are:

Goals for the New Year

Team 50% pickup
It is not inconceivable that we pick up 50% of our spares as a team for a three game series. In fact, we have already gotten close. On the 15th of December, we collected 48.4% of our spares as a team. This equated to 45 spares vs. 48 open frames. If we had picked up two more spares that day, we would have been there. That day, we left seven single pin spares untouched, although Daniele knocked down all four of his chances. Since the start of the BIA, our pickup rate has steadily increased with a slight dip in our most recent outing.

The 700 Club
The 700 Club, as I remember it, was a Sunday morning religious program in the 1970’s and 80’s that got in the way of my cartoon watching. Apparently, it is still on. Our 700 club has one member, Johnebob (JPL has probably pulled off the trick 4-5 times prior to record keeping). To enter the 700 club, you need a 500 series plus a 200 game. I am fairly certain that Daniele has done this in the past, too, but it is not currently reflected in our records. We need to fill out the membership of the 700 club. Whether the Gee-off can do this throwing his Canadian reverse-spin straight ball (see here) remains to be determined, but TS and JD are poised to join its ranks.

Quince Equis
The current individual record for strikes in a series is 13. Let’s get it to 15. There is no better determinant of a series score than the number of strikes thrown. Looking at the graph below, it would be difficult to put up 15 strikes on a night, an average of 5 per game, and not record a 500 series. This one’s for you, Johnny. All you have to do is strike every other frame.

Wednesday, January 7, 2009

Firm BM's, Part II

A few records of note from the 5th of January:

1. With our three game series of 1,938, and Johnebob's 213, we have now met all of the "Near Term Goals" posted a little less than a month ago. A new set of goals is in order.

2. We set new team highs in many categories, series (1,938), handicap series (2,706), marks (80), mark% (65%), strikes (43), strike% (32.6%), fewest opens (43), pickup% (48.4%), and single pin spares (17). Of these, the biggest jumps concern pin totals and strikes. The strikes number is remarkable. Or old record was 33, which we exceeded by 30%.

3. We ended the 1st half six games under .500, and after only two weeks were are 6 games over.


Johnebob led the charge as he has done for the last three weeks of bowling. Following his low game of 145 in the 1st, he added 30 pins to his score in the 2nd, and broke the 200 barrier in the 3rd. He led the team in average, marks, spares, pickup%, fewest opens, single pin spares, and single pin %. He also performed a BM first of marking every frame in a single game, the third, in which he only left three pins standing. He broke two records, previously held by him, the high game and the high series. One hell of a good night for the leadoff man.

On Deck
I have wondered whether it is symbolic to be the #2 roller on a team named after #2, and whether it is symbolic in a good way or bad. On Monday night, it was a good thing. Toad had his best night on record, missing a 500 series by one pin. He set a new team record for strikes with 13, and provided the high score for Game 2. Two down sides to Monday's performance: 1) he continues to struggle with single pins, collecting only 50% (4 of 8), and produced the only single digit average in a frame with a 9.0 for the 2nd.

In the Hole
While it is tempting to chalk up our incredible team performance to the presence of the Friendly Ghost and absence of El Jefe, it would be a bit of a stretch to do so. Becker had a decent night considering he was bowling with a house ball named "Mad Maxine", but he was the only bowler not to hit his average. He came in with a team high average of 157, and ended the night with a 150.3. But this was definitely a good night by Movement standards. Becker contributed a lot to our pin totals, but not our handicapped pin totals. For the 1,007 in Game 3, Becker only put up 8 pins over his average, something El Jefe could have managed with a 136. Stats of note: Rory had the high score in Game 1 (150), and tied with Laugh's for the team high in spares with 12.

The cherry on top of the sundae had to be JD's night. After Game 1, it looked like a typical night for our cleanup man. In the 1st, he had to put up 24 pins in the 10th frame just to reach a 112, but he never looked back. In the 2nd, he landed a 150, and in the 3rd, he shined, recording a 193, the 2nd highest game on record for the team. It was a nice thing to see the reemergence of the old Jeaux. Despite this stellar night, he did not make the leaderboard with the exception of leading the charge in the 3rd frame in which he averaged 19 pins.

Tuesday, January 6, 2009

A Firm Bowl Movement

On the Bernaski front, there is much news to report... prebowling outcomes, the end of the 1st half the season, the start of the 2nd half, and our performance from Monday the 5th. JD gave a nice recap of the night. Here's a bit more.

Prebowl I and the 1st half
Our first effort at prebowling was far from spectacular with the notable exception of the emergence of the Canadian. Our high game that day (bowled on 12/3) was 877, followed up by dual 827's. By some miracle, we managed to take two games against Lesser Fat, the 1st two to be precise. Unbeknownst to the Movements, this day marked the end the first half of the Bernaski season. Despite remaining six games under .500 with a record of 29-35, we moved up in the standings, only missing the top half the league by one position. We ended in 6th, a respectable finish considering the depth our midseason struggles.

Prebowl II
Our second attempt at prebowling occurred on December 12. This day marked the emergence of Johnebob, who on that day recorded the first 500 series of the BIA. This day marked our best bowling to date, nearly cresting the 1,800 pin mark as a team with a 1,788. We put up consistent high handicap pin totals of 882, 887, and 877. This performance was so strong, in fact, that we took every game to begin the 2nd half of the season 4-0. Of course, were aided by the fact that our opponents (who have yet to be identified) did not show up. They are lucky they didn't. If you get your ass kicked, its best to be able say, "I wasn't even trying."

January 5, 2009: Pushing the Deuce
Happy New Year! Our first attempt at bowling of AD 2009 was something to behold. It was initiated by two unusual features, a cameo visit by the Package, who made an emergency delivery of a forgotten jersey, and the absence of our three-man, Gee-off. Thanks to a miracle delivered by Pinnius, the God of Bowling, a prior Movement, Becker, showed up on the scene as reported by JD.

Of course, the miracles did not end there. Facing Lesser Fat once again, we dug ourselves a deep hole in the 1st. They recorded a beefy 925 against our 2nd worst game on record, an 802. Our realistic dream of going undefeated for the 2nd half was over. After one, we were 123 pins in the hole. Except for Johnebob, the 2nd game did not start well. Our lead off man marked the first five frames of game 2, but for the other three bowlers only six marks were had out of 15 tries. Going into the 2nd half of the 2nd game, our handicapped pin lead had evaporated. An 0-4 night was looking not only possible but likely. If we had any chance at winning Game 2, we would have to bowl toe to toe with a superior team. Handicaps were now irrelevant.

As we poured the remaining drops from our 3rd pitcher of Bowling Juice, our eyes met, and we heard the quiet voice of the absent Canadian as it wafted into front door of the Lanes of Laramie. He said, "We will not go quietly into this dark Monday night." The Laughlonian stepped up, and made the pins pay dearly with one throw of the blue ball. Surovellian spared the 6th. [Becker threw an 8 followed by an airball] And JD capped it off with a strike. The pins kept falling, frame after frame. We added 100 pins to our game 1 score. Becker had the low game with a 136. Daniele a 150. Laughlin a 175. Surovell a 183. A 902 was good enough to take the 2nd, but we only knocked 30 or so pins off the Fatty's lead.

When Game 3 arrived, we stood 1-1 on the night hoping to take the 3rd for a 2-2 finish. 3-1 seemed out of reach. But on this night, in this game, at that hour, on Lane 14, the Bowl Movements would not fold. We would not lie down. We would not give up. We would not put our tails between our legs. We would not beg for mercy. We would not throw in the towel. We would not kick the bucket. We would not choke. We would not raise the white flag of surrender. We would not cut and run. We would not cry for our mommies. We would not pull a Chicago Cubs. We would not pull an "early round Gonzaga." We would not drop the ball. What would we do? We would show not only why our team is named after what is excreted from the rectum, but also why our chosen name is ironic.

When the Movements are firm, watch out. Johnebob pushed a huge deuce, breaking the 200 mark for the first time since the start of the BM Report. 213 is now the mark to beat. He did it by marking every frame. T-Bone contributed another 178 pins. [Becker got a 163]. And Giuseppe came out on fire starting the game with a 4-bagger, 9/, X combo, finishing with a 193. In game 3, we averaged 187.3 pins per bowler, setting our high water mark with a handicapped 1007. We took games 3 and 4 to start the season 7-1 and in 1st place. How did this happen? Pinnius, of course.

There is much to be said about January 5, 2009, a day that will be forever enshrined in the Golden Archives of Bowling. No doubt, our children's children's children's children will celebrate this day as Bowl Movement Day, not a national holiday, not a world holiday, but a holiday celebrated across the Universe by Earthlings, Klingons, ET's, and Blongkorks alike. It was on this day that all four bowlers put up their high pin totals of the BIA, including the Casperian [his records extend back to 1/5/09]. JL-513, TS-499, RB-451, JD-455. We came back from adversity to dominate. We dedicate this victory to the Canadian, Pinnius, Package, and our huge contigent of loyal followers (all 3 of you).

Six weeks into the BIA, it is time to give credit where credit is due. Johnebob has established himself as the king of the lanes. He had a disastrous first preBowl by his standards, not even putting up a 400 series, but since that early December day, he has simply outshined every turd on the team. He has recorded the only two 500 series and 200 game of the BIA and his average is growing steadily. He is picking up spares like he picks up cheap women, easily and readily. A 600 series may be on the horizon for the Laughlonian.

Individual reports will follow tomorrow.

Note: Box Scores have been moved to the right hand column. Yesterday's score is here.

Red, White, and Becker

The Becker effect:
To all the millions reading, think about this: Rory Becker's day went from jamming hard to his rod Stewart Box set (extend version) to watching the single best game in Movement history. I can only imagine how special that must have been for him. Just being allowed to hang with such smart, good-looking, strong, funny, personable, witty, skilled men is privelege enough, but to see that game, what a night.
The normal team member from the 51st state (Canada) was busy with green card obligations, thus THE BECKER EFFECT. While not particularly skilled at bowling, Rory was able to provide a steady flow of pitchers for the three constant Bowl Movement members. After a bumpy first game, where other teams would certaimly have conceded the total pin count for the night, this team of juggernuats was undaunted. A nice second game of steady bowling, with Becker in tow, brought the match to 1-1. Normally, when a team blows up for 919 pins in the third and final game of the night, they win. But not on this night. The Movements not only beat the 919, but put up a unimaginable 1,007 pins and took the overall pin count to go 3-1 on the night. 1,007, that is alot of pins, most known cultures do not even have number systems that go that high, thankfully ours does. You know the team score is good when you need a comma when typing it. Statistically based as this blog is, the key stat of last night was the high coefficient of pain we brought, which I calculated using a dominating regression equation.
Now you may ask yourself, What in the hell is this Becker effect? Did he carry the team that night? No, he did not. While the rest of the team all bowled a third game with scoes well over 170, Becker was slummin with a 165. What then did he really do? Nothing really, but he is American. 100% Red, White, and Becker.

Sunday, January 4, 2009

On the Curious Nature of Bowling Scores

Bowling scores have interesting quantitative properties. The scoring system was apparently formalized in 1895 by the American Bowling Congress in New York City. It is a remarkably elegant thing, establishing a maximum possible score of 300 over 10 frames. In this post, I want to explore the relationship between the actual number of pins knocked down versus the score received. Although generally speaking, recording more pins will result in a higher score, in actuality the relationship between these two variables is surprisingly weak. Consider the minimum and maximum scores that can be achieved when a bowler knocks down every possible pin. A total of 120 pins can be recorded in any game assuming three strikes in the 10th. The maximum score is easy; a perfect game with 12 strikes equates to a score of 300. The minimum score is achieved by nine frames comprised of gutter balls on the 1st toss and a spare on the second. The final frame must be a turkey. This game would result in a score of 120 (9x10+ 3x10=120). So, recording every pin in a game of bowling can theoretically result in scores with a range of 180. This is certainly true in theory, but is it also true in practice?

We have 60 games in our current database. Above is a scatter plot showing the relationship between actual pins recorded and score received. While it is generally true that more pins equate to a higher score, the relationship is quite weak. In fact pins recorded only explains approximately 55% of the variance in game score. I have circled two extreme games to illustrate why this is the case. Circled in blue is a game in which the bowler (who shall remain anonymous) recorded 96 pins and received a score of 105. In red is a game in which a bowler recorded fewer pins, only 94, and yet ended with a score of 189. The reason for this discrepancy should be obvious. The first game included only three marks, one strike and two spares, and the latter game seven marks, five strikes and two spares. Another obvious point follows. Your score is not determined so much by the number of pins knocked but instead by the manner in which they are knocked down.

Using the ratio of game score to pins recorded, I have created a statistic I call "pin efficiency". It refers to the number of points received per pin recorded. It's minimum and maximum values are 1.0 and 2.5 respectively. In a game with zero marks, the game score will be identical to the number of pins recorded, so the ratio is equal to 1. In a perfect game, 300 points are derived from 120 pins, so the ratio is 2.5 (300/120=2.5). The histogram below shows the distribution of pin efficiency for our 60 games on record.

The take home message of this graph is that we are bad bowlers, no big surprise there. We average approximately 97 pins per game and approximately 1.4 points per pin recorded, thus our pathetic team average. We have gone as low as 1.08 points per pin in a single game with two marks and as high as 2.01 in a game with 7 marks. Interestingly, we have two games with 9 marks on record, and these equate to pin efficiencies of 1.68 and 1.69 respectively. So what is the key to increasing pin efficiency? Here is the game with the highest recorded pin efficiency to date.

Please disregard the fact that I totally choked at the end of this game. What is important are the pin totals by frame in the last row. These are not the total number of pins but the score received for that frame. For frames 2-7, a score of at least 20 was received for achieving a mark, or knocking down ten pins (pin efficiency≥2.0). This can be done two ways, following a spare with a strike or following a strike with any mark. Either way, you need strikes. Putting up a game of all spares, even 9-spares, won't get you to a pin efficiency above 2.0, but it will get you close. If you want to reach a score of 200, you will likely need a pin efficiency of 2.0 or above.

One more graph, and then I'll end this pointless blather. It should be no surprise that the best single predictor of pin efficiency is the number of strikes in a game:
But there are other factors that are important, too, like timing. Stringing together strikes will make pin efficiency skyrocket. This is not easy to do when you are a bad bowler, but if we ever want to consistently bowl 200 games and get our pin efficiencies in its upper ranges (>1.75), we need to throw more strikes and take advantage of spares. That was a long a convoluted way to get to a really simple and obvious conclusion, so please forgive me. I like numbers.

Friday, January 2, 2009

Advanced Bowling Tips

Are you struggling to elevate your bowling game? Have you been stuck on a 175 average for years, desperately trying to get to 180 or the promised land of 200? Here are a few things that might help you to get there. If you have yet to breach the 150 mark, these pointers may not work for you. You should try more basic approaches to improving your game, like double-socking your rental shoes. This will minimize transfer of bodily humours from the unsanitary feet of less hygienic lane denizens to yours. Also, you might want to consider bowling with two hands instead of one, or kicking the ball instead of rolling it. If you are an advanced bowler, read on. These tips have elevated our scores, and are guaranteed to do the same for you.

1. Avoid gutters
If you have been bowling for a few years, you have likely noticed that paralleling the hardwood lanes on both sides are two long troughs with shallow u-shaped cross sections. These features are typically 10 fathoms in length and about 120,000 microns in depth. They are known as “gutters”. If your ball rolls too far to the right or left, it has a high probability of falling into one of the gutters. Once in a gutter, it usually does not come out, and it continues its journey along the margin of the lane. If this happens, you will not hit any pins. If you do not hit any pins, you will not receive any points for that throw. This is why it is a really good idea to avoid the gutters. The best way to avoid the gutters is to not throw your ball into a gutter. Try to aim more toward the middle.

2. Hit more pins
Since the invention of the computer, many bowling alleys have used this amazing innovation of the modern era to calculate bowling scores. Accordingly, most people do not know how to score a game of bowling and do not understand how ball rolling translates to a bowling score. If you are like most people, you think that bowling elves live inside the bowling computer and score your game. The reason why this belief is so widely held is because it is true. What you probably did not know is that not all bowling elves score games. There are three types of elves in the bowling computer: accounting elves, cookie elves, and beer elves. The accounting elves use an abacus to add up your score. Cookie elves make cookies to feed the accounting elves, and beer elves drink elf beer. In order to understand how accounting elves do their magic, you have to understand the most important rule of bowling scoring:
if you knock down a lot of pins, you are going to get a lot of points. The scoring of strikes and spares is far too complicated to explain herein, and if you have no background in advanced mathematics, just leave this to the elves. But with this new understanding of bowling scores, you should be ready to improve your average. A good way to knock down more pins is to try to roll your bowling ball closer to the center of the pins because there are more pins there.

3. Correct grip on the ball
Most advanced league bowlers know how confusing bowling balls can be. It is unfortunate that the most basic equipment of bowling, the ball, is so complex. One simple way to improve your average is to use a correct grip on the bowling ball. We have tried to simplify the process for you here. A bowling ball is a spherical ball comprised of bowling ball material. Bowling ball material was first invented by NASA for the balls used in the International Space Station’s Bulgarian Bowling Alley Module BA643. Before the use of bowling ball material in the 1990’s, bowling balls were made of ground oysters shells compressed at high pressures into spheres. If you think that is confusing, then you know how confusing the holes in the bowling ball can be. On the surface of the ball, there are three holes that make a triangle shape. The first time everyone looks at a bowling ball they have the following thought, “If I have five fingers, why are there only three holes?” (People with polydactyly are prone to even more complex thoughts.) When you finally figure out that only three fingers are to be put inside of the bowling ball, you then think, “But which fingers should I stick in there?” Because there are three holes and you have five fingers, it turns out that there are actually 60 different ways that you can stick your fingers into bowling ball holes. Thus, all the confusion. This is why you often see amateur bowlers with crossed fingers while bowling. The prolonged use of an incorrect grip can lead to tendonitis and arthitis over the long term, so it is paramount to develop good gripping habits early in your bowling career. Correcting your bowling grip is not difficult, and we have included a simple diagram below that explains the process. On most bowling balls, there is a big hole and two small holes. The big hole is for your thumb. If all of the holes on your ball are the same size, find the hole that is farthest away from any other hole. This is the thumb hole. Put your thumb in it. Now rotate the ball such that the two remaining holes are above your thumb. If you are right-handed, put your middle finger in the left hole and the ring finger in the right hole. If you’re a south paw, do the opposite. You did it. Congratulations. You now grip the ball like a PBA pro!

Follow these simple tips, and watch your average grow. (A free pointer: Print these tips and bring them to the alley with you. You can even post them on your the bulletin board at your local bowling alley to share with your friends.)

Thursday, January 1, 2009

Googling "Bowl Movements"

In my incessant quest to bring the BM Report to the top of blogosphere rankings, I do a bit of googling. The best way to find this humble blog is to google "BM Report" with quotation marks. We currently rank 6th in this search. Another way you might think to find us is through our team name, "Bowl Movements", a gem of name devised by JD. It was barely chosen over our second choice, the "Michael Bowltons". It turns out that neither of these names are unique, but if you are so unfortunate as to google our team name, these are the results you will receive:

1. Stool-Healthy and Unhealthy Stool
2. Green Bowl Movements- Gastroenterology - MedHelp
3. Do I have Irritable Bowel Syndrome? -
4. The Bowl Truth|Natural Health|Finding Articles at BNET
5. Very Painful Bowl Movements--Doctors Lounge (TM)
6. Ask an Expert: No bowl movements
7a. Stomach is always tight and irregular bowl movements ocur...
7b. weird object in my bowl movements
8. TeenHealthFX - Answers - Irregular Bowl Movements
9. All Excessive Bowl Movement messages

Perhaps it is unfortunate that we chose a suitably scatological name for our bowling team. Where do we rank among people with bad spelling who are in search for advice on their discolored, misshapen, too frequent, too infrequent, or foreign object-laden craps? I was surprised to discover that we currently occur as the first listing on page 14 (#131).

I understand that what is excreted from the posterior terminus of your gut is a personal matter and one that can be quite embarrassing. I can sympathize with your web searching for people like you who produce 20-40 #2's a day, have BM's that have massive girth, or a worm-like morphology, and even those of you who wonder how nails, toy cars, and coins end up in your fecal matter. I can see why you might be searching for this on the web rather than talking to your doctor. You could always ask that creepy doctor guy on Oprah. Here is a little bit of advice if you didn't find what you were looking for by the time you reached page 14 of your Google search and landed on this blog.

1. The word you meant to type was "bowel" not "bowl". A bowl is a receptacle for cheerios and soup. It is also a verb pertaining to the act of rolling a ball toward pins. It can also be a receptacle for bowel movements, as in "toilet bowl". You may have better luck if you improve your spelling.

2. If you are crapping foreign objects, it is because you are eating foreign objects. THERE IS NO OTHER WAY FOR THEM TO GET IN THERE. Well, maybe there is one other way. Either way, you should stop doing those things.

3. If you have serious concerns about your G.I. health, stop googling and TALK TO A DOCTOR.

4. If by some strange cosmic coincidence, you were looking for the best bowling team in the world, welcome. I'm sorry you had to wade through so much crap to find us.

Team Stats: The First Five Weeks

Due to holiday travels, we have not bowled in league for sixteen days. My wrist is getting limp, and my ball is itching for some lane grease, like a junkie with a jones. In four days, we return to Bernaski competition. It will be interesting to see if how the hiatus has affected our game. In the meantime, I thought it would be worthwhile to summarize our performance over the first five weeks of the BIA (Bowling Information Age).

It should be no surprise that John leads the team in average over this time period. Over 12 games, he has averaged a fat 153.9 pins, slightly over his average of 149 coming into this period. What may be surprising is that Todd is not far behind with 152.3 pins, approximately 15 pins over his average. It seems that adoption of the spin is paying dividends, as the Green Lady has been a pin killer. The division between the haves and have nots is quite clear, the latter being Geoff with 134.2 pins, and Joe with 133.9. As has been thoroughly documented, Joe has been struggling, but Geoff's average has generally crept upward. His official league average is likely to crest the 130 mark in short order.

Consistency is measured as the standard deviation of game scores. Here's how to interpret standard deviation: roughly 2/3 of scores fall within one standard deviation of the average. The lower the standard deviation, the more consistent a bowler's scores. We all have very similar levels of consistency, shown as the error bars in the graph below. To date, Todd leads with a standard deviation of 18.5 pins, meaning that I have had relatively consistently high scores. Joe is 2nd on the team with 21.8 pins. While consistency is a good thing, for our cleanup man, this means that not only has Joe's average been low lately, but also that his game scores have been consistently low. John ranks third in this category 22.5 pins, and Geoff is last with 23.1 pins, likely attributable to this being his first season on the tour.
John has averaged a stellar 6.9 marks per game followed by Todd with 5.9. Geoff is marking slightly more than half of his frames with 5.1 per game, and Joe rides the caboose with 4.9.

Todd leads in strikes per game with 3.13, but John is only slightly behind at 3.07 per game. Joe's first toss has brought him an average of 2.4 strikes per game, while Geoff records on average 2.0 strikes per 10 frames. It is tempting to postulate that this can be attributed to throwing a straight ball, but at this point it is little more than speculation.

John is the team leader in spares with 3.9 per game, but perhaps surprisingly Geoff is second with 3.1. It should be noted, however, that because Geoff throws the fewest strikes, he also has the most opportunities to pick up spares. Todd and Joe are last in this category with 2.8 and 2.5 spares per game, respectively.

Pickup Percentage
John heard the call for a 50% pickup percentage and quickly pulled his average above 50. He currently stands at 52.3% of spare chances converted. He dominates in this category with Todd at a distant 2nd with 40.0%. Geoff's relatively high spare mark can be in part attributed a 38.2% pickup rate, and Joe finds himself in the basement once again at 31.9%.

Strike:Spare Ratio
Obviously, strikes bring higher scores than spares, and marks are better than open frames. The ratio of strikes to spares speaks in part to whether a bowler throws a better first or second ball. On the team, Todd leads this category with a ratio of 1.12, meaning that I have recorded more strikes than spares over the first five weeks. Joe is second a ratio of 0.97. John comes in third at 0.79, a relatively low mark, which can be attributed to his uncanny ability to convert spares in comparison to the rest of us. Geoff is last at 0.64. He throws relatively few strikes but picks up a fair number of spares.

Single Pin Conversion %
There are few things more frustrating than looking at a single pin at the end of the lanes and throwing an air ball. Two things may be worse... missing a putt from inside 3 feet and hauling in a fish to the edge of the lake only to have it flop off. John has been converting single pin spares at a respectable 57.1% clip, speaking to the accuracy of his 2nd throw. Joe is 2nd in this category at 48.5%. Geoff comes in third at 44.4%, and Todd is easily the worst, converting only 34.5% of single pin chances.

A few more thoughts
It is difficult to know to what extent these data are representative of our respective strengths and weaknesses. My hunch is that much more data (say 10 weeks worth) is needed to truly gauge where we stand on many of these stats. There are a couple of anecdotal observations that suggest that these numbers will change dramatically. Since we began recording these data, Todd has had something of a fluorescence, Joe has struggled, and Geoff and John have shown slow improvement. Given our largely undocumented history, I expect to see Joe making a move upward, and Todd slipping a bit, but only time will tell.

As for the big questions on everyone's minds... are we improving as a team, and does beer consumption positively or negatively or not at all affect scores, we will probably have to wait another five weeks to accumulate the data to definitively answer these pressing issues. Stay tuned...