Saturday, October 3, 2009

Daniele and the Deuce

Last week, Daniele put up a 199 game. He missed the magic number by a single pin. If memory serves me correctly (since our records don't go back that far), he was the first person to roll a 200 game in league. Hell, I've seen him go into the 2-teens, just not in league. Yet, since that groundbreaking 200 game, he has failed to reach the promised land again. He went through a major slump in the 2nd half of last year. It was so bad that he couldn't even bring himself to read the Report. Well, he retooled with a Hammer Raw Acid, ditching his old sidekick, the Qubica house ball. He has come out this season showing marked improvement, now sitting on a once unthinkable 155 average.

He asked me to check how many times he has neared but not toppled the 200 mark. It was fewer than I expected. He has crested 190 three times. His three best games on record are 191, 193, and 199. For the 72 games we have on record, the mode of his game score distribution falls between 120 and 130. He is a better bowler than this, which really speaks to his struggles last year.
I decided to get out our old friend, the BM Simulator. This way, I could check how often he should be hitting 200 given his basic stats. This simulation works on two sets of probabilities, which are determined by past performance: 1) The likelihood of all possible first ball scores; 2) The likelihood of picking up a spare for a given first ball score. It is remarkably good at predicting actual outcomes. Below is a comparison of the predicted vs. actual game score distribution for JD.

The real benefit doing this is that it makes it really easy to estimate the likelihood of any possible outcome, such as a 200 game. I simulated 5000 games of JD bowling, and of these 44 were greater than or equal to 200. This means that given his performance over the last 24 weeks of bowling, he has approximately a 0.88% chance of rolling at least a 200 in each game. It should happen roughly once in every 113 games. He currently has 72 on record.

It is not very difficult to take this a bit further. For example, we can ask what is the probability that he should have a 200 in league over the last 72 games (other than the one not in our records)? It is approximately 47%. Furthermore, we can ask, what is the probability that he will have one by the end of this year? It's about 75%. All of this assumes that he doesn't show any improvement (or decline) in skill over this time. Now that he seems to be rolling the Hammer with a new found sense of confidence,I expect to see that average climb. So, as I like to fancy myself the Nostradamus of Numbers, I will predict a 200 game in his near future. I know what he will say to this:

Never tell me the odds. - Han Solo

Of course, this makes me an effeminate gold-plated human-cyborg relations robot, something my teammates think is not far from the truth.


  1. Hey, Todd-- I like your BM Simulator, and for most bowlers (pros, especially) past performance really is an indicator of future results/growth...except for a square peg in a round hole like me (this is why my stockholders should never sell). I have statisticized (numerically metasticized) my past performance looking for reliable signs of continuity, but there are just too many x-factors (like mood, focus, G-POMS, pace, proof, etc.) that make me the renowned bowling epileptic that I am on any given night. I should be (should, I said) a regular, consistent 500-520 series bowler, yet I haven't gotten to 500 and we've been at this now for 5 weeks. Next Tuesday, my goal is 550, but the stats (and the bookies) just chuckle.

  2. Hey E.B.,

    I hear you. I nearly rolled a 600 series three weeks ago. it was by far my best ever, but then last week, I only mustered a 444. Bowling scores seem to go up and down with the weather. The nice thing about this simulation, though, is that it predicts just that. My scores should fluctuate within a predictable range, and while skill does seem to be improving slowly over time, most of the signal over the short term can be attributed to chance.

    On the other hand, it is hard to accept that something that is just about 100% controlled by myself can be attributed to chance, but I can model the process that way and get a very good fit... whatever that means.

    I like the stock market analogy a lot. It is my impression that our week to week scores seem to show no trends (a lot of short term volatility), but over the long term, they slowly creep up. The improvement is so slow that it's almost imperceptible. I actually tried to look at this about six months ago with the limited data we had on hand. You can find it here if you are interested:



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