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.



Accuracy

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.

2 comments:

  1. The data and equation you provide is very interesting. But where does the 1.56 and the 18.72 get derived from?

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  2. Good question. The 1.56 is a weighting factor which gives strikes a greater weight than spares in calculating accuracy. In choosing how much to weight strikes, I basically kept changing the weighting factor until I maximized the strength of the correlation between accuracy and game score. It turns out that 1.56 did this. Another way to think about this is that a strike on average results in scores approximately 1.5 greater than a spare. The 18.72 standardizes the accuracy measure to 100%. 12 strikes multiplied by 1.56 gives a result of 18.72. Divide this by 18.72, and you get 100%.

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