Sunday, October 18, 2009

Regression to the Mean

In statistics, there is a concept known as "regression to the mean". It refers to extreme values. Essentially, if you have an observation that is really unusual, it will typically be followed by an observation closer to average. Why? Well, really unusual things don't happen very often and only very rarely do they occur back to back. So, if you bowl really well one week, let's say you have your best day of bowling ever, chances are that next week, you won't bowl as well. The same can be said for bowling poorly. If you have your worst day of bowling, the next time you go out, there is a very good chance you will bowl better. These ups and downs don't have much to do with skill. They are more about random factors that affect any system, bowling included.

I don't know if anybody has ever noticed it, but on this blog, I keep a team time series. It's on the right side toward the bottom. This little squiggly graph shows the total number of pins we recorded as a team by date. It is an excellent example of regression to the mean. If you look at the peaks, the days that we bowled really well, they are always followed by a day when we didn't bowl as well. Likewise, the dips, those days we'd rather forget, are always followed by a better day of rolling.

We started the season with one of our best days of bowling ever. Not surprisingly, the next time we went out, we didn't bowl as well. What is interesting, though, is that since that first day, our scores as a team have dropped. For four consecutive weeks, they have dropped, and yesterday during our makeup bowling session, they dropped precipitously. In fact, it was our worst day of bowling ever. We beat our old record low series of 1,629 from March 30 by 38 pins.

How bad was it? As a team we were 222 pins under our average, or 18.5 pins subaverage per bowler per game. For the first time ever, we had more open frames than marks (66 vs. 56), and our average score for all 12 games was a paltry 132. JD took almost every category on the leader board, getting a respectable 155 average, but the rest of us just sucked.

I'm not going to make excuses, but one factor really did not help: splits. I haven't been tracking split statistics for very long. We have stats for 26 weeks of bowling, but for only 16 of those have I been tracking splits. Over that time period, we have had as few as 5 splits as a team and as many as 16. We average just under 10 per night. Yesterday, we had 20! When a split occurs, obviously it means that you probably aren't going to pick up the spare. I haven't checked our stats on this, but my hunch is that we pick up splits about 15% of the time. Yesterday, we picked up 2 of 20. One was a 3-10, and the other a 2-7. We had two or three 7-10's.


I'm not going to dwell on how badly we bowled. I could point out another 20 stats that would suggest that we can't blame it on bad pin falls. What I will say is that we can be thankful for regression to the mean because on Monday, we will bowl better. We will bowl considerably better, and finally that time series will start moving in the other direction.

5 comments:

  1. I need a chart that will tell me I'm going to bowl better on Tuesday... :)

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  2. Well, if you really want to guarantee it, you should go out tomorrow and chuck 30 balls in the gutter...

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  3. I don't know that intentionally sucking will help my chances; however, the fact that I even considered this advice makes me wonder which one of us is saner...

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  4. Well I am looking forward to the shift in better bowling tonight. I am certainly not a very good bowler but flirting with the "fighting 88s" ever game is rare, even for me - I can't remember even doing this last year and I had my share of shitatcular games! On the bright side - I didn't think my average would adjust so quickly, the high handy is back.

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  5. That goes for you and me both. Our averages have come down nicely. It might be just what the doctored ordered to get us back on the winning side of things.

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