Friday, July 24, 2009

A hot hand effect in bowling?


This post was inspired by something I read on the blog The Hot Hand in Sports, which is maintained by Dr. Alan Reifman of Texas Tech University. The basic idea of having a “hot hand” is that athletes are commonly perceived to be streaky. They go through phases during which their batting average or field goal percentage is very high followed by periods when it is very low. Of course, even if skill remains absolutely constant, such streaks, good or bad, can occur by chance. So, are these hot streaks and slumps real, or are they the product of the inevitable role of chance? If you are interested, you should check out his blog. It’s very interesting.

With respect to bowling, this made me ponder the following question. Do prior outcomes affect future outcomes? Specifically, I was wondering if bowling a strike makes us more likely to bowl a strike on the next frame. There is reason to believe it might. I am constantly adjusting my throw and approach depending upon prior outcomes. Generally speaking, if I get a strike, on the next frame, I will try to replicate exactly what I just did. Also, the muscle memory of the prior throw should be fresh. So, it might be expected that a strike is more likely to follow a strike than a prior non-strike first ball. That said, if I don’t get a strike, I adjust my next throw accordingly to try to get one. I assume we all do this to some extent. So, maybe it all balances out. Maybe a strike is equally likely to follow a strike as opposed to any other first ball.

Before you get into the analysis below, I should forewarn you that it’s a little dense. Sorry.

To answer this question, I looked at all 252 games in our database, specifically the first ball outcomes for paired frames (n=2436). For a given bowler, I looked only at frames in which a strike was recorded, and I determined the number of strikes that follow strikes versus the number of strikes that follow non-strike first balls. It should be no surprise that strikes far more commonly follow non-strikes. In our database, we have 456 strikes that follow non-strikes, and only 150 strikes that follow strikes. This alone does not answer the question because we only strike about one out of four of frames as a team, and therefore, we have a lot more opportunities to follow a non-strike with a strike. The question is whether a strike makes the next frame more or less likely to be a strike. In short, when we roll a strike, in 24.8% of cases, we follow this with a strike. When we don’t roll a strike on the first ball, we receive strikes on 24.9% of frames. Strikes appear to be equally common no matter what happened in the prior frame.


To explore this a bit further, I decided to examine the average first ball score on subsequent frames given the outcome of the first ball on the prior frame. Again, there is no evidence for hot hand effects. We average between 7.5 and 8.5 pins on the first ball no matter what happened in the prior frame. If anything, there might be a weak “reverse” hot hand effect, meaning that we do slightly better if we bowl poorly in the prior frame.


What does this mean? It means that we likely do not go through hot and cold phases in bowling in a given night. I’m guessing that your intuition probably disagrees with this, but intuitions are not always good judges of reality. It is very easy to see a “cold streak” if simply by chance you have many unlucky outcomes in a row. Likewise, getting a turkey may seem like you are really “feeling it”, when in fact it should happen from time to time simply due to chance. When you look only at strikes, there is basically no evidence of “hot hands,” that getting a strike does not make a strike on the next frame more likely.

Think of it like rolling dice. There is 1/6 chance that you will roll a one on any given throw. So, occasionally, you will roll five one’s in a row (On average, you’ll have to roll the dice almost 8,000 times for this to happen) This did not happen because you were on a “hot streak,” or because you were very skilled at rolling dice for five throws. It happened because of luck. Now simply substitute bowling strikes in the above analogy. Differences in skill will cause some bowlers to roll more strikes than others which in effect changes the basic probability of a strike, but over a given night of bowling, it really looks like those probabilities don’t change much.

It would be interesting to do this analysis for individual bowlers rather than for the team as a whole, but as always it would require a lot more data. My hunch is that hot and cold streaks may affect some bowlers more than others.

2 comments:

  1. Thanks for mentioning the Hot Hand website and for leaving a comment there. You should read the following article, which is available at Gary Smith's website:

    Bowlers’ Hot Hands. Reid Dorsey-Palmateer and Gary Smith. The American Statistician, 58, 2004, 38-45.

    http://www.economics.pomona.edu/GarySmith/frames/GaryFrameset.html

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  2. Thanks Alan,

    A very interesting read. You have now given me more work to do. I wonder if the same patterns hold true for amateur bowlers. Of course, we have very few opportunities to go for a 5th strike in a row, but it could easily be tested for two or three.

    -Todd Surovell

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