Thursday, September 24, 2009

The Team Turkey

In the first game this week, as a team, we threw seven consecutive strikes beginning with Ebob in the 5th and ending with Gingy in the 6th. Johnebob and I pondered whether we had ever pulled this off before, so I thought I would check. It turns out that it was a new record for the Bowl Movements. Our prior high streak was a team 6-bagger, which occurred on March 16 earlier this year.

A few months ago, I looked at consecutive strikes for individuals in this post, and in thinking about this problem, I started wondering why it is that as a team, we have thrown seven straight X's, but individually, we have never thrown more than five.

It's an interesting problem because I would expect just the opposite, and here's why (reader should start dozing off now). The probability of throwing any number of consecutive strikes is the probability of a strike raised to that power. So, if an individual bowler has a 30% chance of getting a strike on any given frame, then the chance of a turkey (3 in a row) is 0.3 raised to the 3rd, or about 2.7%. We all vary with respect to the probability of getting a strike.

For Johnebob and me, it's around 30%. For Daniele it's 24%. For Gingy, 22%. Canadian, 16%. So, Johnny and I should be the most likely to get long streaks of strikes, and that is in fact what has happened. Johnny has bowled at least a turkey 13 times. I have done it 10 times. Daniele has done it 8 times. But for our team as a whole, the probability of getting a strike is less than for our best strike throwers. It's about 25%.

So, seven in a row should be much more likely for Johnebob than for the team. John's chances are around 1 in 4,500. For our team, it is closer to 1 in 16,384. This shows you how unusual our seven in a row really was. Above is the number of singles, doubles, turkeys, etc. for individuals and for the team. What is interesting, though not really surprising is that the two graphs mirror each other perfectly, at least for anything up to a turkey. Four in a row has occurred more often for individuals, but for anything beyond 5 in a row, we are better as a team.

Individually, we have achieved this feat once, when I got five in a row. As team we have hit at least five in a row on five occasions. So why is this? I think there are likely two explanations. One is chance. It is possible that these slight differences are not meaningful but simply reflect the ever present role of luck. The other possibility is that it is mental, but I'm not sure how. Do we put more pressure on ourselves when we are trying to keep our own streak alive, or is there more pressure when you feel like you are bowling for the team?'

UPDATE: Since I wrote this, I have figured out the right answer. You can find it here.

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