Volleyball and Math

Last night as my wife and I watched the Olympics we were treated to the 4th set of a best of 5 men’s volleyball series between Brazil and the United States. While the game was good (US won by the way), I was particularly struck by a series of events that happened while the US went on a 7 point run. Now 7 point runs are rare at this level of competition especially against the gold medal favorites (Brazil came into the Olympics as the number one ranked men’s team and the US 5th).

What makes those runs so hard is that the games are pretty close, the competitors fairly evenly matched and most importantly, there aren’t that many points to be scored at all! If you look at the final scores and do a simple average of the four sets you will see that the US scored 100 points and Brazil 86 leaving us with a chance of 53.76% chance of the US scoring on any given serve. Each set ends at 25 points and with a little statistical magic we see that the chance of the US having a 7 point run is a little higher than 4.6%. Note that the chance of an 8 point run is a touch about 2.2%. See a pattern yet?

So that is all interesting I suppose, but why am I doing this little math exercise? Well, because of what the coach did during a timeout. He pulled his team in and yelled at them; not a big surprise I suppose at this level of competition and stress levels, but I’m interested in what he thought he got out of it. You see he probably felt pretty good about his negative feedback after they broke the American’s streak…the problem of course is that they were likely to break the streak no matter what. The chance of a 9 point run drops all the way to 1%.

So they were pretty much going to score no matter what during this run as the odds of them finishing up the 25 points starting at 10 with no points by Brazil were very low .02% as a matter of fact. (For you math geeks I used an estimation process for the calculations and you can e-mail me for details or corrections.)

This effect is called regression to the mean. Basically when you do really well at something you are likely to be closer to average the next time you do it. This is an important concept in business as we tend to do things expecting a certain outcome and then repeat it over and over again expecting the change to be permanent. This can be true…but not always!

This occurs both for rewards and punishments so when you make decisions about how to manage your business watch carefully for this effect. This isn’t meant to make you give up on controlling your business; in fact it is the exact opposite of that. I’m not suggesting for one second that we can’t influence future outcomes, just that we need to be watching the average, not the event. If the volleyball coach thought that his yelling changed the next point he missed the boat. That would mean that the team works best with stress and fear…so he should just keep that behavior up over the long run and see how things turn out!

The message for us is to take a long term vision and carefully track our behavior and the resulting effects and how the averages/maximums/minimums change. Hey wait a minute, that sounds like business intelligence! I knew I had a point in here someplace.

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