Thursday, May 14, 2015

Means, Variances, and Coaching.

Malcolm Gladwell writes that basketball teams with inferior talent should run full court presses. The full court press is a high risk defensive strategy: it raises the likelihood that a defensive team gets a steal and an easy basket, but it also raised the likelihood that the opponent will get an easy basket. It is a higher variance strategy than a standard defensive strategy.

Such a strategy makes sense for a team with little talent. Such a team wants to raise the variance of outcomes, because it is the only way it can win. If an inferior team pursues a variance minimizing strategy, it will always lose, because its mean outcomes are lower than those of superior teams.

The worst coach I ever saw in any sport was the football coach for the Wisconsin Badgers before Barry Alvarez, a man named Don Morton. He was a horrible recruiter, so the team's talent was poor. He also ran a minimum variance strategy: three rushes in a row (around 2 yards per rush) and then a punt. During his time at Wisconsin, the Badgers won three Big Ten games in three years.

On the other hand, superior teams should attempt to minimize variance in the game. It is why I am not sure Brett Favre was a net plus to his teams over the past few years--he probably added too much variance. Mike Holmgren was a genius at reducing Favre's variance. I think had he stayed with the Packers, the two of them would have won a couple of more Super Bowls.

A study I would like to do at some point is a determination as to whether Walter Payton was more valuable than Barry Sanders. Sanders yards per carry average was much high than Payton's, but he surely gained the yards with a lot more variance. Someone needs to measure the two variances and run simulations. Perhaps after I retire.

The ideal back would get 3.5 yards per carry with no variance: such a back would guarantee scores and burn clock, giving the defense an opportunity to rest.

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