Comments on: All About Managers

By: Ryan M

Ryan M — Tue, 22 Sep 2009 04:39:27 +0000

I think you’re being kinda pedantic with what constitutes a power law. The classic example of a power (pareto) distribution is income distribution, and its mode is only the lowest value when you’re using and interval of something like $0-$25,000/year. This data could easily follow that as well (and probably does, but I’m not going to recreate that data set by eyeing the graph) using an interval of 0-3 years. The sample is too small to see this either way.

The author’s more general point (whether he knows it or not) is the application of a long tailed distribution to the data, which is definitely right.

I actually think such distributions are greatly underutilized in sabermetrics. I’d go as far as saying that a majority of distributions are really a long tailed/craziness extreme values rather than normalish/well ordered patterns. Like player development- situations like a Ben Zobrist this year or Carlos Pena three years ago or a Cliff Lee last year or Mark Loretta several years ago happen waaaaayy too often to be accurately captured otherwise.

By: Brian Burke

Brian Burke — Mon, 21 Sep 2009 20:24:59 +0000

“threw” not “through”

Ug–It’s a Monday after a late Sunday night game.

By: TanGeng

TanGeng — Mon, 21 Sep 2009 17:10:12 +0000

Looks like a poisson distribution. Ahh some one already mentioned gamma distribution.

Also applying context to winning percentage might help. Comparing managers against historical winning percentage or winning percentages around the time of tenure might give a more meaningful conclusion, or it might not at all.

By: Brian Burke

Brian Burke — Mon, 21 Sep 2009 16:16:30 +0000

Thanks for the kind words. If you through out the 1-2 yr guys, which may be mostly interim managers or other special-circumstance managers, the distribution from 3+ yrs on looks like it’s very power-law. It’s bit of a stretch, I know.

I’d bet All-Star game appearances are power-law distributions. Team playoff or World Series appearances/victories are probably power-law too. The reason is that MLB baseball team strength is a rich-get-richer system like college football. The revenue and prestige that comes from success begets more success. See “Yankees, New York.”

By: Joe R

Joe R — Mon, 21 Sep 2009 15:34:57 +0000

Would that really affect the linear relationship (or lack thereof) in the 2nd chart, though?

By: David A

David A — Mon, 21 Sep 2009 15:30:04 +0000

I was going to say it looks like a lognormal distribution, but gamma probably fits even better. We use these in insurance to model the expected payout on claims. Much like high-value claims, this data suggests that managers with long tenures are rare. Though in both cases, they tend to skew our expectations.

By: Matthew Nolan

Matthew Nolan — Mon, 21 Sep 2009 13:11:46 +0000

Just to clarify why it is close, a gamma distribution with k = 1 is just an exponential (power) distribution with mean theta

By: Matthew Nolan

Matthew Nolan — Mon, 21 Sep 2009 12:57:03 +0000

You’ve drawn an incorrect conclusion about the managers tenure, although it is not that far off of being correct.

You are predicting it is a power distribution when it is obviously not, as the mode is not the lowest value, the mode is 3 and you are ignoring this, as well as the obviously low value at 1 and 2.

This follows a gamma distribution with the argument to the gamma function (k) being 3 and theta being 1.5. This would predict a distribution of the correct shape with mean 4.5 and mode 3