Earlier this year, Brian Burke of the fantastic Advanced NFL Stats site wrote a post in which he detailed and graphed a series of scatter plots that featured the power law distribution. If you have absolutely no idea what that means, click that link; his explanation is superior to anything I can offer. Anyways, he went on to address the idea of whether coaching job spans were a normal distribution or a data set that followed the power law. He found the latter, and I’ve finally gotten around to seeing how baseball managers compare.

First, let me detail my data set. I went team-by-team and collected each manager holding a position that was hired between 1995 and 2005. This means if a manager was hired in 1995, fired in 1996, and a new manager was hired then both count. If a team went through a manager per season they are all included. However I did not include interim managers who managed less than a season. So Bruce Kimm is out of luck, as are managers hired prior to 1995 or after 2005 – sorry Bobby Cox and Joe Maddon.

I ended up with 76 managerial cases. I then took down their organization, length of tenure, and win/loss record with that organization. With such I found the amount of seasons survived with that team by each manager, which was then used to create this graph:

For those who prefer charts:

Years Managers
15 1
12 2
10 1
9 1
8 2
7 4
6 5
5 8
4 15
3 21
2 14
1 2

The data set follows the power rule much like Burke’s examples. There are other questions to be answered though, which I’ll attempt to do now:

How long does the average managerial job last?

The mean of the tenures is 4.3 years, the median is 4, and the range is 14 years. So the mean is skewed to the right, but only barely. This matches up pretty well with what we see above since nearly 66% of the population falls into the 2-4 years group.

How does winning affect the lifespan?

It doesn’t:

That steep red line represents the .500 mark. Some were well below and lasted five or more years, some were well above and received the axe far earlier. That means to last as a baseball manager, you have to juggle player attitudes and egos, get along with management and ownership, and show competence at winning a fair share too. Most people would note that anyways and the numbers back it up.

To summarize, I think all of this is rather intuitive. Most managerial contracts seem to last 2-4 years, which is the average lifespan, and we can’t evaluate mangers well enough to say there’s a huge difference between any two skippers, which means firing a guy is more of a “gut” feeling. If the manager is friendly enough to the media he can probably buy time even if he makes questionable in-game decisions.

I’m not claiming this is a perfect measure and most people will probably read this and think “Duh“, but hopefully it did something for someone.

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Matthew Nolan
14 years ago

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

Joe R
14 years ago