## Thursday, May 25, 2017

### Pete Palmer on luck vs. skill

Pete Palmer has a new article on skill and luck in baseball, in which he crams a whole lot of results into five pages.

It's called "Calculating Skill and Luck in Major League Baseball," and appears in the new issue of SABR's "Baseball Research Journal."  It's downloadable only by SABR members at the moment, but will be made publicly available when the next issue comes out this fall.

For most of the results, Pete uses what I used to call the "Tango method," which I should call the "Palmer method," because I think Pete was actually the first to use it in the context of sabermetrics, in the 2005 book "Baseball Hacks."  (The mathematical method is very old; Wikipedia says it's the "Bienaymé formula," discovered in 1853. But its use in sabermetrics is recent, as far as I can tell.)

Anyway, to go through the method yet one more time ...

Pete found that the standard deviation (SD) of MLB season team wins, from 1981 to 1990, was 9.98. Mathematically, you can calculate that the expected SD of luck is 6.25 wins. Since a team's wins is the total of (a) its expected wins due to talent, and (b) deviation due to luck, the 1853 formula says

SD(actual)^2 = SD(talent)^2 + SD(luck)^2

Subbing in the numbers, we get

9.98 ^ 2 = SD(talent)^2 + 6.25^2

Which means SD(talent) = 7.78.

In terms of the variation in team wins for single seasons from 1981 to 1990, we can estimate that differences in skill were only slightly more important than differences in luck -- 7.8 games to 6.3 games.

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That 7.8 is actually the narrowest range of team talent for any decade. Team skill has been narrowing since the beginning of baseball, but seems to have widened a bit since 1990. Here's part of Pete's table:

ending   SD(talent)
-------------------
1880     9.93
1890    14.44
1900    14.72
1910    15.33
1920    13.06
1930    12.51
1940    13.66
1950    12.99
1960    11.95
1970    11.17
1980     9.75
1990     7.78
2000     8.46
2010     9.87
2016     8.91

Anyway, we've seen that many times, in various forms (although perhaps not by decade). But that's just the beginning of what Pete provides. I don't want to give away his entire article, but here some of the findings I hadn't seen before, at least not in this form:

1. For players who had at least 300 PA in a season, the spread in their batting average is roughly evenly caused by luck and skill.

2. Switching from BA to NOPS (normalized on-base plus slugging), skill now surpasses luck, by an SD of 20 points to 15.

3. For pitchers with 150 IP or more, luck and skill are again roughly even.

In the article, these are broken down by decade. There's other stuff too, including comparisons with the NBA and NFL (OK, that's not new, but still). Check it out if you can.

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OK, one thing that surprised me. Pete used simulations to estimate the true talent of teams, based on their W-L record. For instance, teams who win 95-97 games are, on average, 5.6 games lucky -- they're probably 90 or 91-win talents rather than 96.

That makes sense, and is consistent with other studies that tried to figure out the same thing. But Pete went one step further: he found actual teams that won 95-97 games, and checked how they did next year.

For the year in question, you'd expect them to have been 91 win teams. For the following year, you'd expect them to be *worse* than 91 wins, though. Because, team talent tends to revert to .500 over the medium term, unless you're a Yankee dynasty or something.

But ... for those teams, the difference was only six-tenths of a win. Instead of being 91 wins (90.8), they finished with an average of 90.2.

I would have thought the difference would have been more than 0.6 wins. And it's not just this group. For teams who finished between 58 and 103 wins, no group regressed more than 1.8 wins beyond their luck estimate.

I guess that makes sense, when you think about it. A 90-win team is really an 87-win talent. If they regress to 81-81 over the next five seasons, that's only about one win per year. It's my intuition that was off, and it took Pete's chart to make me see that.

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