## Sunday, April 21, 2013

### Pythagorean good luck associated with Runs Created bad luck

I noticed recently that there's a negative correlation between certain measures that we think are random and independent.  For instance, outshooting Pythagoras tends to be associated with undershooting Runs Created.  I don't know why, and I'm looking for ideas.

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Let me give you some background to what luck numbers I'm doing here.

Back in 2005, I did a study to estimate real teams' historical talent levels from their stats.  I figured that there were five mutually exclusive ways a team could perform differently from its talent:

1.  Its batters could have lucky or unlucky years, in terms of raw batting line.

2.  Its pitchers could have lucky or unlucky years, in terms of the opposition's raw batting line.

3.  It could create more or fewer runs than expected from its batting line (runs created).

4.  Its opponents could create more or fewer runs than expected from their batting line (runs created).

5.  It could over- or undershoot its Pythagorean projection.

The last three were easy -- I just compared them to their estimates.  The first two were harder.  How can you tell whether a player is having a career year?  What I did, for that, is I took the weighted average of the four surrounding seasons, and regressed that to the mean.  The results for players came out fairly reasonable.

The results for teams came out reasonable too, IMO.  The luckiest team from 1960-2001 was the 2001 Mariners (who the study said "should have" won 89 games instead of 116), and the unluckiest was the 1962 Mets ("should have" won 61 instead of 40).

[If you want more details, see my web page (search for "1994 Expos").  You can actually download the spreadsheet there that I'm using.  Also, I wrote up the findings for SABR's "Baseball Research Journal," and I found a repost here (.pdf).]

The "career year" estimates for teams seemed pretty good.  I had tweaked the formulas to make them close to unbiased.  For 1973 to 2001 -- the subset of seasons I'm using for this, less strike years -- the mean batting luck was +1.8 runs, and the mean pitching luck was -0.1 runs.

So, I was pretty happy with the overall results.

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OK, so ... while I was working with the data yesterday, I noticed some correlations I didn't expect.

First: it turns out there's a strong correlation between "Pythagoras luck" and "career year luck" (batting plus pitching).  That correlation is negative 0.1.  Why would that happen?

The only theory I can think of -- when a team plays well, it wins a lot of games.  That means it plays fewer ninth innings on offense, and more ninth innings on defense.  That artificially makes it look lucky in Pythagoras (which is based on run differential).

But that should create a *positive* correlation with player performance luck, not negative!

Pythagoras luck had an SD of around 40 runs per season.  Career year luck was around 65.  So, every four extra Pythagoras wins is related to around negative 6 runs of "career year" effect.  Not a whole lot, but I still don't know what's going on.

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And, worse: there's a strong correlation between "Pythagoras luck" and "Runs Created luck".  This time, negative 0.15.

So: for every win by which a team beats its Pythagoras, it's given up one-tenth of a win in Runs Created luck.  How would that happen?  The only thing I can think of is walkoff wins with runners on base: every one of those might lead RC to believe you were unlucky by ... what, half a run?  So that's not really enough.

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Finally ... there's a huge correlation (minus 0.2) between "career year luck" and "pythagoras + RC luck".  For every four wins a team gained due to Pythagoras/RC luck, they lost one back to player underperformance.

For that, I have a hypothesis.  Runs Created is known for overestimating the best offenses.  So, when a team beats its RC estimate, it's less likely to be having a great year.  That means its batters are more likely to be underperforming.

Here's something to support that idea: when I checked, I found almost all the correlation comes from comparing batting career years with batting RC luck, and from comparing pitching career years with pitching RC luck.  Comparing pitching to batting gives almost zero correlations.

I'm not sure if that explanation is enough to explain the -0.2, but it's something.

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So what's going on?  Shouldn't clutch hitting (which is what RC luck is) be uncorrelated with, say, scoring runs when you need them the most (which is what Pythagoras luck is)?  Shouldn't whether you get a few extra hits one season (which is career year luck) be uncorrelated with *when* those hits happen (which is RC luck)?

Why are these things associated?  It must be something about the way I'm measuring them, as opposed to, being lucky one way causes you to be lucky another way.  Right?

Any ideas?

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At Sunday, April 21, 2013 4:09:00 PM,  David Pinto said...

Those correlations seem rather small. Couldn't a few outlier seasons in what basically are uncorrelated measures produce a result in the opposite direction?

At Sunday, April 21, 2013 4:13:00 PM,  Phil Birnbaum said...

Hmmm ... there are around 700 teams in the spreadsheet. A correlation of 0.1 is significant at about the 99% level. 0.2 is probably beyond coincidence ...

At Sunday, April 21, 2013 4:29:00 PM,  Alex said...

Similar to David's question, is .2 'huge' in baseball? I don't doubt the correlations are all highly significant since you have 700 observations, but I don't think psychologists would call .2 huge, and we have kind of low standards.

At Sunday, April 21, 2013 4:32:00 PM,  Phil Birnbaum said...

Well, given that we claim to think it's all luck, 0.2 is unexpectedly large. It's like if you flipped a nickel and a dime, and there was a correlation of 0.2 between them when you were expecting zero.

At Sunday, January 31, 2016 6:59:00 AM,  Unknown said...

Pythagorus "luck" is about when a run scores; what matters is the inning and the run differential at the time. Timely superb relief pitching nearly always improves the Pythagorean ratio for the team, but only the mid-inning changes effect the runs-to-hits ratio. Since timely can also mean not "wasting" the best pitchers when your team is being blown out, the best mid-inning relievers may/should likewise be leveraged. This will lead to extra runs scored during the high scoring games and less runs during the close games. Pythagorean ratio improves, but the runs-to-hits ratio gets worse.

On the offensive side. On-run strategies risk multiple run innings for a better chance to score the next run. Most of the time this leads to less runs overall for the team yet impacting the Runs Created estimate very little. Ergo, runs scored goes down by more than the RC estimate. But if the manager is using the run run strategies at the right moments of close games, the team winning percentage actually goes up, so wins per run improves.

Neither of the effects I describe can be more than a few percentages points in size, but the direction of the changes will be the same from team to team so that in a 700 team sample they should turn up with a high significance.

At Sunday, January 31, 2016 8:51:00 AM,  bob sawyer said...

Pythagorean luck depends upon how runs are clustered--i.e. in which specific games set amounts of runs are scored and allowed. Pitching changes and one-run strategies are efforts to change the standard distribution to a more favorable one. There is a paper on this posted on retrosheet.org "plawying for the Next run"
To summarize. Some tactics increase win probability while decreasing total expected runs scored. When utilized successfully, actual runs scored go down (a loss of RC efficiency) but wins per run scored increases (gain in Pythagorean efficiency) This is the inverse effect that was found.
Pitching substitution may maximize leverage. If a team is behind or way ahead and chooses not to use a better pitcher to stem a rally, then more runs get scored in big innings-- More actual runs per hit allow, ed due to greater clustering. Defensive efficiency suffer but the better reliever can pitch in a high leverage situation in a subsequent game. That improves Pythagorean efficiency. Again this is the reverse relationship that was found.
The size of these effect cannot be very large, but are the same direction for most teams.

At Sunday, January 31, 2016 9:08:00 AM,  Unknown said...

Dear Phil,

I am a SABR analytics committee member. I am working on an article about luck and the birnbaum algorithms that is highly critical of your earlier work, especially "Why teams do not repeat"
the gist of the criticisms is that that (a) the coin flip model of a major league season is inappropriate--playing a major league season is more like playing the card game of War in which the resources available vary from draw to draw (B) the coin flip model caused analysts to attribute too much result variation to luck (C) The six game expectation may have caused you to dismiss as unimportant the fact that leagues do not show ZERO net batting luck (d) this error in the formula led to Chriss Jaffe finding too much luck from the best offenses.
I am seeking access to actual database (at least for certain players or teams, and also need to correspond with you to make sure that my interpretation of your work in "Why Teams do not repeat" is not wildly incorrect. robert sawyer Baseballnut570@hotmail.com