THE BOOK--Playing The Percentages In Baseball

I’m not surprised at all that Pythport/pat have essentially equal accuracy for actual teams.  The way I “found” the exponent was to try to find a function that matched Davenport’s results in the normal RPG range but also would give an exponent of 1 @ 1 RPG.  So there was never any claim or expectation on my part that there would be any accuracy gain for normal teams.

I found a little bug, and have updated the main entry.  Now, it’s Patriot that “wins” 40-39, with all those ties.

No biggie really.

If I use .289 instead of .287, the Pat289 beats Pat287 36-31 (and those 1700+ ties).

Clay against Pat289 is now 53-47 in favor of Pat.

Comparing Clay against Pat289, with RPG under 8, Clay is 21-17, and at 8+ RPG, Pat is 36-26.

Pat287 v Pat289: at 8+ RPG, Pat289 wins 34-23.  But at under 7, Pat287 is the one that wins 8-2.

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With a straight divide by 10, compared to Pat289 shows that Pat wins 607-385, with 800 ties.  That gives Pat a .562 win%.

Pat and Clay are extremely similar, virtually identical, and world’s apart from simple metrics.

Using the Pythagenport formula, we can find out teams that have been lucky and unlucky, by comparing their actual wins to expected wins based on Pythagenport.

We’ve had this discussion in other threads, but I still say that you can’t design a metric whose standard of accuracy is to get as close as possible to the ACTUAL runs scored and then claim that any residual between that metric and actual runs scored is due to how lucky the teams were.  The residual represents ALL factors that weren’t included in the metric; i.e. the failure of the metric to model reality exactly 100% correctly.

Right in the middle of the pack is RPW=10.

I like that.

I came across the following win estimator in an academic article which I don’t think I’m supposed to link to. It claims to be the most accurate.

W% = Pythag - .03257sdrs + .0323sdra

where pythag is the usual equation with an exponent of 2, sdrs means the SD of RS, and sdra is the SD of RA.

Essentially, this adjusts pythag for the consistency of RS and RA.

I wonder if this approach could be combined with Pythegenpat instead of just using basic pythag.

If you wanted to look at SD’s, wouldn’t the Correlated Gaussian method (click name) be the most accurate, since it’s the most accurate for both basketball and football?

If a StD adjustment like the one David describes can work with Pyth x = 2, then I’m sure one could be devised that would work with a floating exponent.  The same equation would probably do ok, although who knows how it would behave at the extremes without testing.

Personally, I’m not big on StD adjustments, because if you do it, you have to know the team’s exact distribution of runs/runs allowed by game.  And once you have that, why not go all the way and base your estimated W% on the frequency of runs per game, rather than the average of runs/game with a correction?  Once you go down that road, you might as well use that data to its full potential, IMO.