UPDATED: Tweaking the Pythagorean Formula

the better thing to do is to take those 8outliers as given, and calculate the record based on the remaining 153 games the Astros played last season. You want to throw out the outliers so you can accurately eliminatethe “luck” (or whatever it is) from those “standard” games, but you don’t want to take away those games from the record.

if you did it for every team last year. Would it produce closer results to actual records overall…who knows? I don’t intend to take the time to do it…nor am I suggesting that you should spend your time on it. But maybe some enterprising blogger out there might pick up the idea.

An interesting point about the blow outs is that a manager’s action can have a significant effect on the ultimate run differential. Cooper was prone to leave starting pitchers in to take a beating, presumably in order to save the bullpen. That may or may not be good strategy, but it definitely affects the margins. A manager who decides to put a position player in to pitch in a blow out might have the same effect. Another manager (perhaps the manager of a high scoring team) might be less inclined to throw in the towel and will still bring in his better relief pitchers to try to keep the differential within striking distance. The Pythag implicitly assumes that the manager acts in some sort of “average” fashion in those blow outs. In any event, I put less confidence in drawing conclusions from blow outs which are dependent on managers’ predilections.

Impressive stuff, Andy. Well worth a Fan Post…this would make Joe Sheehan’s head spin…

Has taken some statistics courses at university.

I’m throwing this comment in here because it’s not obvious from the FanPost sidebar that anything changed

Arguably, your revision is an improvement, based on what you show for 2008—albeit perhaps a minor improvement.

On average your reconstructed pythag is slightly closer to actual results. The average difference between the standard pythag and the actual is 3.4. The average difference between the reconstructed pythag and the actual is 3.3. OK, it’s slight, but is an improvement.

Moreover, I am impressed by the number of times that the reconstructed pythag hit the actual record on the nose. The reconstructed pythag hit the actual record 5 times. The standard pythag hit the actual record zero times.

The standard pythag is better than the reconstructed pythag 13 times, and the reconstructed pythag is better than the actual pythag 13 times. (The remaining times, the difference is the same.) That’s a tie. But it certainly doesn’t support the idea that the standard pythag is better than your version.

My conclusion is that your revision has some merit and is recognizing something which is problematic in the standard pythag. Perhaps the exact way you have treated the issue is not the optimal solution, but maybe it points to an area of the pythag which can be improved. Based on what you have done, I am more convinced that there are some weaknesses to the standard pythag record as “predictor.”

let me preface my remarks by noting that I have a graduate degree in statistics, which makes me armed and dangerous. Read on at your own amusement.

From a purely mathematical point of view, the ONLY difference between any Pythagorean analyis and reality lies exclusively in the difference in the distribution of margins of victory assumed in the basic theorem and the actual distribution encountered in any real situation. To reconcile any real result with the base theorem would require analyzing the difference between each of the margins of victory (and their number of occurrences) in the real situation vs that assumed in the basic Pythagorean theorem.

The only problem in doing the reconciliation is that it is likely impossible to learn the the real distribution because (a) James’ original work encompasses a span of many years and (b) he refined the correlation between actual results and historical by tweaking the exponentials rather than by examining the real distributions underlying them.

Since the only variables considered are runs scored, there can’t be any other influences which need examination. Your first step of eliminating outliers (blowouts) is a logical one,but, in reality, the base theorem assumes a few outliers (but we will never know how many) in its distribution. To be exactly accurate, we would have to exclude all the outliers beyond those assumed in the base theorem.

Because of all the above factors it is logically correct to assume:

(1) A team wining more (or less) than expected most likely had less (or more) blowout losses than were expected by the original theorem.

(2) A team winning less (or more) than expected most likely had more (or less) close wins than expected by the original theorem.

Also, because the distribution of actual scoring changes through the years, it is necessary to modify the exponent in the Pythagorean theorem from time to time to maximize the correlation between expected results and actual. This explains (and I believe is the only possible explanation) for the several changes in the Pythagorean exponent that have occurred in the past.