Some things I've heard from some A's fans about 2011 go something like this:
"Man, if we only had Bob Melvin for the entire season... then we would have gone somewhere!! Stupid Geren."
"If Jemile Weeks, Hideki Matsui, and Scott Sizemore had played since Opening Day, we could have totally given Texas a run for their money."
"That losing streak really killed us. Without it, we would have been a .500 team at least."
This post is intended to explore similar scenarios using Pythagorean winning percentage.
For the uninitiated, yes, the Pythagorean Theorem actually does have a related use outside of high school algebra! Adapted for baseball use by BIll James, the general formula is as follows:
Winning percentage = (RS)2/((RA)2 + (RS)2)
where RS = runs scored and RA = runs allowed
(A more modern interpretation of it uses 1.83 as the exponent, which is what I will use here.)
The most important thing to keep in mind here is that Pythagorean winning percentage may, or may not, have any bearing on a team's actual winning percentage in any one season. The point of using this formula, then, is to try and keep luck out of the equation as much as possible and to get as close to a team's "true" wins as possible based on their talent.*
So, how do the A's fair using this formula for the 2011 season? Well, over the entire season, the A's scored 645 runs and allowed 679. Plugging that into the Pythagorean win formula yields the following:
2011 Pythag = (645)1.83/((645)1.83 + (679)1.83)) = .477
which, multiplied by 162, yields about 77 wins. As it happens, this formula also tends to regress to the mean, meaning that bad teams will appear less bad by Pythagorean winning percentage.
Now, given that run differentials in each game are easily calculated, is there any way to slice the 2011 season such that any of the initial ideas might be true? Were the A's that bad, or just unlucky and maybe good?
Let's first try and calculate the Pythag for the Melvin era:
First Game 6/9
422 RS, 441 RA
Pythag = .48
Pythag WL = 47-52
Actual record 47-52
Another way to slice it might be to give the team a mulligan. That is, we can eliminate the team's worst losses (and, to be fair, the team's most lopsided wins.) A simple cutoff point is double-digit run differentials. As it happens, there were 5 games where the A's won or lost by 10 or more runs, so let's just eliminate those:
599 RS, 624 RA
Pythag = .48
Pythag WL = 75-82
Actual record in that scenario = 72-85
As A's fans suffered through, there was a horrendous point from 5/30 to 6/14, where the A's only won one game. What if we simply pretend that those games didn't happen?
597 RS, 597 RA
Pythag = .500
Pythag WL = 74-74
Actual record in that scenario = 73-75
It should be noted, however, that the latter two scenarios involve cherry-picking, which is something that as informed baseball fans, we should be leery of doing. Indeed, especially in the no streak scenario, it would be inappropriate to assume that the A's would not have lost somewhere else in there given a 148 game season.
Unequivocally, the A's were indeed that bad. Neither Melvin's actual, nor Pythagorean winning percentage tells us that the A's were simply unlucky. In eliminating the outliers, even that does not show that the A's were significantly better than their record indicated. Finally, while eliminating the losing streak and surrounding losses provide for a better record, that's not really a fair representation of the A's as a team. Indeed, given the under .500 record of the team itself, it would be unwise to think that those losses were simply more than would be expected. It is considerably more likely that those losses were simply clumped in one place due to chance.
*Baseball Prospectus attempts to take this further by calculating 2nd and 3rd order wins, which uses expected runs instead of actual runs and adjusts for strength of schedule, respectively. Technically, these are more precise than Pythagorean winning percentage, but are not used in this discussion