Friday, May 11, 2007

Justifying The Best Record in Baseball

While the Brewers currently own the best record in Major League baseball (34-10), it wasn't that long ago when they were 15-9, despite having been outscored by their opponents, 110 to 113.

"Frauds!" was the cry from opponent message boards.

"Likely to regress" was the prediction from many sabermetric websites.

You see, amateur sabermetricians, such as myself, just love looking at pythagorean records. The theory is that a few close games all falling either for or against a team can skew a team's record (a very high low record in one run games, for instance). So, if you want a better feel for a team's true talent, you might be better off simply looking at a team's runs scored and given up. The Brewers -3 run differential suggested the Brewers had been a mediocre playing team that were simply blessed with some early luck.

What a difference a great ten game home stand can make.

Apparently undeterred by those dire predictions, the Brewers went 9 - 1 on the home stand, outscoring their opponents over that period, 59 to 19. Let's look at that pythagorean record now! We'll look at two different kinds. The first is the raw pythagorean, which simply uses Brewers' actual runs scored and runs given up. The second is the BaseRun pythagorean, which uses the team's raw stats to calculate their expected runs scored and runs given up:

Photo Sharing and Video Hosting at Photobucket

According to the straight pythagorean, the Brewers "should" be about 21-13. At 20-14, their BaseRun pythagorean record is about one game lower (they've scored less runs than expected but also have given up less than expected runs). There are many factors that can cause the difference between a team's pythagorean and actual record and luck is only one of them. Perhaps Yost is a better in-game strategist than the average skipper. Having Turnbow and Cordero dominating the 8th and 9th innings may also give the Brewers an above average advantage. Whatever the exact reason, it's possible that the makeup of the team simply allows them to use their runs more efficiently than the average team.

If we want to be conservative and attribute the entire difference to good luck that isn't likely to continue, an expected record of 20-14 is still damn good, though. Extrapolate that over the rest of the season and Brewer fans should expect a 95 win season, right? Well, not quite. That assumes that the Brewers' raw stats from the first 34 games of the season perfectly echos their true talent. While 1173 AB and 308 IP seems like a decent sample, MGL at "The Book" blog guards against underestimating statistical uncertainty at the team level:

For example, when we see a team bat .290 in 1000 AB’s, the equivalent of a little more than a month into the season, does that mean that this team is likely a great hitting team (assuming we know little else about them)? Well, even though we are talking about 1000 AB’s, it is likely that the regression toward the mean on that .290 is pretty substantial. For an individual player, it might be only 37% or so. For a team, it is probably closer to 70 or 80% (I don’t really know off the top of my head), maybe more.

"The Book" Blog: Groups of Players and Regression Toward the Mean

OK, so even the Brewer BaseRun pythagorian record may not represent the team's true talent very well yet. If we want an even more conservative estimate for the Brewers final record, we might regress their current expected record 90% towards the mean. If we knew nothing about the Brewers' actual talent, we'd regress 90% from .588 (winning percentage from our 20-14 expected record) towards .500. That gives us a regressed expected winning percentage of .509. If the Brewer played at that level for the rest of the year, they'd end up with about 89 wins.

But we do know something about the Brewers' true talent. They've all played professional baseball before, so we have some idea of their expected level of performance. Regressing towards a reasonable preseason expected winning percentage might make more sense. Baseball Prospectus's PECOTA based 2007 projections pegged the Brewers for an 85 win season (.525 winning percentage). Regressing 90% from .588 to .525 gives us a .531 regressed expected winning percentage. If the Brewers played at that level for the rest of the season, their final record would be 92-60. Sold!

While it might be tempting to assume that the Brewers will "fall apart, like they always do", that's not what the facts say. As conservative as I've tried to be with my estimates, this is a legitimate playoff contending team, no matter how you slice it.