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Friday, July 20, 2007

Pythagorean Standings

In honor of the Reds tying the Everett-less Astros for last in the NL Central last night, I thought it would be fun to take a look at the standings based on teams' Pythagorean records, which are based on their runs scored and runs allowed per game. Here they are:
Pythagorean Standings - As of 7/18/07
National League East
Team Wins W% Games Back Real position
NYN 50 0.532 0 1st
ATL 48 0.505 2.5 2nd, 2.5 out
PHI 47 0.500 3 3rd, 5 out
FLA 44 0.463 6.5 4th, 7.5 out
WAS 36 0.383 14 5th, 13 out

National League Central
Team Wins W% Games Back Real position
CHN 52 0.559 0 2nd, 3.5 out
MIL 51 0.543 1.5 1st
CIN 45 0.474 8 5th, 13.5 out
HOU 42 0.442 11 5th, 13.5 out
STL 39 0.429 12 3rd, 8.5 out
PIT 39 0.415 13.5 4th, 13 out

National League West
Team Wins W% Games Back Real position
SD 55 0.591 0 2nd, 1 out
LAN 52 0.547 4 1st
COL 47 0.500 8.5 4th, 5.5 out
SF 44 0.478 10.5 5th, 13.5 out
ARI 45 0.469 11.5 3rd, 4.5 out

American League East
Team Wins W% Games Back Real position
BOS 56 0.596 0 1st
NYA 54 0.587 1 2nd, 7 out
TOR 47 0.500 9 3rd, 11 out
BAL 46 0.489 10 4th, 14 out
TB 35 0.376 20.5 5th, 18.5 out

American League Central
Team Wins W% Games Back Real position
DET 56 0.609 0 1st
CLE 52 0.553 5 2nd, 2 out
MIN 51 0.543 6 3rd, 8 out
KC 44 0.468 13 5th, 16 out
CHA 40 0.430 16.5 4th, 14.5 out

American League West
Team Wins W% Games Back Real position
LAA 51 0.548 0 1st
OAK 49 0.516 3 3rd, 11 out
SEA 47 0.511 3.5 2nd, 1.5 out
TEX 43 0.457 8.5 4th, 14.5 out

In two cases, the NL Central and the NL West, the top two teams are reversed. Otherwise, the leaders are maintained, though some teams look closer or further from contention than they actually are. Pythagorean Wild Card leaders are currently the Dodgers over the Brewers in the National League, and the Yankees over the Indians in the American League.

There's a sense in which these standings are irrelevant, of course, as these games have already been played and the wins/losses determined. Nevertheless, all things being equal, we can probably expect teams to regress toward their Pythagorean records over the course of the rest of this season. So as a follow-up, I was interested in seeing which teams were helped and hurt the most by the reality of playing actual games (as opposed to just scoring and allowing runs). Because teams play against one another, I opted to compare actual Games Back with the Games Back according to the above Pythagorean standings.

Here are the differences (positive values indicate teams that are doing better than predicted, whereas negative values indicate teams that are doing worse than expected):
Team ExpGB-ActualGB
STL 3.5
TB 2
MIL 1.5
PIT 0.5
FLA -1
SD -1
PHI -2
TOR -2
MIN -2
HOU -2.5
SF -3
KC -3
CHN -3.5
BAL -4
CIN -5.5
NYA -6
TEX -6
OAK -8
A combination of a an unfortunate Pythagorean division leader (San Diego) and a very fortunate Arizona team puts the D-backs seven games better in their division than you'd expect based on run differentials. Seven games! The Dodgers, Cardinals, Rockies, and Indians round out the five most lucky (or, perhaps, overperforming?) teams.

At the opposite end of the spectrum, Oakland is about eight games behind where they "should be" in their division, thanks to an "overperforming" Angels ballclub and an A's team that is four games below expectations. Interestingly for the New York/Boston-centered sports media, the Yankees also show up as being much worse than run differentials predict, one game behind the Red Sox according to Pythagoras--and that's all on the Yanks, as Boston is spot-on with their predicted record. Other top "unlucky"/"underperforming" teams include the Rangers, Reds, Orioles, and Cubs.

It will be interesting to compare these predicted standings to actual standings at the end of the season. My guess is that teams will be ranked closer to their present Pythagorean standings than their present actual standings.