Under performing Tigers

One of the fundamental concepts of sabermetrics is the Pythagorean Theorem. Invented by Bill James in the late 1970s, the Pythagorean Theorem is a formula that shows the relationship between a team's runs scored (RS), runs allowed (RA) and winning percentage (PCT). It is as follows:

PCT=(RS squared)/(RS squared + RA squared)

The formula works reasonably well in most years for most teams. This indicates that winning games is essentially a function of how many runs a team scores and allows and when the runs were scored is not so important in most cases.

For example, the 2008 Tigers scored 821 runs and allowed 857. Plugging those numbers into the above formula yields a winning percentage of .479 which translates into 78 predicted wins. In reality, they won 74 games so they underperformed their pythagorean estimate by four wins.

When a team under performs like the Tigers did, it usually means they either they did poorly in close games or they won a disproportionate number of blowouts. In this case, both were true. They were 16-25 in one run games and 4-0 in games decided by 13 runs or more.

The results for all American and National League teams are presented in tables 1 and 2 below. All American League teams but two finished within five runs of their Pythagorean estimate. Thanks to an outstanding record of 61-28 in games decided by one or two runs, the Angels out did their estimate by 11 wins. The Blue Jays, on the other hand, fell eight wins below their predicted wins. This is because they were 9-1 in games decided by eight or more runs and 16-25 in one run games.

There were also only two National League teams that fell more than five wins outside their Pythagorean estimate. The Braves under performed by 6 wins partly because of their 11-30 record in one run games. The Astros over performed by 9 wins thanks, in part, to a 2-9 record in games decided by eight or more runs.

Because performance in close games and blow outs are not consistent from year to year, there is good chance that the Braves and Blue Jays will win more games next year. Conversely, the Angels and Astros might have a difficult time matching their 2008 win totals next year.

Table 1: Pythagorean estimates for American League teams in 2008

team	runs	runs allowed	actual wins	pred wins	difference	% difference
LAA	765	697	100	89	11	12.4
TB	774	671	97	92	5	5.4
KC	691	781	75	71	4	5.6
TEX	901	967	79	75	4	5.3
NYA	789	727	89	88	1	1.1
OAK	646	690	75	75	0	0.0
CHA	811	729	89	90	-1	-1.1
BOS	845	694	95	97	-2	-2.1
MIN	829	745	88	90	-2	-2.2
BAL	782	869	68	72	-4	-5.6
DET	821	857	74	78	-4	-5.1
CLE	805	761	81	86	-5	-5.8
SEA	671	811	61	66	-5	-7.6
TOR	714	610	86	94	-8	-8.5

Table 2: Pythagorean estimates for National League teams in 2008

team	runs	runs allowed	actual wins	pred wins	difference	% difference
HOU	712	743	86	77	9	11.7
SF	640	759	72	67	5	7.5
CIN	704	800	74	71	3	4.2
FLA	770	767	84	81	3	3.7
MIL	750	689	90	88	2	2.3
COL	747	822	74	73	1	1.4
PIT	735	884	67	66	1	1.5
ARI	720	706	82	83	-1	-1.2
NYN	799	715	89	90	-1	-1.1
STL	779	725	86	87	-1	-1.1
PHI	799	680	92	94	-2	-2.1
WAS	641	825	59	61	-2	-3.3
CHN	855	671	97	100	-3	-3.0
LAN	700	648	84	87	-3	-3.4
SD	637	764	63	66	-3	-4.5
ATL	753	778	72	78	-6	-7.7