The Tigers were what they were in 2007

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 2007 Tigers scored 887 runs and allowed 797. Plugging those numbers into the above formula yields a winning percentage of .553 which translates into 90 predicted wins (PW1). In reality, they won 88 games so theory was very close to reality. Alternatively, we can use runs created (RC) and runs created against (RCA), both of which I discussed in articles last week. In that case, the formula works like this:

PCT=(RC squared)/(RC squared + RCA squared)

The Tigers had 891 RC and 815 RCA allowed in 2007 which translates into 88 predicted wins (PW2) according to the formula. This matches their actual wins precisely so they Tigers were a very sabermetrically correct team this year.

Tables 1 and 2 below show that the formula did not work as well for all teams in 2007. In the tables, R, RA, PW1, RC, RCA, and PW2 are as defined above. D1 is the difference between wins and PW1 and D2 is the difference between wins and PW2.

Using PW2 and D2, we can see that the formula worked better for the National League in 2007 as all but 1 team came within 5 wins of their pythagorean estimate. The one team was the Arizona Diamondbacks who finished a whopping 14 games ahead of their predicted wins. This tells me that the DBacks were probably very lucky this year. Teams which substantially outperform their expected win totals one year tend to slip back in the following year. It doesn't work that way all the time but it works often enough to make me think the DBacks are a candidate to fall in the standings next year.

In the American League, 4 teams fell 6 or more wins away from their predicted wins. The Mariners (+11) and Angels (+9) outperformed their predicted wins which makes me think they could regress next year if they don't improve significantly. On the other hand, the Red Sox and Athletics underperformed their Pythagorean estimates by 7 wins which makes them candidates to improve their records next year. I'm sure that Billy Beane, Theo Epstein and Bill James are well aware of that.


Table 1: Pythagorean estimates for American League teams in 2007

TEAM	Wins	R	RA	PW1	D1	RC	RCA	PW2	D2
SEA	88	794	813	79	9	786	830	77	11
LAA	94	822	731	90	4	787	753	85	9
CHA	72	693	839	66	6	682	827	66	6
CLE	96	811	704	92	4	821	730	90	6
KC	69	706	778	73	-4	669	834	63	6
MIN	79	718	725	80	-1	707	766	75	4
TEX	75	816	844	78	-3	769	845	73	2
DET	88	887	797	90	-2	891	815	88	0
NYA	94	968	777	99	-5	962	799	96	-2
TB	66	782	944	66	0	812	934	70	-4
TOR	83	753	699	87	-4	751	692	88	-5
BAL	69	756	868	70	-1	771	832	75	-6
BOS	96	867	657	103	-7	898	680	103	-7
OAK	76	741	758	79	-3	768	748	83	-7

Table 2: Pythagorean estimates for National League teams in 2007

TEAM	Wins	R	RA	PW1	+/-	RC	RCA	PW2	+/-
ARI	90	712	732	79	11	722	768	76	14
WAS	73	673	783	69	4	691	816	68	5
HOU	73	723	813	72	1	749	868	69	4
STL	78	725	829	70	8	738	807	74	4
PHI	89	892	821	88	1	932	865	87	2
PIT	68	724	846	68	0	732	875	67	1
SD	89	741	666	90	-1	739	678	89	0
COL	90	860	758	92	-2	877	780	91	-1
MIL	83	801	776	84	-1	827	792	85	-2
NYN	88	804	750	87	1	846	759	90	-2
SF	71	683	720	77	-6	685	753	73	-2
CHN	85	752	690	88	-3	780	716	88	-3
CIN	72	783	853	74	-2	811	876	75	-3
ATL	84	810	733	89	-5	822	753	88	-4
FLA	71	790	891	71	0	846	913	75	-4
LAN	82	735	727	82	0	772	715	87	-5