Not All Wins Are Created Equal: The 2013 NFL Standings in Context (Through Week 16!)

I embarked on a pretty sweet mini-project today, if I do say so myself. It starts with a couple of… “problems” that had been nagging me, regarding the lack of use of football’s Pythagorean formula. Pythagorean wins (or winning percentage) have been showing up in NFL analysis for, I dunno, at least a few years now. I learned of them in a Bill Barnwell preseason piece before the 2012 NFL Season (on Grantland.com). A team’s Pythagorean winning percentage (PW%) is as follows:
PW% = (Points Scored ^ 2.37) / {(Points Scored ^ 2.37) + (Points Allowed ^ 2.37)}¹
Say the Bengals and Browns are both 8-8. The Bengals blew out their opponents in their eight wins, and lost narrowly in their eight losses, while the Browns won narrowly in their wins and lost big in their losses. You probably agree that even with the same record, the Bengals are likely better than the Browns. PW% is a measure of how much.

What’s bothered me is that Pythagorean analysis usually stops there: with a team’s points scored and points allowed. But one could apply the same analysis to a group of teams, say the 49ers’ opponents in the 2013 season, and determine that group’s PW%. Then one would know how tough the 49ers’ competition had been this year, beyond simple wins and losses. And, instead of using this year’s record as a strength of schedule statistic for next year’s season, one could use it for this very season itself, adding context to those final standings. We don’t have to just assume that all ten-win teams are equally skilled (or that they aren’t); we can quantify other useful metrics and see if there’s any evidence for our assumptions. And that’s exactly what I’ve done. For all 32 teams, and all 13 of their opponents, through 15 games.² Let’s take a look!

First off, we have our sin-context base, nothing but the ‘W’s:

Rank	Team	W	W%
1	SEA	12	80.00%
1	DEN	12	80.00%
3	SF	11	78.57%
4	CAR	11	73.33%
4	KC	11	73.33%
4	NE	11	73.33%
7	CIN	10	66.67%
7	NO	10	66.67%
7	ARI	10	66.67%
7	IND	10	66.67%
11	PHI	9	60.00%
12	SD	8	53.33%
12	DAL	8	53.33%
12	MIA	8	53.33%
12	BAL	8	53.33%
12	CHI	8	53.33%
17	GB	7.5	50.00%
18	DET	7	46.67%
18	STL	7	46.67%
18	PIT	7	46.67%
18	NYJ	7	46.67%
22	TEN	6	40.00%
22	BUF	6	40.00%
22	NYG	6	40.00%
25	MIN	4.5	30.00%
26	ATL	4	28.57%
27	TB	4	26.67%
27	CLE	4	26.67%
27	OAK	4	26.67%
27	JAC	4	26.67%
31	WAS	3	20.00%
32	HOU	2	13.33%

Alright. Mostly, all that’s good for is figuring out who gets the first pick in the draft. Let’s add some context. Here are the same figures, for Pythagorean wins:

Rank	Team	Pythagorean Wins	PW%
1	SEA	11.9	79.17%
2	CAR	11.1	74.18%
3	SF	10.9	72.95%
4	DEN	10.8	71.88%
5	KC	10.7	71.05%
6	CIN	10.2	68.02%
7	NO	9.7	64.90%
8	NE	9.7	64.62%
9	ARI	9.0	60.29%
10	PHI	8.8	58.76%
11	SD	8.6	57.65%
12	IND	8.4	56.01%
13	DET	8.0	53.18%
14	DAL	7.7	51.29%
15	STL	7.6	50.35%
16	PIT	7.4	49.34%
17	MIA	7.4	49.05%
18	GB	7.1	47.58%
19	BAL	7.1	47.14%
20	CHI	6.9	46.16%
21	TEN	6.9	45.88%
22	BUF	6.6	43.86%
23	MIN	5.6	37.58%
24	ATL	5.4	36.32%
25	TB	5.4	35.76%
26	CLE	5.4	35.68%
27	OAK	4.9	32.53%
28	NYG	4.8	31.94%
29	WAS	4.7	31.19%
30	NYJ	4.6	30.79%
31	HOU	3.9	26.17%
32	JAC	3.1	20.58%

Now Carolina and San Francisco appear a little bit better than Denver; Jacksonville still has a firm grip on last place, in the Pythagorean world. Curious how these little differences do add up and do affect rankings. You can get an idea of how teams landed where they did by checking out their point totals, presented here, in order of most net points through the 15 games so far:

Rank	Team	Net Points	PF	PF Rank	PA	PA Rank
1	DEN	187	572	1	385	22
2	SEA	168	390	8	222	2
3	SF	131	383	10	252	3
4	KC	128	406	6	278	4
5	CAR	124	345	19	221	1
6	CIN	108	396	7	288	6
7	NE	92	410	5	318	9
8	NO	85	372	13	287	5
9	PHI	58	418	2	360	16
9	ARI	58	359	16	301	7
11	SD	45	369	14	324	11
12	IND	35	361	15	326	12
13	DET	20	382	11	362	17
14	DAL	9	417	3	408	25
15	STL	2	339	20	337	13
16	PIT	-4	359	16	363	18
17	MIA	-5	310	24	315	8
18	BAL	-15	303	26	318	9
19	GB	-16	384	9	400	24
20	TEN	-25	346	18	371	19
21	CHI	-28	417	3	445	30
22	BUF	-35	319	23	354	15
23	TB	-76	271	29	347	14
24	CLE	-85	301	27	386	23
25	ATL	-89	333	21	422	29
26	MIN	-90	377	12	467	32
27	NYG	-103	274	28	377	20
28	NYJ	-110	270	30	380	21
29	OAK	-111	308	25	419	27
30	WAS	-130	328	22	458	31
31	HOU	-146	266	31	412	26
32	JAC	-182	237	32	419	27

Those are the inputs. And the outputs? Subtracting actual wins from Pythagorean wins, we reveal how many “lucky” wins (or losses) each team has:

Rank	Team	W – PW	W	PW
1	NYJ	2.4	7	4.6
2	IND	1.6	10	8.4
3	NE	1.3	11	9.7
4	DEN	1.2	12	10.8
5	NYG	1.2	6	4.8
6	CHI	1.1	8	6.9
7	ARI	1.0	10	9.0
8	BAL	0.9	8	7.1
9	JAC	0.9	4	3.1
10	MIA	0.6	8	7.4
11	GB	0.4	7.5	7.1
12	KC	0.3	11	10.7
13	DAL	0.3	8	7.7
14	NO	0.3	10	9.7
15	PHI	0.2	9	8.8
16	SEA	0.1	12	11.9
17	SF	0.1	11	10.9
18	CAR	-0.1	11	11.1
19	CIN	-0.2	10	10.2
20	PIT	-0.4	7	7.4
21	STL	-0.6	7	7.6
22	BUF	-0.6	6	6.6
23	SD	-0.6	8	8.6
24	OAK	-0.9	4	4.9
24	TEN	-0.9	6	6.9
26	DET	-1.0	7	8.0
27	MIN	-1.1	4.5	5.6
28	CLE	-1.4	4	5.4
29	TB	-1.4	4	5.4
30	ATL	-1.4	4	5.4
31	WAS	-1.7	3	4.7
32	HOU	-1.9	2	3.9

The Jets have outperformed by more than two wins! And Rex Ryan still might get fired. Also, Jacksonville’s good luck has ruined formerly promising chances of getting the first pick in the draft, as likely they’ll instead see it go to Houston. It’s really Houston that has performed better, losing by significantly fewer points, albeit more often. Well, perhaps Houston’s competition was much easier? Or perhaps not? You don’t have to wonder, let’s see! Here are the teams ranked by the average net points of their opponents, adjusted by removing totals from games against the team in question.³

Tm	Rk	O Nt Pts	/Gm	O PF	/Gm	Rk	O PA	/Gm	Rk
DET	1	-338	-1.64	5,043	24.48	23	5,381	26.12	3
GB	2	-304	-1.48	5,047	24.50	24	5,351	25.98	4
PHI	3	-282	-1.37	5,106	24.79	27	5,388	26.16	2
KC	4	-279	-1.35	5,118	24.84	28	5,397	26.20	1
CHI	5	-259	-1.26	4,964	24.10	19	5,223	25.35	10
BAL	6	-216	-1.05	5,105	24.78	26	5,321	25.83	6
PIT	7	-211	-1.02	4,859	23.59	11	5,070	24.61	14
BUF	8	-179	-0.87	4,539	22.03	1	4,718	22.90	23
DAL	10	-177	-0.86	5,140	24.95	29	5,317	25.81	7
CIN	9	-177	-0.86	4,934	23.95	16	5,111	24.81	12
OAK	11	-176	-0.85	4,979	24.17	22	5,155	25.02	11
CLE	12	-129	-0.63	4,883	23.70	13	5,012	24.33	15
NYJ	13	-89	-0.43	4,722	22.92	4	4,811	23.35	19
NE	14	-84	-0.41	4,679	22.71	2	4,763	23.12	20
SD	15	-56	-0.27	5,195	25.22	30	5,251	25.49	8
MIN	16	-28	-0.14	5,048	24.50	25	5,076	24.64	13
JAC	17	-1	0.00	4,912	23.84	15	4,913	23.85	16
DEN	18	15	0.07	4,833	23.46	9	4,818	23.39	17
TEN	19	29	0.14	4,846	23.52	10	4,817	23.38	18
WAS	20	78	0.38	5,417	26.30	31	5,339	25.92	5
SEA	21	81	0.39	4,783	23.22	5	4,702	22.83	24
SF	22	109	0.53	4,808	23.34	6	4,699	22.81	25
MIA	23	127	0.62	4,823	23.41	7	4,696	22.80	26
CAR	24	161	0.78	4,829	23.44	8	4,668	22.66	27
ATL	25	208	1.01	4,701	22.82	3	4,493	21.81	32
HOU	26	220	1.07	4,969	24.12	21	4,749	23.05	21
IND	27	222	1.08	4,967	24.11	20	4,745	23.03	22
STL	28	255	1.24	4,902	23.80	14	4,647	22.56	28
NYG	29	328	1.59	5,571	27.04	32	5,243	25.45	9
ARI	30	333	1.62	4,871	23.65	12	4,538	22.03	30
NO	31	361	1.75	4,954	24.05	17	4,593	22.30	29
TB	32	458	2.22	4,961	24.08	18	4,503	21.86	31

You see, there’s really quite a difference. Buffalo’s opponents, in games not against Buffalo, scored an average of 22.03 a game; five points a game fewer than the unfortunate New York Giants, who went up against all four top offenses in the league, two of them (Philadelphia and Dallas) twice! Notice Washington is down there too; teams in the same division tend to clump together, as 75% of their opponents are in common. Kansas City played the worst defenses overall (through 15 games), while Atlanta faced the toughest. All in all, Detroit’s opponents, in games not against Detroit, lost by 1.64 points on average, while Tampa Bay’s opponents won by 2.22 points, nearly a four-point swing between extremes.

Putting it all together, these are the Pythagorean winning percentages of the opponents of all thirty-two teams, along with the PW% of the team itself. The difference, which I quite originally dub “Relative Performance” (actual PW% minus expected PW% given those opponents), indicates how well a team fared against its competition, relative to other teams against the same opponents.

Team	Rank	Relative Performance	Opp. PW%	Rank	Expected PW%	Actual PW%
SEA	1	30.19%	51.01%	21	48.99%	79.17%
CAR	2	26.19%	52.01%	24	47.99%	74.18%
SF	3	24.31%	51.36%	22	48.64%	72.95%
DEN	4	22.06%	50.18%	18	49.82%	71.88%
NO	5	19.37%	54.47%	31	45.53%	64.90%
KC	6	17.90%	46.86%	4	53.14%	71.05%
CIN	7	15.93%	47.91%	9	52.09%	68.02%
ARI	8	14.48%	54.19%	30	45.81%	60.29%
NE	9	13.56%	48.95%	14	51.05%	64.62%
IND	10	8.72%	52.71%	27	47.29%	56.01%
SD	11	7.01%	49.36%	15	50.64%	57.65%
PHI	12	5.58%	46.82%	3	53.18%	58.76%
STL	13	3.51%	53.16%	28	46.84%	50.35%
MIA	14	0.63%	51.58%	23	48.42%	49.05%
DET	15	-0.65%	46.16%	1	53.84%	53.18%
DAL	16	-0.71%	48.00%	11	52.00%	51.29%
PIT	17	-3.17%	47.48%	6	52.52%	49.34%
TEN	18	-3.77%	50.36%	19	49.64%	45.88%
BAL	19	-5.31%	47.55%	7	52.45%	47.14%
GB	20	-5.88%	46.54%	2	53.46%	47.58%
CHI	21	-6.85%	46.99%	5	53.01%	46.16%
BUF	22	-8.43%	47.71%	8	52.29%	43.86%
TB	23	-8.53%	55.71%	32	44.29%	35.76%
ATL	24	-11.00%	52.68%	25	47.32%	36.32%
MIN	25	-12.75%	49.67%	16	50.33%	37.58%
NYG	26	-14.47%	53.59%	29	46.41%	31.94%
CLE	27	-15.87%	48.46%	12	51.54%	35.68%
WAS	28	-17.95%	50.86%	20	49.14%	31.19%
OAK	29	-19.52%	47.94%	10	52.06%	32.53%
NYJ	30	-20.32%	48.89%	13	51.11%	30.79%
HOU	31	-21.15%	52.68%	26	47.32%	26.17%
JAC	32	-29.43%	49.99%	17	50.01%	20.58%

So take my 49ers. Their average opponent should expect to win 51.36% of their games not against the 49ers, but only 27.05% of their games against the 49ers.⁴ That difference, 24.31%, is the third largest in the league. GO NINERS! Only Carolina and Seattle have dominated more thoroughly, giving their opponents quite a whooping, much more so than their opponents receive from other teams. Kansas City, meanwhile, boasts a healthy 71.05 PW%; but against its crummy competition, other teams have been averaging a 53.14 PW% anyway, so it’s a little less impressive, knocking their relative performance to sixth in the league.

Oh, and check out the Jets! Further evidence that I was right when I declared that their 2013 campaign was quite impressive earlier this week. Other teams facing the Jets’ competition have a respectable 51.11 PW%; they outperform them over half the time. The Jets, meanwhile, only manage 30.79%, getting badly outperformed by mediocre teams. Ick. I should point out that by these measures, Tampa Bay had the toughest schedule, while Detroit had the easiest– and still missed the playoffs. Ouch.

Lastly, we’ll return to the “real” numbers, straight-up wins, side-by-side with their Pythagorean expectations. This post has been about context. Wins and losses mean different things in different contexts; a context of narrow defeats and blowout wins suggests a team is merely having some bad breaks, and inspires optimism; a context of blowout defeats and narrow wins indicates the opposite, and the tempering of future expectations. But context is only that: context. The real content, the wins and losses themselves, is what we care about. Here they are, side by side:

Team	Rank	W	Expected PW	Actual PW	PW Over/Under Expected	W Over/Under PW
SEA	1	12	7.3	11.9	4.5	0.1
DEN	1	12	7.5	10.8	3.3	1.2
CAR	3	11	7.2	11.1	3.9	-0.1
SF	3	11	7.3	10.9	3.6	0.1
KC	3	11	8.0	10.7	2.7	0.3
NE	3	11	7.7	9.7	2.0	1.3
NO	7	10	6.8	9.7	2.9	0.3
CIN	7	10	7.8	10.2	2.4	-0.2
ARI	7	10	6.9	9.0	2.2	1.0
IND	7	10	7.1	8.4	1.3	1.6
PHI	11	9	8.0	8.8	0.8	0.2
SD	12	8	7.6	8.6	1.1	-0.6
MIA	12	8	7.3	7.4	0.1	0.6
DAL	12	8	7.8	7.7	-0.1	0.3
BAL	12	8	7.9	7.1	-0.8	0.9
CHI	12	8	8.0	6.9	-1.0	1.1
GB	17	7.5	8.0	7.1	-0.9	0.4
STL	18	7	7.0	7.6	0.5	-0.6
DET	18	7	8.1	8.0	-0.1	-1.0
PIT	18	7	7.9	7.4	-0.5	-0.4
NYJ	18	7	7.7	4.6	-3.0	2.4
TEN	22	6	7.4	6.9	-0.6	-0.9
BUF	22	6	7.8	6.6	-1.3	-0.6
NYG	22	6	7.0	4.8	-2.2	1.2
MIN	25	4.5	7.5	5.6	-1.9	-1.1
TB	26	4	6.6	5.4	-1.3	-1.4
ATL	26	4	7.1	5.4	-1.6	-1.4
CLE	26	4	7.7	5.4	-2.4	-1.4
OAK	26	4	7.8	4.9	-2.9	-0.9
JAC	26	4	7.5	3.1	-4.4	0.9
WAS	31	3	7.4	4.7	-2.7	-1.7
HOU	32	2	7.1	3.9	-3.2	-1.9