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

  1. Multiply the % by the number of games played to obtain Pythagorean wins. You may then compare the number of Pythagorean wins to actual wins; if actual wins are greater, the team has been lucky, while if Pythagorean wins are greater, they’ve been unlucky. The two figures even out in the long run but may differ over short stretches. (Even a full sixteen game season. Sixteen games isn’t that many. You know they play 162 in baseball?) 
  2. Remember, teams play 16 games against 13 opponents because they play each team in their division twice; the last game of the season is always an intra-division match-up, so at the moment each team has played 15 games against 13 teams. 
  3. Sorry this chart’s headers are a little lacking; it was the only way I could get it to fit onto one page. It was either that or splitting it into three separate charts, which I thought worse. 
  4. 100% – San Francisco’s actual PW% of 72.95% = 27.05%. 
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