Pythagoras, Bill James, Rufio and the Browns prospects in 2013

Greg M. Cooper-USA TODAY Sports

I was a big fan of Bill James in the 80's. I still have a few copies of his legendary "Bill James Baseball Abstract" from the 86-89 moldering away in the basement somewhere. He was the father of modern sports analytics and moneyball. One of his early formulas was the pythagorean theorem which is (RS^2)/(RS^2+RA^2)= expected winning%. A team that deviates from it's expected win rate either up or down (from random events than can be called good or bad luck) is likely to have a worse win rate the following season. This mean regression works well in baseball, which has a huge sample size, and I always figured it would have some application in football but likely not as accurate due to the smaller sample size.

During the Indy game, I commented that Indianapolis is likely not a playoff caliber team this year due to fact that they actually scored less points than they allowed last year and would experience a mean regression this season. This started a conversation with the well respected Rufio about the Pythagorean Theorem. He posted a link to an article by Bill Barnwell about the application of the theorem to football. Using the formula provided I calculated the expected wins for all teams last year. The article also provides a breakdown of how much a deviation in expected win rate translates to wins the following year.

Expected Wins vs. Actual Wins Teams Avg. Change in Wins
-3 to -2 57 Improved by 2.6 wins
-2 to -1.5 44 Improved by 2.5 wins
-1.5 to -1 86 Improved by 2.0 wins
-1 to -0.5 124 Improved by 0.6 wins
-0.5 to 0 119 Neither improved nor declined
0 to 0.5 123 Neither improved nor declined
0.5 to 1 127 Declined by 0.9 wins
1 to 1.5 97 Declined by 1.5 wins
1.5 to 2 66 Declined by 1.8 wins
2 to 3 33 Declined by 2.5 wins

So how does this relate to the Browns prospects in 2013? Quite favorably actually, last year the Browns won 5 games but according to Pythagoras they should have won 6.2 games or -1.2 from their expected total. As we see from the above table teams that fell in this category on average will improve by 2.0 wins the following season. This would put the Browns at 7-9 which most of us here would be pleased with. The following table is the breakdown of all the AFC North (the projected column is 2013 win total adjusted by the table above):

Division Team Scored Allowed Wins Expected Difference Projected
AFCNorth Bengals 391 320 10 9.9 0.14 10
Browns 302 368 5 6.2 -1.16 7
Ravens 398 344 10 9.4 0.63 9.1
Steelers 336 314 8 8.6 -0.64


This projection would have the Browns finishing last and the Bengals winning the division but overall a narrowed gap within the division.

The problem with this is the small sample size of one NFL team in one NFL season. The Browns are not really likely to improve by 2 games as much as they are in a group of teams that on average will improve in the aggregate by two games each. I divided all of last years teams in to groups based on the deviation from expected win totals. These are my groupings

--Teams that will on average decline by 1.8-2.5 wins: Texans, Falcons, Colts (the Colts are actually off the chart with 11 wins versus 7.24 expected wins for a -3.76 but i threw them in this group anyway).

-- Teams that will on average decline by 0.9-1.5 wins: Ravens, Titans, Jets, Broncos, Packers, Vikings, Cowboys

--Teams that will have no change on average: Bengals, Patriots, Bills, Dolphins, Raiders. Eagles, Niners, Rams, Cardinals

--Teams that will win on average 0.6 more games: Steelers, Chiefs, Bucs, Panthers, Chargers, Bears

--Teams that will win on average 2-2.6 more games: Browns Jaguars, Lions, Saints, Giants, Seahawks

In the Browns group those 6 teams won 38 games last year and the expectation would be that they will win 50.6 this year. That could be 4 more wins each by the Lions and Saints and 2 more wins each by the Giants and Seahawks with the Browns and Jags standing pat but I like that we are in that group. The Lions actually had the largest negative deviation in expected wins at -2.49 so I would look for an improvement from them. It seems every year a team goes from worst to first. The Lions seem like the most likely candidate with Vikings and Packers both set to decline.

I then used the projected win totals for 2013 to calculate SOS for this season. Normally SOS is compiled using last years win loss. The table is in rank order of my calculations based on the projected wins of all teams using the pythagorean theorem adjustment. The SOS rank from 2012 win loss record is in the column next and the last column is the change with a positive number indicating an increase in SOS and a negative indicating a decrease in SOS.

Team Proj 2013 rec 2012 rec change
1 Vikings 0.555 10 9
2 Panthers 0.555 1 -1
3 Ravens 0.552 5 2
4 Packers 0.549 6 2
5 Rams 0.54 4 -1
6 Lions 0.539 2 -4
7 Saints 0.534 3 -4
8 Cardinals 0.528 7 -1
9 Dolphins 0.523 8 -1
10 Falcons 0.522 15 5
11 Jets 0.521 19 8
12 Bears 0.521 16 4
13 Eagles 0.52 20 7
14 Bengals 0.519 12 -2
15 Redskins 0.518 18 3
16 Bucs 0.517 17 1
17 Niners 0.515 9 -8
18 Cowboys 0.509 25 7
19 Bills 0.507 26 7
20 Seahawks 0.504 11 -9
21 Browns 0.5 21 0
22 Patriots 0.498 14 -8
23 Steelers 0.497 22 -1
24 Giants 0.489 24 0
25 Cheifs 0.484 28 3
26 Jaguars 0.483 13 -13
27 Titans 0.482 23 -4
28 Raiders 0.471 29 1
29 Texans 0.466 27 -2
30 Colts 0.464 30 0
31 Chargers 0.449 31 0
32 Broncos 0.441 32


As we can see the Browns schedule is still ranked 21st either way a relatively easy schedule. I think all this bodes well for an improvement in our record in 2013.

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