## Data Dump: Schedule-Adjusted Pythagorean Ratings (1970-2012)

This is mostly a huge end-of-regular-season data dump, but I’ll explain a little before the table…

PFR’s Simple Rating System can be broken into offensive and defensive components, which represent the number of points per game the team scored/allowed per game compared to the league average, after adjusting for the strength of opposing offenses and defenses faced. If you want to derive an expected winning percentage from that, you have to “back out” to total points scored/allowed again. To do that, you just add OSRS (or subtract DSRS) to the league’s average PPG, then multiply by the number of games the team played. This will give you adjusted points scored/allowed totals for the season.

To get that into a winning percentage-like form, you then need to plug those totals into the Pythagorean Formula. It usually takes the form of

(Pts Scored ^ x) / (Pts Scored ^ x + Pts Allowed ^ x)

where x was determined to be around 2.4 for the NFL in the 1990s, when current Houston Rockets (yep, basketball) GM Daryl Morey researched it for STATS, Inc. Last year, Football Outsiders decided to employ a “floating” exponent that varies with the scoring environment in which a team played, recognizing that a single point is more important to winning in lower-scoring environments. To that end, they used what’s known as the “Pythagenport” method of determining the exponent, which is

1.5 * log10((PF + PA) / G)

I was poking around in the data the other day, though, and found that the so-called “Pythagenpat” variant actually correlates slightly better with teams’ actual won-lost records since the NFL-AFL merger. That formula suggests for each team an exponent of

((PF + PA) / G) ^ 0.2466

This gives you a 1.204 RMSE vs. wins since 1970, a very slight improvement over the 1.205 RMSE you get using FO’s formula.

At any rate, I applied the Pythagenpat exponent to each team’s schedule-adjusted points scored/allowed totals since 1970, and tweaked the pythagorean win/loss totals up/down at the league-season level to match actual league-wide win/loss totals. The result was a definitive set of pythagorean ratings for every team since the merger:

2012Buffalo BillsbufAFC East1661000.375344435-0.9-5.8349.84456.840.3331
2012Miami DolphinsmiaAFC East167900.438288317-5.52.9276.24317.640.4174
2012New England PatriotsnweAFC East1612400.75055733112.20.5559.44356.040.7747
2012New York JetsnyjAFC East1661000.375281375-5.1-0.9282.64378.440.3267
2012Baltimore RavensravAFC North1610600.6253983441.91.0394.64348.040.5819
2012Cincinnati BengalscinAFC North1610600.6253913201.20.9383.44349.640.5606
2012Cleveland BrownscleAFC North1651100.313302368-4.6-0.7290.64375.240.3467
2012Pittsburgh SteelerspitAFC North168800.500336314-2.82.1319.44330.440.4806
2012Houston TexanshtxAFC South1612400.7504163311.81.7393.04336.840.5993
2012Indianapolis ColtscltAFC South1611500.688357387-1.9-2.8333.84408.840.3740
2012Jacksonville JaguarsjaxAFC South1621400.125255444-8.1-4.9234.64442.440.1700
2012Tennessee TitansotiAFC South1661000.375330471-2.6-7.4322.64482.440.2595
2012Denver BroncosdenAFC West1613300.8134812896.33.8465.04303.240.7539
2012Kansas City ChiefskanAFC West1621400.125211425-10.3-3.7199.44423.240.1368
2012Oakland RaidersraiAFC West1641200.250290443-4.6-6.2290.64463.240.2322
2012Dallas CowboysdalNFC East168800.5003764001.4-1.2386.64383.240.5074
2012New York GiantsnygNFC East169700.5634293444.02.2428.24328.840.6662
2012Washington RedskinswasNFC East1610600.6254363884.6-1.2437.84383.240.5887
2012Chicago BearschiNFC North1610600.6253752771.06.0380.24268.040.7066
2012Detroit LionsdetNFC North1641200.2503724372.1-4.4397.84434.440.4436
2012Green Bay PackersgnbNFC North1611500.6884333364.92.4442.64325.640.6911
2012Minnesota VikingsminNFC North1610600.6253793481.61.8389.84335.240.5971
2012Atlanta FalconsatlNFC South1613300.8134192992.04.5396.24292.040.6855
2012Carolina PantherscarNFC South167900.438357363-0.51.3356.24343.240.5252
2012New Orleans SaintsnorNFC South167900.4384614546.5-5.1468.24445.640.5351
2012Tampa Bay BuccaneerstamNFC South167900.4383893941.3-1.3385.04384.840.5020
2012Arizona CardinalscrdNFC West1651100.313250357-4.81.6287.44338.440.4022
2012Seattle SeahawksseaNFC West1611500.6884122454.57.7436.24240.840.8186
2012St. Louis RamsramNFC West167810.469299348-2.12.4330.64325.640.5112
2011Buffalo BillsbufAFC East1661000.3753724341.2-4.5374.03426.930.4200
2011Miami DolphinsmiaAFC East1661000.375329313-2.23.2319.63303.730.5374
2011New England PatriotsnweAFC East1613300.8135133429.4-0.1505.23356.530.7234
2011New York JetsnyjAFC East168800.5003773631.2-0.3374.03359.730.5310
2011Baltimore RavensravAFC North1612400.7503782662.63.5396.43298.930.6776
2011Cincinnati BengalscinAFC North169700.5633443230.7-0.2366.03358.130.5199
2011Cleveland BrownscleAFC North1641200.250218307-7.21.8239.63326.130.3284
2011Pittsburgh SteelerspitAFC North1612400.750325227-0.86.0342.03258.930.6698
2011Houston TexanshtxAFC South1610600.6253812781.43.2377.23303.730.6393
2011Indianapolis ColtscltAFC South1621400.125243430-6.0-5.3258.83439.730.2127
2011Jacksonville JaguarsjaxAFC South1651100.313243329-7.11.4241.23332.530.3212
2011Tennessee TitansotiAFC South169700.563325317-2.21.2319.63335.730.4753
2011Denver BroncosdenAFC West168800.500309390-3.6-1.7297.23382.130.3527
2011Kansas City ChiefskanAFC West167900.438212338-10.22.1191.63321.330.2347
2011Oakland RaidersraiAFC West168800.5003594330.2-5.1358.03436.530.3790
2011Dallas CowboysdalNFC East168800.5003693470.70.9366.03340.530.5518
2011New York GiantsnygNFC East169700.5633944003.1-1.5404.43378.930.5484
2011Washington RedskinswasNFC East1651100.313288367-4.30.2286.03351.730.3804
2011Chicago BearschiNFC North168800.500353341-1.53.1330.83305.330.5555
2011Detroit LionsdetNFC North1610600.6254743876.9-0.8465.23367.730.6569
2011Green Bay PackersgnbNFC North1615100.93856035911.5-0.1538.83356.530.7589
2011Minnesota VikingsminNFC North1631300.188340449-1.6-4.1329.23420.530.3530
2011Atlanta FalconsatlNFC South1610600.6254023501.81.7383.63327.730.6050
2011Carolina PantherscarNFC South1661000.3754064292.6-3.9396.43417.330.4722
2011New Orleans SaintsnorNFC South1613300.81354733910.60.8524.43342.130.7642
2011Tampa Bay BuccaneerstamNFC South1641200.250287494-4.0-6.6290.83460.530.2397
2011Arizona CardinalscrdNFC West168800.500312348-1.7-0.5327.63362.930.4416
2011Seattle SeahawksseaNFC West167900.438321315-0.51.3346.83334.130.5295
2011St. Louis RamsramNFC West1621400.125193407-8.4-2.1220.43388.530.2053
2010Buffalo BillsbufAFC East1641200.250283425-1.5-3.1328.74402.040.3740
2010Miami DolphinsmiaAFC East167900.438273333-2.83.1307.94302.840.5106
2010New England PatriotsnweAFC East1614200.87551831312.62.8554.34307.640.8287
2010New York JetsnyjAFC East1611500.6883673042.24.2387.94285.240.6846
2010Baltimore RavensravAFC North1612400.7503572700.95.5367.14264.440.6929
2010Cincinnati BengalscinAFC North1641200.2503223950.4-1.9359.14382.840.4593
2010Cleveland BrownscleAFC North1651100.313271332-3.42.0298.34320.440.4565
2010Pittsburgh SteelerspitAFC North1612400.7503752322.57.7392.74229.240.7908
2010Houston TexanshtxAFC South1661000.3753904271.8-3.7381.54411.640.4508
2010Indianapolis ColtscltAFC South1610600.6254353883.7-0.9411.94366.840.5753
2010Jacksonville JaguarsjaxAFC South168800.500353419-1.2-3.3333.54405.240.3777
2010Tennessee TitansotiAFC South1661000.375356339-0.91.9338.34322.040.5312
2010Denver BroncosdenAFC West1641200.250344471-1.1-7.8335.14477.240.2831
2010Kansas City ChiefskanAFC West1610600.625366326-1.50.8328.74339.640.4799
2010Oakland RaidersraiAFC West168800.5004103712.3-2.2389.54387.640.5035
2010Dallas CowboysdalNFC East1661000.3753944362.5-4.7392.74427.640.4444
2010New York GiantsnygNFC East1610600.6253943471.70.4379.94346.040.5599
2010Washington RedskinswasNFC East1661000.375302377-3.4-0.5298.34360.440.3843
2010Chicago BearschiNFC North1611500.688334286-0.64.7343.14277.240.6288
2010Detroit LionsdetNFC North1661000.3753623692.4-0.5391.14360.440.5530
2010Green Bay PackersgnbNFC North1610600.6253882403.17.9402.34226.040.8065
2010Minnesota VikingsminNFC North1661000.375281348-3.31.7299.94325.240.4505
2010Atlanta FalconsatlNFC South1613300.8134142883.82.2413.54317.240.6641
2010Carolina PantherscarNFC South1621400.125196408-9.1-4.1207.14418.040.1505
2010New Orleans SaintsnorNFC South1611500.6883843071.50.8376.74339.640.5661
2010Tampa Bay BuccaneerstamNFC South1610600.625341318-1.00.4336.74346.040.4832
2010Arizona CardinalscrdNFC West1651100.313289434-5.6-7.1263.14466.040.1879
2010Seattle SeahawksseaNFC West167900.438310407-3.9-5.5290.34440.440.2559
2010St. Louis RamsramNFC West167900.438289328-6.3-0.4251.94358.840.2960
2009Buffalo BillsbufAFC East1661000.375258326-4.52.7271.47300.270.4395
2009Miami DolphinsmiaAFC East167900.4383603902.9-1.2389.87362.670.5466
2009New England PatriotsnweAFC East1610600.6254272856.74.5450.67271.470.7853
2009New York JetsnyjAFC East169700.5633482361.17.5361.07223.470.7623
2009Baltimore RavensravAFC North169700.5633912612.64.9385.07265.070.7173
2009Cincinnati BengalscinAFC North1610600.625305291-2.53.2303.47292.270.5230
2009Cleveland BrownscleAFC North1651100.313245375-6.0-2.4247.47381.870.2549
2009Pittsburgh SteelerspitAFC North169700.5633683241.00.7359.47332.270.5497
2009Houston TexanshtxAFC South169700.5633883332.7-0.7386.67354.670.5554
2009Indianapolis ColtscltAFC South1614200.8754163074.41.5413.87319.470.6604
2009Jacksonville JaguarsjaxAFC South167900.438290380-3.8-2.6282.67385.070.3153
2009Tennessee TitansotiAFC South168800.5003544020.9-3.6357.87401.070.4268
2009Denver BroncosdenAFC West168800.500326324-1.01.3327.47322.670.5092
2009Kansas City ChiefskanAFC West1641200.250294424-2.5-5.9303.47437.870.2801
2009Oakland RaidersraiAFC West1651100.313197379-8.7-1.6204.27369.070.1932
2009Dallas CowboysdalNFC East1611500.6883612500.46.7349.87236.270.7220
2009New York GiantsnygNFC East168800.5004024274.6-4.5417.07415.470.5026
2009Washington RedskinswasNFC East1641200.250266336-5.51.0255.47327.470.3538
2009Chicago BearschiNFC North167900.438327375-1.9-2.0313.07375.470.3871
2009Detroit LionsdetNFC North1621400.125262494-5.2-9.2260.27490.670.1628
2009Green Bay PackersgnbNFC North1611500.6884612976.31.1444.27325.870.6912
2009Minnesota VikingsminNFC North1612400.7504703126.60.6449.07333.870.6844
2009Atlanta FalconsatlNFC South169700.5633633252.72.3386.67306.670.6427
2009Carolina PantherscarNFC South168800.500315308-0.64.5333.87271.470.6241
2009New Orleans SaintsnorNFC South1613300.81351034111.2-0.5522.67351.470.7435
2009Tampa Bay BuccaneerstamNFC South1631300.188244400-4.6-1.1269.87361.070.3273
2009Arizona CardinalscrdNFC West1610600.6253753250.1-0.4345.07349.870.4913
2009Seattle SeahawksseaNFC West1651100.313280390-5.0-4.4263.47413.870.2429
2009St. Louis RamsramNFC West1611500.063175436-11.7-5.8156.27436.270.0758
2008Buffalo BillsbufAFC East167900.438336342-2.8-0.6307.67362.070.3972
2008Miami DolphinsmiaAFC East1611500.688345317-2.41.8314.07323.670.4794
2008New England PatriotsnweAFC East1611500.6884103092.31.6389.27326.870.6078
2008New York JetsnyjAFC East169700.5634053562.2-1.9387.67382.870.5062
2008Baltimore RavensravAFC North1611500.6883852444.25.6419.67262.870.7631
2008Cincinnati BengalscinAFC North1641110.281204364-6.9-0.1242.07354.070.2814
2008Cleveland BrownscleAFC North1641200.250232350-5.20.6269.27342.870.3539
2008Pittsburgh SteelerspitAFC North1612400.7503472231.68.2378.07221.270.7854
2008Houston TexanshtxAFC South168800.5003663942.8-3.2397.27403.670.4876
2008Indianapolis ColtscltAFC South1612400.7503772982.63.9394.07290.070.6823
2008Jacksonville JaguarsjaxAFC South1651100.313302367-2.1-0.4318.87358.870.4242
2008Tennessee TitansotiAFC South1613300.8133752341.57.5376.47232.470.7635
2008Denver BroncosdenAFC West168800.5003704480.7-6.5363.67456.470.3524
2008Kansas City ChiefskanAFC West1621400.125291440-3.9-5.3290.07437.270.2569
2008Oakland RaidersraiAFC West1651100.313263388-6.5-1.0248.47368.470.2730
2008Dallas CowboysdalNFC East169700.5633623651.7-1.2379.67371.670.5118
2008New York GiantsnygNFC East1612400.7504272945.52.8440.47307.670.7143
2008Washington RedskinswasNFC East168800.500265296-5.84.1259.67286.870.4389
2008Chicago BearschiNFC North169700.5633753501.11.0370.07336.470.5583
2008Detroit LionsdetNFC North1601600.000268517-4.0-9.1288.47498.070.1916
2008Green Bay PackersgnbNFC North1661000.3754193804.1-1.2418.07371.670.5744
2008Minnesota VikingsminNFC North1610600.6253793331.12.9370.07306.070.6153
2008Atlanta FalconsatlNFC South1611500.6883913251.32.5373.27312.470.6085
2008Carolina PantherscarNFC South1612400.7504143292.82.9397.27306.070.6580
2008New Orleans SaintsnorNFC South168800.5004633936.8-2.8461.27397.270.5965
2008Tampa Bay BuccaneerstamNFC South169700.563361323-0.62.9342.87306.070.5683
2008Arizona CardinalscrdNFC West169700.5634274264.1-6.0418.07448.470.4512
2008Seattle SeahawksseaNFC West1641200.250294392-4.9-2.8274.07397.270.2804
2008St. Louis RamsramNFC West1621400.125232465-8.1-7.0222.87464.470.1332
2007Buffalo BillsbufAFC East167900.438252354-5.61.5257.55322.950.3735
2007Miami DolphinsmiaAFC East1611500.063267437-4.1-4.2281.55414.150.2805
2007New England PatriotsnweAFC East1616001.00058927415.94.2601.55279.750.8940
2007New York JetsnyjAFC East1641200.250268355-4.00.3283.15342.150.3926
2007Baltimore RavensravAFC North1651100.313275384-5.0-1.8267.15375.750.3072
2007Cincinnati BengalscinAFC North167900.4383803851.6-4.0372.75410.950.4440
2007Cleveland BrownscleAFC North1610600.6254023822.2-3.3382.35399.750.4783
2007Pittsburgh SteelerspitAFC North1610600.6253932690.94.3361.55278.150.6646
2007Houston TexanshtxAFC South168800.5003793842.5-2.5387.15386.950.5076
2007Indianapolis ColtscltAFC South1613300.8134502626.65.4452.75260.550.8110
2007Jacksonville JaguarsjaxAFC South1611500.6884113044.82.0423.95314.950.6897
2007Tennessee TitansotiAFC South1610600.625301297-2.93.6300.75289.350.5308
2007Denver BroncosdenAFC West167900.438320409-0.2-3.8343.95407.750.3991
2007Kansas City ChiefskanAFC West1641200.250226335-7.41.9228.75316.550.3226
2007Oakland RaidersraiAFC West1641200.250283398-3.5-2.5291.15386.950.3355
2007Dallas CowboysdalNFC East1613300.8134553257.81.7471.95319.750.7421
2007New York GiantsnygNFC East1610600.6253733512.80.4391.95340.550.5966
2007Washington RedskinswasNFC East169700.5633343100.24.3350.35278.150.6462
2007Chicago BearschiNFC North167900.438334348-0.21.4343.95324.550.5437
2007Detroit LionsdetNFC North167900.4383464441.4-5.0369.55426.950.4138
2007Green Bay PackersgnbNFC North1613300.8134352915.73.3438.35294.150.7431
2007Minnesota VikingsminNFC North168800.5003653111.42.4369.55308.550.6190
2007Atlanta FalconsatlNFC South1641200.250259414-5.8-4.8254.35423.750.2239
2007Carolina PantherscarNFC South167900.438267347-5.7-0.1255.95348.550.3268
2007New Orleans SaintsnorNFC South167900.4383793881.9-4.5377.55418.950.4396
2007Tampa Bay BuccaneerstamNFC South169700.563334270-2.33.6310.35289.350.5500
2007Arizona CardinalscrdNFC West168800.5004043991.9-5.9377.55441.350.4057
2007Seattle SeahawksseaNFC West1610600.6253932910.80.9359.95332.550.5573
2007St. Louis RamsramNFC West1631300.188263438-6.5-6.5243.15450.950.1803
2006Buffalo BillsbufAFC East167900.438300311-0.22.4327.33292.080.5747
2006Miami DolphinsmiaAFC East1661000.375260283-3.34.0277.73266.480.5296
2006New England PatriotsnweAFC East1612400.7503852374.35.9399.33236.080.7913
2006New York JetsnyjAFC East1610600.6253162950.41.7336.93303.280.5699
2006Baltimore RavensravAFC North1613300.8133532011.57.8354.53205.680.7922
2006Cincinnati BengalscinAFC North168800.5003733314.00.0394.53330.480.6165
2006Cleveland BrownscleAFC North1641200.250238356-4.5-1.3258.53351.280.3253
2006Pittsburgh SteelerspitAFC North168800.5003533153.00.4378.53324.080.6024
2006Houston TexanshtxAFC South1661000.375267366-3.2-1.3279.33351.280.3669
2006Indianapolis ColtscltAFC South1612400.7504273606.9-1.1440.93348.080.6548
2006Jacksonville JaguarsjaxAFC South168800.5003712742.64.9372.13252.080.7284
2006Tennessee TitansotiAFC South168800.5003244001.0-2.3346.53367.280.4680
2006Denver BroncosdenAFC West169700.563319305-0.82.1317.73296.880.5466
2006Kansas City ChiefskanAFC West169700.5633313150.40.6336.93320.880.5355
2006Oakland RaidersraiAFC West1621400.125168332-10.30.7165.73319.280.1843
2006Dallas CowboysdalNFC East169700.5634253505.0-1.3410.53351.280.6047
2006New York GiantsnygNFC East168800.5003553621.2-1.1349.73348.080.5080
2006Washington RedskinswasNFC East1651100.313307376-2.1-2.0296.93362.480.3828
2006Chicago BearschiNFC North1613300.8134272554.93.0408.93282.480.7233
2006Detroit LionsdetNFC North1631300.188305398-1.8-4.6301.73404.080.3273
2006Green Bay PackersgnbNFC North168800.500301366-2.3-2.1293.73364.080.3739
2006Minnesota VikingsminNFC North1661000.375282327-3.7-0.4271.33336.880.3754
2006Atlanta FalconsatlNFC South167900.438292328-2.8-0.2285.73333.680.4106
2006Carolina PantherscarNFC South168800.500270305-4.21.5263.33306.480.4145
2006New Orleans SaintsnorNFC South1610600.6254133224.9-0.9408.93344.880.6134
2006Tampa Bay BuccaneerstamNFC South1641200.250211353-7.2-0.8215.33343.280.2510
2006Arizona CardinalscrdNFC West1651100.313314389-2.6-4.3288.93399.280.3112
2006Seattle SeahawksseaNFC West169700.563335341-1.6-1.9304.93360.880.4009
2006St. Louis RamsramNFC West168800.5003673810.8-4.7343.33405.680.3989
2005Buffalo BillsbufAFC East1651100.313271367-4.0-1.8265.68358.630.3255
2005Miami DolphinsmiaAFC East169700.563318317-1.10.3312.08325.030.4774
2005New England PatriotsnweAFC East1610600.6253793383.7-0.5388.88337.830.5918
2005New York JetsnyjAFC East1641200.250240355-5.2-1.2246.48349.030.3023
2005Baltimore RavensravAFC North1661000.375265299-3.51.7273.68302.630.4420
2005Cincinnati BengalscinAFC North1611500.6884213506.5-2.7433.68373.030.6003
2005Cleveland BrownscleAFC North1661000.375232301-6.01.7233.68302.630.3536
2005Pittsburgh SteelerspitAFC North1611500.6883892583.84.0390.48265.830.7259
2005Houston TexanshtxAFC South1621400.125260431-4.4-5.7259.28421.030.2301
2005Indianapolis ColtscltAFC South1614200.8754392475.65.2419.28246.630.7935
2005Jacksonville JaguarsjaxAFC South1612400.7503612691.13.7347.28270.630.6514
2005Tennessee TitansotiAFC South1641200.250299421-2.0-5.5297.68417.830.2988
2005Denver BroncosdenAFC West1613300.8133952585.05.8409.68237.030.7987
2005Kansas City ChiefskanAFC West1610600.6254033255.11.9411.28299.430.6944
2005Oakland RaidersraiAFC West1641200.250290383-1.2-1.6310.48355.430.4186
2005Dallas CowboysdalNFC East169700.563325308-0.13.2328.08278.630.6014
2005New York GiantsnygNFC East1611500.6884223145.81.7422.48302.630.7041
2005Washington RedskinswasNFC East1610600.6253592932.63.4371.28275.430.6803
2005Chicago BearschiNFC North1611500.688260202-5.26.6246.48224.230.5568
2005Detroit LionsdetNFC North1651100.313254345-4.3-2.4260.88368.230.3015
2005Green Bay PackersgnbNFC North1641200.250298344-1.5-2.2305.68365.030.3929
2005Minnesota VikingsminNFC North169700.563306344-1.4-2.1307.28363.430.3987
2005Atlanta FalconsatlNFC South168800.5003513411.1-2.3347.28366.630.4681
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1999Indianapolis ColtscltAFC East1613300.8134233336.6-0.5438.63341.080.6543
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1999Chicago BearschiNFC Central1661000.375272341-3.01.0285.03317.080.4312
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1999Green Bay PackersgnbNFC Central168800.5003573412.5-0.9373.03347.480.5412
1999Minnesota VikingsminNFC Central1610600.6253993355.2-0.8416.23345.880.6137
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1999Atlanta FalconsatlNFC West1651100.313285380-4.0-3.0269.03381.080.2916
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1999New Orleans SaintsnorNFC West1631300.188260434-5.3-6.9248.23443.480.1831
1999St. Louis RamsramNFC West1613300.8135262428.73.2472.23281.880.7875
1998Baltimore RavensravAFC Central1661000.375269335-5.2-0.2257.35343.590.3389
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1998Pittsburgh SteelerspitAFC Central167900.438263303-5.11.3258.95319.590.3838
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1998Indianapolis ColtscltAFC East1631300.188310444-0.1-5.3338.95425.190.3656
1998Miami DolphinsmiaAFC East1610600.625321265-0.76.5329.35236.390.6983
1998New England PatriotsnweAFC East169700.5633373291.12.8358.15295.590.6261
1998New York JetsnyjAFC East1612400.7504162665.45.8426.95247.590.8060
1998Denver BroncosdenAFC West1614200.8755013099.5-0.6492.55349.990.7211
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1998Oakland RaidersraiAFC West168800.500288356-4.1-1.5274.95364.390.3405
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1998Chicago BearschiNFC Central1641200.250276368-3.4-0.3286.15345.190.3945
1998Detroit LionsdetNFC Central1651100.313306378-1.9-1.5310.15364.390.4085
1998Green Bay PackersgnbNFC Central1611500.6884083194.30.7409.35329.190.6451
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1998Arizona CardinalscrdNFC East169700.563325378-1.6-5.8314.95433.190.3137
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1998Atlanta FalconsatlNFC West1614200.8754422897.03.0452.55292.390.7637
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1998New Orleans SaintsnorNFC West1661000.375305359-1.51.6316.55314.790.5120
1998St. Louis RamsramNFC West1641200.250285378-2.30.0303.75340.390.4382
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1997Indianapolis ColtscltAFC East1631300.188313401-0.6-3.8322.41392.650.3771
1997Miami DolphinsmiaAFC East169700.5633393271.00.3348.01327.050.5393
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1996Baltimore RavensravAFC Central1641200.2503714413.9-6.8389.18435.630.4254
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1987Green Bay PackersgnbNFC Central155910.367255300-5.41.8242.96297.020.3829
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1979St. Louis CardinalscrdNFC East1651100.313307358-0.7-2.0309.95352.920.4211
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1978Pittsburgh SteelerspitAFC Central1614200.8753561952.65.6334.86203.720.7660
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1977Cleveland BrownscleAFC Central146800.4292692672.40.1274.06239.060.5856
1977Houston OilersotiAFC Central148600.5712992304.42.3302.06208.260.7148
1977Pittsburgh SteelerspitAFC Central149500.6432832433.92.3295.06208.260.7023
1977Baltimore ColtscltAFC East1410400.7142952213.61.5290.86219.460.6679
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1977Miami DolphinsmiaAFC East1410400.7143131974.43.5302.06191.460.7531
1977New England PatriotsnweAFC East149500.6432782172.51.5275.46219.460.6369
1977New York JetsnyjAFC East1431100.214191300-3.8-2.0187.26268.460.3027
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Now, as an aside, I wouldn’t go plugging those directly into the log5 formula to predict this weekend’s games just yet. You first need to regress to the mean to account for the uncertainty we see in any observed result. To do that, just add about 17.65 games of .500 performance to each team’s pythagorean Wpct, and you’ll get a “true talent” number that should yield more accurate probabilities regarding future outcomes.

• Neil

According to SOS-adjusted Pythagorean ratings, the 2012 Colts (.374 pyth%) are:

By far the worst team ever to win 11 games (next-worst were the .438 2004 Falcons)
Also the worst team ever to win 10+ games (next-worst were the .404 1979 Bucs)
Also the fourth-worst team ever to win 9+ games (behind only 1992 Indy, 1998 Arizona, and 1978 Atlanta)

Then again, both the ’04 Falcons and ’79 Bucs won their 1st playoff games, so apparently all is not lost for Indy vs. Baltimore.

• dan

Sea 2012 in top 20 all-time. Awesome! have been beating their drum for a long time! #gohawks

• George

Really interesting post. I haven’t really looked into the Pythagorean Formula too much (I did a little bit of investigating into trying to use it for European Soccer and it didn’t work out too well because of the volume of tied games).

Out of interest is there an easier way of doing OSRS and DSRS without resorting to Matrix’s (or Matrices) (as I can see how everything else above would work with the data)? I’m assuming doing it with Matrix’s, it would be SRS*Matrix of Total Games Played (with games played is on the diagonal to get (T*SRS)). T*SRS – Points Scored, to get (T*SRS)-F, and then to calculate DSRS it would be the inverse of a matrix of (Total Games Played+Pairwise Matches between teams)*(T*SRS-F) so (T*SRS-F) is effectively the right hand side vector?. And then SRS – DSRS to get OSRS? I’m not 100% on the maths (as I’m not great at it) but I’ve got something to work fairly similarly in Excel and just wondered if there was a tidier way of doing it?

• What I do is set up the matrix in Excel, then feed it into R and run an OLS regression.

For basic SRS, you need to create a 257 x 32 (or more) matrix with games as the rows and team variables as the columns. For each game, the home team will be a dummy variable with value 1, the road team will be -1, and all other teams will take a value of 0. You can also add dummies for home-field advantage, or anything else you want to throw in. The dependent variable will be score margin for each game. To avoid singularities, you must also add a row of all 0’s to the end of the matrix. Run a regression predicting score margin from all of your variables, and the resulting coefficients should be the SRS values.

If you want offense/defense, just split each team into 2 variables, one for each side of the ball, and predict home/away points vs average in each game setting the appropriate team dummies to 1 or -1.

• George

Thanks – this is really helpful. I had bought the Meyer book after you mentioned it a while back and figured out how to do it that way (as I hadn’t figured out how to do the SRS at that point by the other way that you’d mentioned on the PFR blog) and I set up about 4 or 5, 32×32 matrix’s with various combination’s (total games, games between teams with a 1 or -1 etc.) and did it step by step by step to get a rating (didn’t get the maths behind it but could get the figures to match the example so knew I had the procedure right). I just wondered if there was a way of avoiding using matrix’s (as I ended up using large formulas to get the numbers right in the matrix’s) to break it down into OSRS or DSRS.

Incidentally re: the Colts totally agree, I just don’t get how a team that I’d say on performance isn’t in the top 20 teams in the league have made it into the playoffs (I’ve only really started looking at this thing in the last year and it just struck me that the Colts that I have about 5 points below the average are there).

• lucky irvin

Salute!