Tuesday, October 30, 2007

Predictions 2007 Week 9 and Accuracy Report

The predictions are based on yards per play on rushing and passing plays (sacks and sack yards included), sack rates, third down conversion rates, penalty yards per game, and fumble and interception rates. The models are trained on the 1996-2006 seasons. Linear regression predicts the final score margin (home team points - away team points). Logistic regression estimates the probability that the home team will win.


The predictions are based on yards per play on rushing and passing plays (sacks and sack yards included), sack rates, third down conversion rates, penalty yards per game, and fumble and interception rates. The models are trained on the 1996-2006 seasons. Linear regression predicts the final score margin (home team points - away team points). Logistic regression estimates the probability that the home team will win.


















Predictions based on opponent-adjusted stats
GamePredicted Final Score MarginP(Home Team Wins)
CIN @ BUF1.004552.7523
WAS @ NYJ-3.220539.4645
SEA @ CLE1.353753.5113
BAL @ PIT7.539275.2282
NE @ IND2.904761.2232
CAR @ TEN5.564167.9738
GB @ KC-0.930948.7180
HOU @ OAK1.155852.2015
DAL @ PHI-1.750943.1141
DEN @ DET2.194255.9526
SD @ MIN1.312857.3044
SF @ ATL5.207066.1927
JAX @ NO-0.492749.1553
ARI @ TB7.859973.8157




















Predictions based on unadjusted stats
GamePredicted Final Score MarginP(Home Team Wins)
CIN @ BUF1.393155.0238
WAS @ NYJ-2.939040.8522
SEA @ CLE1.234453.1285
BAL @ PIT7.510675.0971
NE @ IND1.949158.4803
CAR @ TEN5.070667.4653
GB @ KC-0.249251.1181
HOU @ OAK2.425554.9057
DAL @ PHI-0.584246.7032
DEN @ DET6.257266.6293
SD @ MIN0.714253.3107
SF @ ATL5.601467.5739
JAX @ NO-0.074050.9851
ARI @ TB6.055270.9135


Quick Summary of Accuracy
LAST WEEK
Linear regression, opponent adjusted: 6 out of 13
Logistic regression, opponent adjusted: 5 out of 13
Linear regression, unadjusted: 8 out of 13
Logistic regression, unadjusted: 8 out of 13

YEAR SO FAR
Linear regression, opponent adjusted: 66.6667%
Logistic regression, opponent adjusted: 65.4762%
Linear regression, unadjusted: 61.9048%
Logistic regression, unadjusted: 63.0952%

Full accuracy numbers after the jump...

OPPONENT ADJUSTED
Linear regression
Win prediction accuracy: 66.6667%
Mean absolute error: 11.2464 points
Correlation with result: 0.3735
% of games predicted as home team wins: 69.0476%
Logistic regression
Win prediction accuracy: 65.4762%
Correlation with result: 0.3749
% of games predicted as home team wins: 72.6190%
Win prediction accuracy when 20%≤P(home team wins)<30%: 100.0000
Win prediction accuracy when 30%≤P(home team wins)<40%: 88.8889
Win prediction accuracy when 40%≤P(home team wins)<50%: 58.3333
Win prediction accuracy when 50%≤P(home team wins)<60%: 50.0000
Win prediction accuracy when 60%≤P(home team wins)<70%: 76.4706
Win prediction accuracy when 70%≤P(home team wins)<80%: 58.8235
Win prediction accuracy when 80%≤P(home team wins)<90%: 80.0000

UNADJUSTED
Linear regression
Win prediction accuracy: 61.9048%
Mean absolute error: 11.1272 points
Correlation with result: 0.3770
% of games predicted as home team wins: 64.2857%
Logistic regression
Win prediction accuracy: 63.0952%
Correlation with result: 0.3777
% of games predicted as home team wins: 63.0952%
Win prediction accuracy when 10%≤P(home team wins)<20%: 100.0000
Win prediction accuracy when 20%≤P(home team wins)<30%: 100.0000
Win prediction accuracy when 30%≤P(home team wins)<40%: 66.6667
Win prediction accuracy when 40%≤P(home team wins)<50%: 50.0000
Win prediction accuracy when 50%≤P(home team wins)<60%: 42.8571
Win prediction accuracy when 60%≤P(home team wins)<70%: 70.5882
Win prediction accuracy when 70%≤P(home team wins)<80%: 78.5714
Win prediction accuracy when 80%≤P(home team wins)<90%: 42.8571
Win prediction accuracy when 90%≤P(home team wins)<100%: 100.0000

Read More......

Power Rankings 2007 Week 8

The power rankings for this site were developed in this article. The idea behind them is simple: if each team played one home game and one away game against every other team in the league, who would be the most successful?

The power rankings use logistic regression to predict the probability of winning. The score you see along with the rankings is the expected win total over a 16-game season based on the expected winning percentages over the 62 games (i.e. the sum of those probabilities).

San Diego is making a huge comeback to #6 after being bottom of the barrel to start. The Saints are climbing upwards from dead last towards mediocrity.



































Power Rankings, Opponent-adjusted
RankTeamExpected Wins
1NE11.5856
2IND11.5305
3DAL11.0685
4TB10.0434
5PIT9.6449
6SD8.9480
7TEN8.8901
8NYG8.8737
9WAS8.8413
10PHI8.6632
11SEA8.6215
12JAX8.6040
13GB8.4589
14MIN8.3500
15CIN7.9932
16DEN7.8561
17CLE7.7744
18ARI7.6103
19MIA7.5862
20CAR7.3970
21DET7.3160
22HOU7.2904
23BAL6.9235
24KC6.9199
25NO6.8708
26ATL6.7046
27BUF6.6202
28CHI6.1950
29OAK6.1287
30STL6.0256
31NYJ5.4028
32SF5.2618

Read More......

The Value of Homefield Advantage 2007 Week 8

One of the things I've learned in my football research is that the value of home-field advantage varies pretty widely from year to year, especially with interconference games. Because prediction systems tend to have a big bias towards the home team, this can have a large impact on accuracy. So throughout the season, I'll be keeping track of home team winning percentage and average final score margin (home team points - away team points) for interconference, interdivision, and intradivision matchups. If you're interested in that sort of thing, it can help you with betting on the spread (hint).

Home field advantage dropped off 3% after this week, with interconference HFA taking the biggest hit. Only 41% of divisional games have been won by the home team so far, dropping even further from last week. Bizarre. HFA is still strong in interdivisional games, though (good news for Indy).

All Games
Home Team Win %: 55.1724%
Avg. Final Score Margin: 1.6983

Interconference
Home Team Win %: 59.3750%
Avg. Final Score Margin: 3.3125

Interdivision, Intraconference
Home Team Win %: 65.8537%
Avg. Final Score Margin: 4.0976

Intradivsion
Home Team Win %: 41.8605%
Avg. Final Score Margin: -1.7907

Read More......

Projected Final Standings 2007 Week 8

Using the projected win probabilities from the logistic regression power rankings, I estimated which games each team would win on the rest of their respective schedules. And then I summed the projected wins with the actual wins so far to get their projected win totals. The teams are sorted by division.




















































Projected Final Standings
TeamProjected Win Total
AFC East
BUF5
MIA4
NE15
NYJ2
AFC North
BAL6
CIN7
CLE9
PIT13
AFC South
HOU6
IND16
JAX10
TEN11
AFC West
DEN8
KC6
OAK4
SD9
NFC East
DAL15
NYG11
PHI8
WAS8
NFC North
CHI4
DET8
GB13
MIN8
NFC South
ATL3
CAR7
NO5
TB12
NFC West
ARI8
STL1
SF3
SEA11

Read More......

Stats (Raw and VOLA) 2007 Week 8

This is the data I use to make my predictions and power rankings. Below are the tables for the raw stats and the values over league average for all of the inputs I use. Rush and pass stats are yards per play. See for yourself where your team's strengths and weaknesses are.






































Rush offense, Unadjusted (League Avg = 4.0915)
RankTeamVOLA (%)Actual Stat
1MIN26.51105.1762
2MIA18.60304.8526
3DAL17.18804.7947
4PIT16.35604.7607
5NYG13.64604.6498
6CLE11.75004.5722
7DEN11.00304.5417
8PHI10.97504.5405
9IND8.11304.4234
10JAX8.02724.4199
11OAK7.56254.4009
12CAR7.13714.3835
13SD3.00994.2146
14NE2.48244.1930
15DET2.29624.1854
16TB1.44214.1505
17SF1.04474.1342
18TEN0.42694.1089
19BAL-4.46913.9086
20CIN-4.62383.9023
21ATL-4.63503.9018
22ARI-6.86693.8105
23NO-11.84803.6067
24BUF-12.01203.6000
25SEA-13.79903.5269
26WAS-14.04703.5168
27NYJ-14.98303.4785
28STL-15.48603.4579
29GB-17.59403.3716
30KC-20.15003.2670
31HOU-20.90403.2362
32CHI-22.88903.1550




































Rush defense, Unadjusted (League Avg = 4.0915)
RankTeamVOLA (%)Actual Stat
1BAL28.93702.9075
2MIN28.86202.9106
3TEN17.23403.3864
4WAS11.17403.6343
5NO11.15903.6349
6DAL10.87103.6467
7PHI10.57103.6590
8SD9.66833.6959
9PIT7.02163.8042
10GB6.96213.8066
11TB5.64633.8605
12CAR4.99153.8873
13SF4.98833.8874
14DET4.97933.8878
15SEA2.75323.9788
16KC2.10734.0053
17NYJ0.94474.0528
18IND0.65064.0649
19STL0.02284.0906
20NYG-0.02024.0923
21ARI-2.43864.1913
22JAX-3.05964.2167
23ATL-3.99184.2548
24NE-4.06184.2577
25MIA-9.72824.4895
26HOU-11.25304.5519
27CHI-12.23604.5921
28BUF-14.52704.6859
29CLE-14.68504.6923
30CIN-14.88504.7005
31DEN-20.85304.9447
32OAK-28.62405.2626




































Pass offense, Unadjusted (League Avg = 6.1566)
RankTeamVOLA (%)Actual Stat
1NE40.46208.6477
2DAL23.51007.6040
3IND23.01007.5732
4CLE17.06007.2069
5DEN15.71207.1239
6HOU13.53806.9901
7CIN13.20906.9698
8TB12.66006.9360
9GB12.10306.9017
10SD12.07506.9000
11PIT10.41906.7980
12SEA4.39026.4269
13ARI3.46066.3696
14PHI-0.54356.1231
15DET-0.79706.1075
16NO-4.67195.8690
17KC-4.91895.8538
18WAS-5.10025.8426
19JAX-5.83915.7971
20NYG-6.58935.7509
21NYJ-6.64955.7472
22MIA-7.43865.6986
23CHI-10.19905.5287
24BUF-12.34105.3968
25OAK-12.39405.3935
26ATL-12.78605.3694
27CAR-12.89805.3625
28TEN-13.08105.3512
29BAL-13.23905.3415
30STL-16.36505.1491
31MIN-20.07104.9209
32SF-38.03703.8148




































Pass defense, Unadjusted (League Avg = 6.1566)
RankTeamVOLA (%)Actual Stat
1IND22.27604.7852
2NE17.24705.0948
3PIT15.83305.1818
4WAS13.88505.3018
5NYG13.59105.3199
6TB12.80505.3682
7TEN10.40105.5162
8ARI9.97445.5425
9KC9.51415.5708
10SEA9.07725.5977
11DAL9.01575.6015
12PHI5.86885.7953
13OAK2.77675.9856
14GB1.29896.0766
15SF-1.46796.2470
16DET-1.96846.2778
17JAX-2.11636.2869
18BAL-2.29956.2982
19HOU-3.61756.3793
20SD-3.81776.3916
21CAR-4.13706.4113
22CHI-5.95636.5233
23BUF-7.45676.6157
24MIN-9.25966.7267
25CLE-10.32306.7921
26STL-10.47806.8017
27ATL-11.31706.8533
28CIN-13.89707.0122
29NO-16.39507.1660
30MIA-17.07607.2079
31DEN-19.14407.3352
32NYJ-28.66707.9215




































Sack rate made, Unadjusted (League Avg = 6.0561%)
RankTeamVOLA (%)Actual Stat
1NYG55.67109.4276
2PHI49.52009.0551
3CHI47.95908.9606
4SEA42.77508.6466
5KC40.38808.5021
6PIT29.64207.8513
7DEN29.14607.8212
8JAX28.57907.7869
9NE27.46307.7193
10DAL13.87806.8966
11ARI13.64706.8826
12BAL13.61606.8807
13DET8.93496.5972
14GB7.55106.5134
15SD6.73316.4639
16TB2.40156.2015
17MIN-0.92656.0000
18WAS-7.29975.6140
19OAK-13.09305.2632
20TEN-16.54505.0541
21HOU-17.75504.9808
22IND-18.12104.9587
23STL-18.12104.9587
24MIA-18.25604.9505
25CIN-19.45204.8781
26SF-19.77904.8583
27NO-20.68404.8035
28ATL-33.95104.0000
29NYJ-45.41403.3058
30BUF-50.71002.9851
31CLE-58.57102.5090
32CAR-73.36701.6129




































Sack rate allowed, Unadjusted (League Avg = 6.0561%)
RankTeamVOLA (%)Actual Stat
1NO77.22401.3793
2IND65.45602.0920
3NE52.99002.8470
4ARI48.60003.1128
5BAL47.67203.1690
6NYG45.56403.2967
7CIN37.69003.7736
8GB30.47504.2105
9HOU28.92104.3046
10DAL27.34604.4000
11MIA20.83204.7945
12TB20.74104.8000
13DEN19.63104.8672
14SD17.43905.0000
15CAR17.43905.0000
16TEN11.39805.3658
17WAS8.26535.5556
18CLE7.47455.6034
19SEA-4.42536.3241
20CHI-10.43206.6879
21NYJ-22.76807.4350
22PIT-27.01707.6923
23STL-28.20107.7640
24KC-30.53207.9052
25BUF-39.78608.4656
26MIN-45.92208.8372
27JAX-51.56209.1788
28ATL-54.03209.3284
29PHI-66.355010.0746
30OAK-75.825010.6482
31SF-76.674010.6996
32DET-95.306011.8279




































Third down % converted, Unadjusted (League Avg = 40.9772%)
RankTeamVOLA (%)Actual Stat
1PIT34.470055.1020
2IND31.616053.9325
3NE19.181048.8370
4DEN17.500048.1482
5NO14.698047.0000
6DAL14.061046.7390
7CLE12.201045.9768
8HOU11.146045.5445
9TEN6.766743.7500
10NYG6.618643.6893
11NYJ4.587842.8572
12SD4.162642.6829
13JAX1.682641.6667
14PHI1.481241.5842
15OAK0.900441.3462
16ATL0.352141.1215
17BAL0.230041.0714
18CIN-0.577040.7407
19GB-0.775740.6593
20TB-1.346340.4255
21CAR-2.858639.8058
22MIA-3.401639.5833
23ARI-5.943638.5417
24CHI-9.295637.1681
25WAS-12.660035.7895
26STL-12.684035.7797
27KC-14.587034.9999
28SEA-15.117034.7827
29BUF-21.559032.1429
30MIN-24.524030.9280
31SF-25.294030.6124
32DET-27.692029.6298




































Third down % allowed, Unadjusted (League Avg = 40.9772%)
RankTeamVOLA (%)Actual Stat
1NE29.874028.7357
2BAL19.519032.9789
3KC16.923034.0426
4GB16.923034.0426
5WAS15.229034.7368
6CHI11.455036.2833
7PHI9.705937.0000
8TEN8.157737.6344
9ATL8.126837.6471
10STL6.328838.3838
11OAK4.397439.1753
12JAX3.519839.5349
13SEA2.858639.8058
14DAL1.854240.2174
15NYG0.577040.7407
16SD0.032640.9639
17ARI-0.055641.0000
18TB-3.085142.2414
19SF-4.249342.7184
20CIN-5.380143.1818
21CLE-5.666043.2990
22MIN-6.313743.5644
23HOU-7.376844.0000
24CAR-8.181944.3299
25PIT-8.461444.4444
26NO-10.211045.1614
27BUF-11.409045.6523
28IND-12.835046.2366
29DET-13.214046.3919
30DEN-17.713048.2355
31NYJ-18.245048.4535
32MIA-22.019050.0000




































Int. Rate Given, Unadjusted (League Avg = 2.8921%)
RankTeamVOLA (%)Actual Stat
1PHI74.19600.7463
2JAX66.59200.9662
3NE63.08501.0676
4IND56.59801.2552
5BAL51.30001.4085
6ATL48.39301.4925
7TB44.67701.6000
8CAR42.37201.6667
9GB39.33901.7544
10SEA17.99902.3716
11SF14.62502.4691
12KC4.33262.7668
13WAS3.95302.7778
14MIN3.50632.7907
15DET0.85472.8674
16PIT0.25892.8846
17TEN-1.20082.9268
18BUF-9.76803.1746
19NYG-13.99003.2967
20CIN-17.43103.3962
21NO-19.23103.4483
22SD-21.01903.5000
23DEN-22.39603.5398
24DAL-24.47703.6000
25MIA-30.25603.7671
26CLE-34.13503.8793
27ARI-34.54103.8911
28HOU-37.39203.9735
29NYJ-41.39304.0892
30OAK-44.07104.1667
31STL-71.81104.9689
32CHI-76.18805.0955




































Int. Rate Taken, Unadjusted (League Avg = 2.8921%)
RankTeamVOLA (%)Actual Stat
1OAK65.44004.7847
2BAL58.61004.5872
3DET56.07604.5139
4SD44.61804.1825
5BUF41.92004.1045
6TEN37.30903.9711
7NE33.45503.8597
8DAL32.47903.8314
9IND28.59203.7190
10DEN15.90003.3519
11JAX13.36703.2787
12CIN12.44503.2520
13KC11.99003.2389
14ATL7.57263.1111
15SEA3.99073.0075
16WAS-2.94202.8070
17TB-6.18662.7132
18NYJ-14.27202.4793
19PIT-14.27202.4793
20ARI-16.00702.4292
21NYG-18.50602.3569
22MIN-19.32102.3333
23GB-20.51302.2988
24CLE-25.64102.1505
25STL-28.56002.0661
26CAR-30.28802.0161
27MIA-31.53101.9802
28PHI-31.93501.9685
29SF-44.00501.6194
30HOU-47.00901.5326
31CHI-50.42701.4337
32NO-54.70301.3100




































Fum. Rate Given, Unadjusted (League Avg = 3.0151%)
RankTeamVOLA (%)Actual Stat
1SEA52.07101.4451
2BUF48.81701.5432
3IND47.63201.5789
4NE36.21801.9231
5ATL31.71602.0588
6SD31.51402.0649
7NYJ31.26102.0725
8PHI25.67702.2409
9NYG24.62102.2727
10DAL24.40602.2792
11CIN23.75502.2988
12PIT20.18702.4064
13NO19.75802.4194
14MIA19.10602.4390
15STL12.94802.6247
16TB11.31902.6738
17JAX8.88282.7473
18MIN8.43562.7607
19KC3.58532.9070
20BAL-4.46193.1496
21TEN-11.70103.3679
22CLE-15.45403.4810
23DEN-15.69803.4884
24CAR-21.79803.6723
25GB-26.44203.8123
26HOU-30.06503.9216
27ARI-35.37404.0816
28CHI-43.83504.3367
29DET-60.63604.8433
30SF-73.34505.2265
31WAS-75.07305.2786
32OAK-94.01105.8496




































Fum. Rate Taken, Unadjusted (League Avg = 3.0151%)
RankTeamVOLA (%)Actual Stat
1DET81.50905.4726
2SEA48.23104.4693
3TEN43.72204.3333
4PIT36.77004.1237
5SD34.58904.0580
6IND33.42904.0230
7DAL32.26003.9877
8NYG31.96303.9788
9WAS29.70203.9106
10MIN28.55303.8760
11CAR21.79803.6723
12HOU19.98303.6176
13GB17.75103.5503
14CHI1.69033.0660
15NO-0.10043.0120
16STL-1.72842.9630
17MIA-2.68952.9340
18NE-3.02142.9240
19TB-6.57282.8169
20CIN-11.31902.6738
21BUF-18.44302.4590
22JAX-20.79602.3881
23ARI-21.49902.3669
24KC-23.31402.3121
25BAL-23.37702.3102
26ATL-25.67702.2409
27DEN-26.90502.2039
28CLE-38.74201.8470
29PHI-39.69701.8182
30SF-48.44601.5544
31NYJ-69.07500.9324
32OAK-69.57200.9174




































Rush offense, Adjusted (League Avg = 4.0915)
RankTeamVOLA (%)Actual Stat
1MIN27.65705.2231
2DAL18.41204.8448
3PHI16.82504.7799
4NYG16.65904.7731
5MIA12.23304.5920
6CLE8.89164.4553
7PIT8.26794.4298
8IND8.18534.4264
9SF7.30204.3902
10CAR7.14014.3836
11DEN5.80704.3291
12TB5.27024.3071
13ATL4.69234.2835
14JAX4.42604.2726
15DET1.86194.1677
16OAK1.61734.1577
17ARI0.75664.1224
18NE0.01234.0920
19CIN-2.48223.9899
20TEN-4.45483.9092
21BUF-7.28013.7936
22SD-8.42273.7469
23NO-8.59863.7397
24BAL-9.53233.7015
25STL-10.51603.6612
26SEA-12.19103.5927
27WAS-13.10403.5553
28CHI-13.69203.5313
29NYJ-14.89603.4820
30GB-16.88203.4008
31HOU-18.74503.3245
32KC-23.64403.1241




































Rush defense, Adjusted (League Avg = 4.0915)
RankTeamVOLA (%)Actual Stat
1MIN25.36903.0535
2BAL24.02903.1083
3TEN16.98103.3967
4WAS13.99703.5188
5DAL12.19503.5925
6NO11.45703.6227
7GB10.35303.6679
8PIT4.27623.9165
9DET4.06293.9252
10PHI3.86943.9332
11SF3.80563.9358
12TB2.87443.9739
13STL2.69083.9814
14NYJ2.58033.9859
15IND2.50233.9891
16SEA0.88344.0553
17NYG0.67434.0639
18ATL0.34694.0773
19KC-0.36634.1065
20NE-1.44364.1505
21CAR-1.77404.1641
22SD-1.84504.1670
23JAX-3.63794.2403
24CHI-5.79254.3285
25ARI-6.63204.3628
26HOU-7.53814.3999
27MIA-8.94234.4574
28CLE-10.39104.5166
29BUF-11.44204.5596
30CIN-16.80104.7789
31DEN-17.72104.8165
32OAK-25.31905.1274




































Pass offense, Adjusted (League Avg = 6.1566)
RankTeamVOLA (%)Actual Stat
1NE34.00308.2500
2DAL21.77807.4974
3IND21.34407.4707
4DEN19.93007.3836
5CIN16.88207.1959
6CLE16.43907.1687
7TB14.71407.0625
8HOU14.60607.0558
9SD12.24206.9103
10GB10.42306.7983
11ARI8.15136.6584
12PIT5.53046.4971
13SEA3.28666.3589
14NO1.05006.2212
15DET-0.34486.1354
16WAS-0.37786.1333
17JAX-3.26765.9554
18PHI-3.80745.9222
19MIA-5.73325.8036
20NYG-6.82105.7367
21NYJ-7.10535.7191
22KC-9.59865.5656
23CHI-9.79135.5538
24TEN-10.73605.4956
25CAR-10.87505.4871
26OAK-13.29205.3383
27ATL-14.95005.2362
28STL-14.95005.2362
29BUF-17.65105.0699
30BAL-18.90904.9924
31MIN-19.71604.9428
32SF-35.02004.0006




































Pass defense, Adjusted (League Avg = 6.1566)
RankTeamVOLA (%)Actual Stat
1IND21.74504.8178
2NE21.03504.8616
3WAS19.00804.9863
4TEN14.16205.2847
5PIT12.76305.3708
6TB10.45605.5129
7NYG9.79715.5534
8KC8.89245.6091
9SEA8.83265.6128
10DAL7.96505.6662
11OAK7.36715.7030
12JAX4.15395.9009
13SD3.63025.9331
14BUF1.72236.0506
15PHI0.33866.1357
16ARI-0.06036.1603
17GB-1.44806.2457
18CHI-2.32886.3000
19MIA-2.79206.3285
20CAR-3.75386.3877
21SF-7.71336.6315
22CIN-8.34846.6706
23BAL-8.54726.6828
24DET-8.62106.6874
25HOU-8.66696.6902
26MIN-9.13856.7192
27STL-9.46566.7394
28DEN-10.20606.7849
29CLE-11.51306.8654
30ATL-18.21707.2781
31NO-23.65707.6131
32NYJ-30.09008.0091




































Sack rate made, Adjusted (League Avg = 6.0561%)
RankTeamVOLA (%)Actual Stat
1JAX45.30208.7997
2NE37.87308.3497
3TB36.65408.2759
4KC36.13708.2446
5PIT34.62708.1532
6SEA28.72307.7956
7DAL26.55307.6642
8PHI25.98007.6295
9ARI23.81907.4986
10CHI17.62407.1234
11GB15.47806.9935
12NYG12.74506.8280
13IND12.46506.8110
14TEN10.01706.6628
15SD9.51766.6325
16MIA4.62116.3360
17WAS1.46726.1450
18BAL-1.09705.9897
19DEN-5.23775.7389
20STL-5.91485.6979
21DET-8.78395.5241
22HOU-8.97395.5126
23OAK-13.81205.2196
24CIN-19.55804.8717
25SF-20.09604.8391
26MIN-20.82504.7949
27ATL-30.15904.2296
28NO-34.53503.9646
29BUF-42.52803.4806
30NYJ-53.48202.8172
31CLE-59.54202.4502
32CAR-64.57702.1453




































Sack rate allowed, Adjusted (League Avg = 6.0561%)
RankTeamVOLA (%)Actual Stat
1NO75.10301.5078
2IND64.29602.1623
3NE48.05903.1456
4GB43.17203.4416
5NYG42.25003.4974
6BAL39.10203.6881
7CIN36.68903.8342
8DAL35.85503.8847
9SD32.55604.0845
10TB32.27304.1016
11HOU23.79104.6153
12WAS20.32004.8255
13CLE16.02705.0855
14DEN15.26005.1319
15ARI13.39705.2448
16TEN6.03125.6909
17MIA3.37775.8516
18CHI2.90555.8802
19CAR2.71555.8917
20SEA-15.18306.9756
21MIN-15.98707.0243
22KC-31.03007.9353
23PIT-34.12508.1228
24NYJ-34.51408.1463
25BUF-40.60608.5153
26STL-40.72408.5224
27PHI-48.92309.0189
28SF-51.44009.1714
29DET-62.40009.8351
30ATL-62.87409.8638
31JAX-63.19009.8830
32OAK-90.651011.5460




































Third down % converted, Adjusted (League Avg = 40.9772%)
RankTeamVOLA (%)Actual Stat
1PIT26.584051.8706
2IND26.306051.7567
3NE16.188047.6106
4DEN16.098047.5737
5DAL15.539047.3446
6SD14.685046.9947
7CLE14.605046.9619
8NO13.159046.3694
9HOU12.813046.2276
10NYG11.411045.6531
11NYJ8.693744.5396
12PHI4.350942.7601
13TEN4.088942.6527
14JAX2.395141.9586
15GB1.849741.7352
16MIA0.480241.1740
17CIN-2.268140.0478
18ARI-2.550639.9320
19ATL-3.332539.6116
20BAL-4.515939.1267
21OAK-4.869138.9820
22TB-4.926538.9585
23CAR-6.954938.1273
24CHI-8.891137.3339
25WAS-11.368036.3189
26STL-12.267035.9505
27KC-14.220035.1502
28SEA-17.755033.7017
29MIN-19.060033.1669
30BUF-20.809032.4503
31DET-23.672031.2771
32SF-26.056030.3002




































Third down % allowed, Adjusted (League Avg = 40.9772%)
RankTeamVOLA (%)Actual Stat
1NE28.821029.1672
2WAS16.915034.0459
3KC15.826034.4921
4TEN15.207034.7458
5BAL14.477035.0449
6GB13.566035.4182
7ATL10.385036.7217
8JAX9.606437.0408
9SEA5.949838.5391
10STL4.966738.9420
11SD3.542239.5257
12BUF3.379539.5924
13CHI3.014639.7419
14OAK1.594440.3239
15TB1.271140.4563
16DAL0.716440.6836
17CIN0.013540.9716
18PHI-0.366841.1275
19SF-1.533941.6057
20NYG-1.952241.7772
21HOU-3.387342.3652
22CLE-3.395642.3686
23CAR-3.934642.5895
24ARI-5.565543.2578
25IND-6.690843.7189
26DEN-8.921744.6331
27MIN-11.744045.7896
28PIT-15.408047.2910
29MIA-16.606047.7819
30NO-18.094048.3916
31NYJ-21.250049.6849
32DET-25.194051.3010




































Int. Rate Given, Adjusted (League Avg = 2.8921%)
RankTeamVOLA (%)Actual Stat
1JAX74.02000.7514
2PHI68.71900.9047
3NE62.57701.0823
4IND61.28101.1198
5TB52.64401.3696
6ATL49.22501.4685
7BAL44.93001.5927
8MIN23.60102.2095
9GB17.81502.3769
10CAR14.44602.4743
11SF12.14402.5409
12PIT5.23382.7407
13BUF2.48202.8203
14DEN-0.94172.9193
15DET-4.81053.0312
16CLE-8.94143.1507
17OAK-10.03803.1824
18NO-11.27803.2183
19HOU-11.53503.2257
20SEA-13.95903.2958
21TEN-17.13103.3875
22CIN-18.26503.4203
23KC-18.36703.4233
24WAS-21.47003.5130
25DAL-23.32203.5666
26SD-23.85903.5821
27MIA-26.94903.6715
28NYJ-30.07103.7618
29NYG-31.14303.7928
30CHI-42.75504.1286
31STL-60.06904.6294
32ARI-84.28005.3296




































Int. Rate Taken, Adjusted (League Avg = 2.8921%)
RankTeamVOLA (%)Actual Stat
1IND92.59605.5701
2CIN64.59304.7602
3JAX60.20204.6332
4TEN54.93404.4808
5OAK41.44104.0906
6SD37.83003.9862
7NYJ17.07603.3860
8DET14.13503.3009
9BAL13.44603.2810
10BUF11.80003.2334
11NE10.59203.1984
12GB8.95143.1510
13WAS3.79533.0019
14TB2.01872.9505
15ATL1.33332.9307
16DEN-3.44512.7925
17DAL-5.35822.7371
18MIA-5.52812.7322
19MIN-7.37502.6788
20SEA-15.05102.4568
21KC-17.22702.3939
22NYG-19.48102.3287
23STL-20.51902.2987
24PIT-21.18902.2793
25CLE-27.20302.1054
26PHI-28.08502.0799
27ARI-32.91201.9403
28HOU-39.14501.7600
29NO-40.46601.7218
30CAR-45.52401.5755
31CHI-46.41901.5496
32SF-49.83801.4507




































Fum. Rate Given, Adjusted (League Avg = 3.0151%)
RankTeamVOLA (%)Actual Stat
1IND52.56401.4302
2PHI45.82301.6335
3SEA45.46201.6444
4ATL40.31201.7996
5MIA35.47401.9455
6TB33.50002.0050
7NE31.05802.0787
8DAL28.29102.1621
9BUF27.11402.1976
10SD26.75602.2084
11NO22.48002.3373
12NYJ20.94102.3837
13CIN20.34102.4018
14MIN19.16502.4372
15JAX10.27602.7052
16NYG8.81142.7494
17KC8.34972.7633
18STL-3.95653.1344
19PIT-4.14283.1400
20CHI-10.53303.3327
21CAR-11.90703.3741
22GB-18.38903.5695
23HOU-25.91003.7963
24DEN-26.08303.8015
25ARI-26.38703.8107
26TEN-34.41504.0527
27CLE-34.95304.0689
28BAL-41.59504.2692
29WAS-48.15204.4669
30SF-56.43204.7165
31DET-62.12604.8882
32OAK-91.13605.7629




































Fum. Rate Taken, Adjusted (League Avg = 3.0151%)
RankTeamVOLA (%)Actual Stat
1DAL61.50904.8696
2SEA49.95704.5213
3CAR40.76504.2442
4DET38.07104.1629
5PIT36.61304.1190
6NYG32.78704.0036
7TEN32.47303.9942
8HOU25.97003.7981
9SD24.15203.7433
10IND23.67203.7288
11NO20.68303.6387
12GB19.10303.5910
13MIN15.82103.4921
14NE12.49103.3917
15WAS11.17603.3520
16TB10.65603.3364
17BUF2.91443.1029
18ARI-1.45462.9712
19MIA-7.29612.7951
20CHI-9.47952.7293
21CIN-10.89502.6866
22STL-13.30002.6141
23BAL-18.90702.4450
24JAX-20.76102.3891
25KC-25.05002.2598
26ATL-29.27002.1326
27DEN-29.29102.1319
28SF-42.56801.7316
29CLE-44.68401.6678
30NYJ-55.11701.3533
31PHI-60.55301.1894
32OAK-73.36800.8030

Read More......

Monday, October 29, 2007

The Key to Good Predictions (though not yet a solution)

(Credit goes to Aaron Hermann of accuscore.com for bringing the central fact of the article to my attention.)

As previously discussed here, averages aren't very good for predictions because players and teams perform above and below averages. That's how you get the averages. "We" here at the blog use a system that classifies games as home wins or losses based on the stats from the game, which is 85% accurate, a large number of the misclassification being due to recovered fumbles. But it uses almost 15 individual stats to get this accurate. Is there one or two stats that we could try predicting and get close to the same accuracy?

Yes. As it turns out (unsurprisingly), the key statistic is yards per pass. Including sacks and sack yards lost, the team with the higher pass efficiency wins ~70% of games. Here's the year-by-year breakdown:















Year% of games home team has higher pass eff.Correlation of (Home yds/pass - Away yds/pass) with (Home pts - Away pts)% of games won by team with higher pass eff.
199753.33330.599268.0952
199854.28570.658976.6667
199959.63300.641676.6055
200053.21100.633368.3486
200147.94520.653470.3196
200253.57140.686073.6607
200358.03570.676570.9821
200454.01790.675276.3393
200554.01790.660970.0893
200649.55360.639173.2143



So not only does the more pass efficient team win, but the correlation shows that the stronger the advantage is, the higher the margin of victory will be. The home team is more efficient passing only 53-54% of the time, showing that playing at home gives a slight edge in actual performance, but it's a smaller edge than what the actual results might indicate (~58% of games are won by the home team).

Using unadjusted stats translated into a percentage over the league average (VOLA), I tried using a logistic regression model based on home and away passing efficiency, sack rates, and interception rates on offense and defense to try and predict (Home yards per pass - Away yards per pass). Training on 1996-2005 and testing on 2006, the model was only 58% accurate in picking the team with the higher pass efficiency, while picking only 46% of home teams to be more pass efficient. On average, the absolute error was a whopping 2.11 yards. Given that each team runs 30 pass plays, we're off the mark by 63 total pass yards/game.

Predictions are only as good as your inputs. You can throw all the complicated algorithms in the world at a problem, but if the data's no good, your results won't be any good. So this is where I'm going to focus most of my creative efforts, and I hope to have a different prediction model for the 2008 season. This might require a complete redo of the data I work with, but like the Yankees and the Dolphins, if you're in "we're one piece away" mode for too long, you need to rebuild.

Read More......

Sunday, October 28, 2007

Win Probabilities and Expected Wins 2007 - Week 8

The following table lists the probabilities that the home team would win each game given the rushing averages, passing averages (includes sack yards lost and sacks as pass attempts), sack rates, third down conversion rates, penalty yards, and interception and fumble rates (by number of completions and rushing plays) for both teams. A logistic regression model trained on 1996-2006 data computes the probabilities. The final score margin is Home team points - Away team points. The sum of these probabilities of victory form the expected win totals in the second table after the jump. The tables will be updated as more box scores come in. By the way, Detroit's expected win total projects out to 10 wins. "The scary thing is that Jon Kitna was right!" "I know, kids. I'm scared, too." They're 3 or 4 wins from a playoff berth with 9 games to go. I won't brag yet, but it's lookin' good.

















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
STLCLE38.2935-7
CHIDET1.9709-9
SFNO1.4568-21
SDHOU99.456325
CARIND1.7713-24
MIANYG84.6793-3
MINPHI7.4477-7
CINPIT10.8698-11
TENOAK92.06234
NYJBUF1.4476-10
TBJAX59.7037-1
NEWAS99.873645
DENGB5.5953-6


Teams that "should have" won but didn't

Miami Dolphins (vs. Giants), Win Prob = 84.6973% Pardon my language, but **** me... Miami loses 2 of their 4 fumbles; the Giants lose only 1 of their 3 fumbles, one of which bounced directly into their O-lineman's hands. The Giants had a strong rushing game (5.1 ypc vs. 4.1), but Eli Manning managed only 2.13 yards/pass compared to Lemon's 4.45 yards/pass. So despite the lack of Ronnie Brown, they managed to outplay the Giants and still lose. This team is not an 0-16 team, not even a 1-15 team, but their terrible "luck" might make them 1-15. And by luck, I just mean that their good plays are coming more regularly but they're not coming in large enough bunches to amount to overall success.

Tampa Bay Buccaneers (vs. Jaguars), Win Prob = 59.7037% 6.47 yards/carry vs. 3.02. 5.79 yards/pass vs. 4.78. The Bucs, however, threw 3 picks. The Jags fumbled once but recovered it. That was the difference in the game.

Even without the 82-yard pass, Green Bay is pegged as having had a 76% chance of winning that game.





















































TeamActual WinsExpected WinsProjected Win Total
AFC East
BUF3.02.86846.5564
MIA0.02.50355.0071
NE8.07.641815.2835
NYJ1.01.58043.1609
AFC North
BAL4.03.57398.1690
CIN2.02.66226.0851
CLE4.03.40827.7903
PIT5.05.404212.3525
AFC South
HOU3.02.88805.7759
IND7.06.311014.4251
JAX5.04.389910.0340
TEN5.04.24609.7051
AFC West
DEN3.02.77846.3506
KC4.04.04519.2460
OAK2.02.27885.2088
SD4.04.20579.6131
NFC East
DAL6.05.594512.7875
NYG6.04.41918.8382
PHI3.04.424310.1127
WAS4.03.51018.0232
NFC North
CHI3.01.43552.8710
DET5.04.398310.0532
GB6.04.417010.0960
MIN2.02.60315.9500
NFC South
ATL1.03.08757.0572
CAR4.02.91836.6703
NO3.02.97116.7911
TB4.04.93719.8741
NFC West
ARI3.02.58305.9040
STL0.02.16164.3232
SF2.01.12212.5649
SEA4.04.631710.5868

Read More......

Tuesday, October 23, 2007

Predictions 2007 Week 8


















Predictions based on opponent-adjusted stats
GamePredicted Final Score MarginP(Home Team Wins)
NYG @ MIA0.705352.9249
WAS @ NE5.573468.5039
BUF @ NYJ2.414659.6878
PIT @ CIN1.514451.4854
OAK @ TEN10.903780.3202
GB @ DEN2.987959.8897
HOU @ SD5.185865.5187
DET @ CHI1.696351.1043
PHI @ MIN2.207459.1040
IND @ CAR-4.935433.7619
JAX @ TB3.514762.9880
CLE @ STL-0.242447.8315
NO @ SF-0.693352.1203



















Predictions based on unadjusted stats
GamePredicted Final Score MarginP(Home Team Wins)
NYG @ MIA-1.670344.5811
WAS @ NE6.686771.3328
BUF @ NYJ4.504966.3088
PIT @ CIN-1.966041.2437
OAK @ TEN9.886378.0157
GB @ DEN3.412860.4828
HOU @ SD6.162268.7253
DET @ CHI-0.510341.1834
PHI @ MIN1.075654.5478
IND @ CAR-3.662139.7302
JAX @ TB3.995264.9115
CLE @ STL-0.029848.0630
NO @ SF0.846658.1237

Read More......

Win Probabilities and Expected Wins 2007 - Week 7

Night games, commentary, and expected wins table added.
The following table lists the probabilities that the home team would win each game given the rushing averages, passing averages (includes sack yards lost and sacks as pass attempts), sack rates, third down conversion rates, penalty yards, and interception and fumble rates (by number of completions and rushing plays) for both teams. A logistic regression model trained on 1996-2006 data computes the probabilities. The final score margin is Home team points - Away team points. The sum of these probabilities of victory form the expected win totals in the second table to be added after the Monday night game. The first table will be updated as more box scores come in.

















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
BUFBAL77.47585
DETTB64.66207
OAKKC33.6400-2
SEASTL97.980527
MIANE1.2794-21
NOATL71.45816
NYGSF97.301418
HOUTEN7.1356-2
WASARI60.53032
PHICHI61.6652-3
CINNYJ97.89117
DALMIN97.716710
DENPIT40.18223
JAXIND2.9836-22


Teams that "should have" won but didn't
Philadelphia Eagles (vs. Bears), Win Prob = 61.6652% Astoundingly, Chicago had a better passing game than the Eagles (7.48 yards/pass vs. 5.7), but Chicago's one fumble (which they recovered) probably a large factor in this probability (without it, P(Eagles win) goes down to about 48%). Philly was much better in the running game (4.92 yards/rush vs. 3.23). But given that the game turned on that one recovered fumble, it's not surprising the game ended up being won by 3 points.

Pittsburgh Steelers (@ Broncos), Win Prob = 59.8178% Denver recovered both of their fumbles. Otherwise, Denver did indeed outperform Pittsburgh.





















































TeamActual WinsExpected WinsProjected Win Total
AFC East
BUF2.01.88295.0211
MIA0.01.65683.7869
NE7.06.643015.1841
NYJ1.01.56603.5793
AFC North
BAL4.03.57398.1690
CIN2.02.55356.8094
CLE3.02.79127.4431
PIT4.04.512912.0345
AFC South
HOU3.02.88256.5886
IND6.05.328714.2098
JAX4.03.986910.6318
TEN4.03.32548.8676
AFC West
DEN3.02.72247.2598
KC4.04.04519.2460
OAK2.02.19955.8652
SD3.03.21128.5631
NFC East
DAL6.05.594512.7875
NYG5.04.26599.7506
PHI2.03.49889.3300
WAS4.03.50899.3570
NFC North
CHI3.01.41583.2361
DET4.03.41809.1146
GB5.03.47299.2612
MIN2.02.52876.7431
NFC South
ATL1.03.08757.0572
CAR4.02.90057.7348
NO2.01.98575.2951
TB4.04.34009.9200
NFC West
ARI3.02.58305.9040
STL0.01.77874.0656
SF2.01.10762.9535
SEA4.04.631710.5868


Read More......

Power Rankings 2007 Week 7

The power rankings for this site were developed in this article. The idea behind them is simple: if each team played one home game and one away game against every other team in the league, who would be the most successful?

The power rankings use logistic regression to predict the probability of winning. The score you see along with the rankings is the expected win total over a 16-game season based on the expected winning percentages over the 62 games (i.e. the sum of those probabilities). Adjusted and unadjusted rankings included.




































Power Rankings, Logistic Regression
RankTeamExpected Wins
1IND11.4905
2NE11.0967
3DAL11.0366
4TB9.7785
5PIT9.5315
6WAS9.3918
7NYG9.1441
8TEN9.0731
9JAX8.7938
10SD8.7205
11SEA8.4443
12PHI8.4076
13MIN8.4011
14GB8.3821
15DEN8.2858
16ARI7.9302
17CIN7.8663
18CLE7.7844
19HOU7.6298
20MIA7.3475
21CAR7.2920
22DET7.2118
23KC7.0735
24BAL6.8962
25ATL6.8204
26NO6.5023
27CHI6.2434
28BUF6.1996
29STL6.0449
30OAK5.9200
31NYJ5.6766
32SF5.5834




































Power Rankings, Opponent-adjusted
RankTeamExpected Wins
1IND11.4905
2NE11.0967
3DAL11.0366
4TB9.7785
5PIT9.5315
6WAS9.3918
7NYG9.1441
8TEN9.0731
9JAX8.7938
10SD8.7205
11SEA8.4443
12PHI8.4076
13MIN8.4011
14GB8.3821
15DEN8.2858
16ARI7.9302
17CIN7.8663
18CLE7.7844
19HOU7.6298
20MIA7.3475
21CAR7.2920
22DET7.2118
23KC7.0735
24BAL6.8962
25ATL6.8204
26NO6.5023
27CHI6.2434
28BUF6.1996
29STL6.0449
30OAK5.9200
31NYJ5.6766
32SF5.5834





































Power Rankings, Unadjusted
RankTeamExpected Wins
1NE11.4613
2IND11.1798
3DAL11.0478
4PIT10.6005
5TB9.6857
6WAS9.3622
7NYG9.2132
8PHI9.0649
9SD9.0305
10SEA8.8872
11MIN8.6806
12TEN8.6470
13JAX8.4937
14BAL8.3515
15CAR8.2901
16GB8.0074
17DEN7.9614
18ARI7.8753
19DET7.6292
20KC7.6011
21CIN7.5983
22CLE7.5684
23HOU7.4236
24ATL6.7335
25MIA6.4393
26OAK6.2238
27STL5.7106
28NO5.6194
29NYJ5.4792
30SF5.4567
31CHI5.4103
32BUF5.2663

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The Value of Homefield Advantage 2007 Week 7

One of the things I've learned in my football research is that the value of home-field advantage varies pretty widely from year to year, especially with interconference games. Because prediction systems tend to have a big bias towards the home team, this can have a large impact on accuracy. So throughout the season, I'll be keeping track of home team winning percentage and average final score margin (home team points - away team points) for interconference, interdivision, and intradivision matchups. If you're interested in that sort of thing, it can help you with betting on the spread (hint).

The pattern this season so far shows that you should bet on interconference home teams, especially if they're the underdogs, and stay away from intradivision games. There could be regression to the mean, but I don't believe it would be severe enough that betting on home teams in intradivision games would become good.

All Games
Home Team Win %: 59.2233%
Avg. Final Score Margin: 2.1553

Interconference
Home Team Win %: 69.2308%
Avg. Final Score Margin: 3.9231

Interdivision, Intraconference
Home Team Win %: 67.5676%
Avg. Final Score Margin: 4.5135

Intradivsion
Home Team Win %: 45.0000%
Avg. Final Score Margin: -1.1750

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Projected Final Standings 2007 Week 7

Using the projected win probabilities from the logistic regression power rankings, I estimated which games each team would win on the rest of their respective schedules. And then I summed the projected wins with the actual wins so far to get their projected win totals. The teams are sorted by division. For the record, New England's only projected loss is on the road to Indianapolis. If you look at the stats page for week 6, you'll see the major reason likely has to do with the perceived disparity in rush offense.


Using opponent-adjusted stats


















































Projected Final Standings
TeamProjected Win Total
AFC East
BUF4
MIA5
NE15
NYJ3
AFC North
BAL6
CIN8
CLE9
PIT12
AFC South
HOU6
IND16
JAX10
TEN11
AFC West
DEN9
KC8
OAK3
SD8
NFC East
DAL15
NYG10
PHI7
WAS8
NFC North
CHI5
DET6
GB12
MIN9
NFC South
ATL3
CAR7
NO4
TB13
NFC West
ARI8
STL1
SF4
SEA11

Read More......