Showing posts with label probability. Show all posts
Showing posts with label probability. Show all posts

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

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......

Tuesday, October 16, 2007

Win Probabilities and Expected Wins 2007 - Week 6

Sunday night game and commentary (you'll be real surprised) added
Monday night game added (another surprise) 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.

Cleaning up from last week, where clearly I was not on the ball, I had to re-update the week 5 article with the P(win) for DAL@BUF, where the probability of Buffalo winning given their stats was 46.9886% despite the 6 turnovers Dallas coughed up. Without further ado, here are the week 6 numbers.

















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
BALSTL94.370919
CLEMIA98.414610
SDOAK99.555314
GBWAS22.31863
JAXHOU96.863920
KCCIN89.20487
CHIMIN28.3672-3
NYJPHI9.5042-7
TBTEN87.72183
ARICAR0.2296-15
DALNE25.6264-21
SEANO55.3389-11
ATLNYG54.1972-21


Teams that "should have" won but didn't
Washington Redskins (@ Packers), Win Prob = 77.6814% Favre threw 2 interceptions; Campbell threw only one. Favre averaged 4.33 yards a pass; Campbell averaged 5.25 yards. Green Bay was lucky enough to recover all four of their fumbles, while Washington recovered all of theirs. Washington really did outplay Green Bay, but they seem to have lost it on a couple of unlucky bounces.

Seattle Seahawks (vs. Saints), Win Prob = 55.3389% I was at the game, and I can tell you the Seahawks were never in it. Holmgren essentially forfeited the game when he decided to punt down 3 scores with 11 minutes left in the game. Hmm, think you'll need to score there sometime, Bubba? That said, this might reflect garbage time stats. Seattle managed 4.4 yards per carry, while the Saints gained only 3.7. Shaun Alexander was getting booed because he was slow and couldn't find holes. Leonard Weaver, the FB taking over for Mack Strong, is inflating this average (3 for 40) as is Hasselbeck's scramble. The Saints had 5 rushes (4 by Brees, 1 by Karney) of 0 yards to deflate their average. Seattle also managed to gain 6.9375 yards per pass versus 6.833 for the Saints. On the other hand, the Seahawks allowed sacks on over 10% of their pass plays. The Saints O-line pulled it together and gave Brees all the time in the world. The reason this game is in the Seahawks favor is probably the Saints' 2 fumbles, only one of which was actually lost. Remember, going by the FO philosophy of fumble recovery being random, I count all fumbles. In the end, however, take out the botched punt and give the Seahawks that blocked field goal, and it probably would have been 21-13 at the half and a very different game, considering that the Seahawks shut out the Saints in the second half. Yes, the Saints were likely trying to run out the clock, but there were a couple drives where the Hawks D prevented a couple of what would have been surefire scores.

So what does this mean? Except for Hail Mary passes, I don't remove any garbage time data from the system, so maybe this means that the system is wrong. On the other hand, if the stats were so close before garbage time that some ultimately meaningless drives led by Hasselbeck could tip the stats in the Seahawks' favor, maybe the game was closer than everyone thinks. Again, despite the Saints' great pass protection, which had been a problem in their first four games, that game could have easily been 21-13 at halftime. And remember, the Saints' offense had only one productive quarter. Nobody goes 0-16, and the Saints finally got some luck bouncing their way. Why the hell can't the Dolphins get some of that?!

Atlanta Falcons (vs. Giants), Win Prob = 54.1972% Manning threw two picks, and I threw out Harrington's Hail Mary interception at the end of the first half. Manning was also probably a little lucky that the picks he threw were around midfield rather than backed up in his own territory. Otherwise, it looks like the Giants did outplay the Falcons.


















































TeamActual WinsExpected WinsProjected Win Total
AFC East
BUF1.01.10823.5461
MIA0.01.64404.3839
NE6.05.655815.0822
NYJ1.01.54494.1197
AFC North
BAL4.03.34878.9298
CIN1.01.57465.0388
CLE3.02.79127.4431
PIT4.03.914712.5272
AFC South
HOU3.02.81127.4964
IND5.04.358513.9473
JAX4.03.957112.6627
TEN3.02.39677.6695
AFC West
DEN2.02.32067.4259
KC3.03.38159.0174
OAK2.01.86315.9618
SD3.03.21128.5631
NFC East
DAL5.04.617412.3129
NYG4.03.29298.7810
PHI2.02.88219.2228
WAS3.02.90369.2914
NFC North
CHI2.01.03252.7532
DET3.02.77148.8683
GB5.03.47299.2612
MIN2.02.50588.0186
NFC South
ATL1.02.80217.4722
CAR4.02.90057.7348
NO1.01.27114.0675
TB4.03.986610.6310
NFC West
ARI3.02.18835.8354
STL0.01.75854.6893
SF2.01.08063.4579
SEA3.03.65199.7385

Read More......

Wednesday, October 10, 2007

Win Probabilities and Expected Wins 2007 - Week 5

Edit: I decided to remove the Hail Mary interception that Favre threw at the end of the Bears-Packers game from the box score. I have posted the resulting changes for this article, but as it does not significantly affect this week's predictions, I am not going back and fixing this week's other articles. Starting with Week 6, however, the stats will reflect the removed play. I have also done this with the bizarre Hail Mary play at the end of regulation in the week 1 MIA@WAS matchup.


Well, so far I'm 11-1 in predicting this week's game (with adjusted stats) and got some of the margins close to dead on. I don't know how many people saw the Chargers killing Denver either. Denver had a 0.0134% chance of winning that game. Damn! And to end the weekend, the predictions based on adjusted stats go 12-2.

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.

Monday night update In spite of Romo's 6 turnovers, a preliminary look at the stats shows that the Cowboys still had a 54% chance of winning that game. I'll update sometime tomorrow with the final numbers. In every other way, the Cowboys were more efficient, especially in pass efficiency (surprisingly enough).

















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
STLARI74.3333-3
NOCAR68.7236-3
INDTB94.942019
DENSD0.0134-38
HOUMIA79.05243
KCJAX2.2035-10
NECLE94.824117
NYGNYJ85.779711
PITSEA96.065021
TENATL77.00537
WASDET99.894931
SFBAL9.0122-2
GBCHI53.3206-7
BUFDAL46.9886-1


Teams that "should have" won but didn't
St. Louis Rams (vs. Cardinals), Win Prob = 74.3333% Arizona's 2 fumbles, both of which they recovered, were the difference between a P(Rams win)=74.333% and a P(Rams win)=49.99% In other words, this game was very evenly matched. The Cardinals had better numbers but just good enough to neutralize homefield advantage.

New Orleans Saints (vs. Panthers), Win Prob=68.7236% Same story here. Carolina fumbled twice but recovered both fumbles. Excluding the 2 fumbles, P(Saints win)=34.92%. David Carr somehow managed to average 7 yards a pass.

Green Bay Packers (vs. Bears), Win Prob=53.3206% They were about equal in yards per pass, but the Packers had a huge advantage in rushing averages (5.5 vs. 2.5) and third down conversions (6-14, 3-14). But the Bears had short field position on their TD drive in the 3rd quarter off an interception and were more efficient in the red zone. It speaks poorly on the Bears that they couldn't do better on 4 turnovers. That said, the Bears did manage 7.5 yards per pass, which is pretty good even if against a mediocre pass defense.

Read More......

Sunday, September 30, 2007

Win Probabilities and Expected Wins 2007 - Week 4 (Updated)

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. Updates added

















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
ATLHOU91.029210
BUFNYJ58.88563
SFSEA0.0325-20
CARTB1.4607-13
CLEBAL80.768914
DALSTL99.906728
DETCHI98.304710
MINGB55.6513-7
MIAOAK11.8727-18
ARIPIT96.50657
INDDEN97.473318
SDKC10.5059-14
NYGPHI98.650713
CINNE1.2293-21


Teams that "should have" won but didn't
Minnesota Vikings (vs. Packers), Win Prob = 55.6513% Green Bay was significantly more efficient in the passing game (7.34 ypa vs. 5.28) but four fumbles and a far lower rushing efficiency (2.3 vs 7) probably led to this estimate.


















































TeamActual WinsExpected WinsProjected Win Total
AFC East
BUF1.00.63832.5531
MIA0.01.41865.6745
NE4.03.963815.8554
NYJ1.01.30765.2305
AFC North
BAL2.01.49515.9804
CIN1.01.46675.8667
CLE2.01.75537.0211
PIT3.02.954111.8164
AFC South
HOU2.01.98937.9571
IND4.03.409113.6364
JAX2.02.010510.7225
TEN2.01.50398.0207
AFC West
DEN2.02.32059.2819
KC2.02.46749.8697
OAK2.01.85867.4344
SD1.01.21574.8630
NFC East
DAL4.03.831015.3239
NYG2.01.97707.9082
PHI1.01.97727.9086
WAS2.01.12786.0150
NFC North
CHI1.00.28201.1280
DET3.02.770311.0812
GB4.02.716610.8662
MIN1.01.78957.1580
NFC South
ATL1.02.03028.1207
CAR2.01.59016.3603
NO0.00.13720.7319
TB3.03.058812.2353
NFC West
ARI2.01.92937.7173
STL0.00.95893.8354
SF2.00.99053.9619
SEA3.03.059212.2368

Read More......

Tuesday, September 25, 2007

Win Probabilities and Expected Wins 2007 - Week 3 (Updated)

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. Updates finished.



















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
BALARI80.36083
GBSD87.80777
DENJAX32.4010-9
WASNYG16.6049-7
OAKCLE92.23922
SEACIN66.49043
HOUIND0.6929-6
KCMIN79.09213
NEBUF99.811931
NYJMIA37.48403
PHIDET99.778735
PITSF94.512821
TBSTL99.042821
ATLCAR40.0107-7
CHIDAL1.4154-24
NOTEN13.2432-17


Teams that "should have" won but didn't
Miami Dolphins (@ Jets), Win Prob = 62.5160% So yeah, this post is going up earlier than normal because I'm a bitter Dolfan right now. Blame this one on terrible red zone offense and special teams. Ted Ginn's had TWO punt returns. TWO. I'm glad we spent a #9 pick on someone to call for a fair catch. Meanwhile, Leon Washington gets a 98-yard return. Lots of 2-TE formations and no real noticable attempts to go deep. But this week, dumping off to the running back proved real successful for the Fins. The Dolphins outperformed the Jets in most of the stats used in this system and still lost.




















































TeamActual WinsExpected WinsProjected Win Total
AFC East
BUF0.00.04940.2636
MIA0.01.29996.9328
NE3.02.976115.8728
NYJ1.00.89654.7812
AFC North
BAL2.01.30286.9482
CIN1.01.45447.7567
CLE1.00.94765.0538
PIT3.02.919215.5688
AFC South
HOU2.01.899610.1311
IND3.02.434412.9833
JAX2.02.010510.7225
TEN2.01.50398.0207
AFC West
DEN2.02.295212.2411
KC1.01.57258.3866
OAK1.00.97735.2125
SD1.01.11075.9236
NFC East
DAL3.02.831915.1035
NYG1.00.99055.2828
PHI1.01.963710.4728
WAS2.01.12786.0150
NFC North
CHI1.00.26501.4135
DET2.01.78739.5320
GB3.02.273112.1230
MIN1.01.23306.5759
NFC South
ATL0.01.11995.9727
CAR2.01.57558.4025
NO0.00.13720.7319
TB2.02.073411.0584
NFC West
ARI1.00.96435.1427
STL0.00.95795.1089
SF2.00.99015.2808
SEA2.02.059510.9841


Detroit still looks like a 10-win team, eerily matching Kitna's prediction. The small sample size, however, will bring them down immensely in the power rankings going up next. That one game made their pass defense look like one of the worst in the league. This is also why you shouldn't trust averages entirely.

Read More......

Sunday, September 16, 2007

Win Probabilities and Expected Wins - 2007 Week 2

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. (Edit: Second table added.)



















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
CLECIN86.30766
NYGGB12.3475-22
CHIKC22.084410
MIADAL12.0833-17
DENOAK99.96703
DETMIN83.96563
NESD98.120224
PHIWAS48.4337-8
CARHOU10.4949-13
TENIND55.4136-2
JAXATL41.66666
PITBUF98.093223
STLSF81.8986-1
TBNO99.976317
ARISEA52.21313
BALNYJ48.15397


The following games "should have been" won by the team that didn't actually win:
KC @ CHI - I don't take punt returns into consideration anymore.
IND @ TEN - 55/45 chance and the Titans lost by 2 points. I find the Colts' 6.8 yards per pass more encouraging for future performance, however.
ATL @ JAX - A 60/40 split in favor of Atlanta. Again, Jacksonville's pass efficiency (8.6 yards/pass) is more encouraging for future performance. I am disturbed at how close the first two games have been for Jacksonville, however.
SF @ STL - It came down to a 50+-yard field goal that was short by about 6 inches, but it shouldn't have to begin with. The Rams' were much more efficient on offense. Alex Smith averaged 4.6 yards per attempt against what is considered a poor defense. Beware of regression with the 49ers.
NYJ @ BAL - 52/48 split. Kellen Clemens was the more efficient passer.


















































TeamActual WinsExpected WinsProjected Win Total
AFC East
BUF0.00.04750.3803
MIA0.00.67475.3979
NE2.01.978015.8242
NYJ0.00.52164.1731
AFC North
BAL1.00.49923.9934
CIN1.01.11938.9543
CLE1.00.87006.9598
PIT2.01.974015.7922
AFC South
HOU2.01.892615.1412
IND2.01.441311.5303
JAX1.01.334510.6759
TEN1.00.63635.0905
AFC West
DEN2.01.971215.7696
KC0.00.78166.2525
OAK0.00.05490.4396
SD1.00.98887.9101
NFC East
DAL2.01.846114.7685
NYG0.00.15661.2526
PHI0.00.96597.7270
WAS2.00.96187.6940
NFC North
CHI1.00.25092.0071
DET2.01.785014.2803
GB2.01.395011.1599
MIN1.01.02398.1912
NFC South
ATL0.00.71985.7582
CAR1.00.97567.8046
NO0.00.00480.0385
TB1.01.08308.6641
NFC West
ARI1.00.76796.1430
STL0.00.94847.5868
SF2.00.93537.4822
SEA1.01.394611.1569

Read More......

Monday, September 10, 2007

2007 Season Week 1 - Win Probabilities and Expected Wins

Monday night games now 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.




















Home TeamAway TeamP(Home Team Won) (%)Final Score Margin
INDNO99.542831
STLCAR12.9369-14
OAKDET5.4616-15
SDCHI96.996011
SEATB91.674714
DALNYG96.689510
CINBAL98.23677
SFARI75.42623
BUFDEN2.8474-1
GBPHI51.84653
HOUKC99.759317
MINATL86.355721
NYJNE0.3179-24
CLEPIT0.6903-27
JAXTEN91.7820-3
WASMIA44.60933

* That 54-yard Hail Mary to Antwan Randel El is removed from the stats because it was a random play that inflated Jason Campbell's passing average by 50%. Now that I'm doing these stats live, I hope to be able to catch plays like this throughout the season and remove them from my data. Unfortunately, it's too prohibitive to go back and comb my 1996-2006 data. So be aware that the noise does exist in my training data. And I should point out that I am a Dolphins fan.


















































TeamActual WinsExpected WinsProjected Win Total
AFC East
BUF0.00.02850.4556
MIA0.00.55398.8625
NE1.00.996815.9491
NYJ0.00.00320.0509
AFC North
BAL0.00.01760.2821
CIN1.00.982415.7179
CLE0.00.00690.1104
PIT1.00.993115.8896
AFC South
HOU1.00.997615.9615
IND1.00.995415.9269
JAX0.00.917814.6851
TEN1.00.08221.3149
AFC West
DEN1.00.971515.5444
KC0.00.00240.0385
OAK0.00.05460.8739
SD1.00.970015.5194
NFC East
DAL1.00.966915.4703
NYG0.00.03310.5297
PHI0.00.48157.7046
WAS1.00.44617.1375
NFC North
CHI0.00.03000.4806
DET1.00.945415.1261
GB1.00.51858.2954
MIN1.00.863613.8169
NFC South
ATL0.00.13642.1831
CAR1.00.870613.9301
NO0.00.00460.0731
TB0.00.08331.3321
NFC West
ARI0.00.24573.9318
STL0.00.12942.0699
SF1.00.754312.0682
SEA1.00.916714.6679

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Thursday, September 6, 2007

Win Probability Report: Week 1 - Colts-Saints

One of the features I plan on posting over the season is the probability for each that the winning team would have won that game given the in-game statistics, specifically, rushing and passing averages, sack rates, third down conversion rates, penalty yards, and fumble and interception rates. As explained here, these probability estimates make for a good approximate model of total wins that should allow us to see who's over- and underachieving as the season progresses. As it turns out, fewer games are given a 60/40 split than 99/1 splits. The Colts-Saints game tonight was one of those 99/1 games.

Given the stats, the Colts had a 99.481% probability of winning tonight's game.

For the record, the Cardinals had a 98.963% probability of winning that debacle against the Bears. They certainly did have every opportunity to crown the Bears' asses.

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Friday, August 24, 2007

Probabilities of Playoff Droughts and Some Bold Playoff Predictions

Arizona, Buffalo, Detroit, Houston, and Miami are the only 5 teams in the league not to have a postseason appearance in the 5 postseasons since the 2002 realignment. Cleveland, San Francisco, and Oakland have not appeared in the last 4 postseasons. "Probability is like gravity. You cannot fight gravity." (A chocolate chip cookie to the person that gets that reference.) Eventually, the unlikely scenarios will happen, and fortunes will reverse. It's the cyclical nature of the league. So what are the odds of a team going on a 5-year postseason drought?


To simplify the calculations, I'm making two assumptions. First, each team has an equal probability of reaching the postseason. Second, the results of each year are independent of each other. Obviously there's a wide array of influences that affect the actual probabilities, but let's keep things simple. As it turns out, the simplest solution is pretty accurate. So the probability of a team having a playoff drought for X seasons is simply .625X. The following table lists the probabilities and the expected number of teams experience such a drought at any given point in time.













Playoff drought of ≥X yearsProbabilityExpected number of teamsActual number of teamsYear (latest possible) of last playoff berth
162.5%20202005
239.063%12.5132004
324.414%7.812592003
415.259%4.882882002
59.5367%3.051852001
6*6.1527%1.907332000
7*3.9695%1.230531999
8*2.561%0.793911998


* Probabilities adjusted to account for there being 31 teams in the league 1999-2001. P(Missing playoffs 1999-2001) = 20/31 = 64.516%. Actual number of teams does not include Houston.

For the most part, the number of actual teams with such playoff droughts match up with the expected number. The only aberration is the number of teams with droughts of at least 4 years. That list of teams is: Arizona, Buffalo, Detroit, Miami, Cleveland, Houston, San Francisco, and Oakland. The probability of having a drought of 6 seasons is 5.9605%, so only 2 (1.9073 to be exact) teams are expected to not have made the playoffs in the 2002-7 timeframe. In other words, expect two or three teams in the ARI, BUF, HOU, MIA, DET set to make the playoffs. Guess what two of the teams are expected to improve in 2007 based on actual vs. expected wins in 2006? Miami and Detroit.

That's right. I'm calling it right now: Miami and Detroit are making the playoffs. And will fail immediately thereafter. Trent Green will have a lot to do with Miami's success. And with a tough schedule, I don't expect them to go more than 9-7. Jon Kitna put up some very good yards per attempt numbers in 2006 but was hampered by really poor pass protection. The defense was very bad, too, but teams with good passing offenses tend to make the playoffs. Detroit could wind up 8-8 with an average passing offense made good to very good with better pass protection and the addition of Calvin Johnson. Plus, the NFC North is not a particularly strong division. At the same time, the article about rising and falling teams projects Detroit to finish last in the division (and Miami to finish first in the AFC East). Honestly, calling Miami and Detroit goes against every instinct I have as a football aficionado, but there it is. Both teams, after runs of bad luck, should gets runs of good luck. Regression to the mean. No risk, no reward. If I'm wrong, I will post a picture of myself with JACKASS written across it.

So I'm predicting neither Arizona nor Buffalo will break their skids. Both teams have not done anything to get appreciably better, but what are the odds of their playoff droughts continuing into 2008? Buffalo's last playoff game was the Music City Miracle in the 1999 season. 2 seasons of 31 teams and 6 seasons of 32 teams. (20/31)2*(20/32)6 = 2.4809%. The chances of a team not making the playoffs from 2000-7 is 2.4809%. The expected number of teams with such a drought out of 31 teams is 0.76909. Based on my predictions for ARI and BUF, the actual number will be 2. The difference of 1.231 teams between expected and actual is not abnormal, looking at the table. Meanwhile, for the Cardinals, the probability of a team not making the playoffs from 1999-2007 is (20/31)3*(20/32)6 = 1.6006%. Given 31 teams, the expected number of teams to experience such a drought would be 0.49619. So it's not ridiculous to think Arizona's not quite ready for primetime based on those odds.

Buffalo had a very good pass defense in 2006, which carries a high probability of a playoff berth (just not as high as with pass offense), but they lost their shut-down corner, Nate Clements, to San Francisco. Since the probable loss in pass defense won't be offset by the possible gain in rush offense with Marshawn Lynch, I don't see Buffalo improving, let alone enough to make the playoffs. Arizona will improve in Leinart's second year, but given how bad the other parts of the team are, I think it will be another year or two before Leinart will drag that team into the playoffs. Showing how much I think of them, I forgot to include Houston in my analysis in the first draft of this article. Houston actually came very close to being predicted as a faller to begin with (4.7810 expected wins, 6 actual, 1.2190 difference, with barrier being 1.233). They're just not very good in any area, and the division should be very competitive with Indy and the Jags.

In case you were wondering, the Bengals did a phenomenal job of fighting gravity from 1991-2004. The probability of a team experiencing a playoff drought in that time frame was 0.33711%.

To recap, the odds show that one or two of the Fantastic Four (ARI, BUF, DET, MIA) should make the playoffs this year. Given the last 6-8 years to color our perceptions, none of them seem likely to make the playoffs. But surprises happen every year, and streaks have endings. That doesn't mean you should expect great things from these teams. It just means things will swing their way for once. Both Detroit and Miami underperformed their expected wins based on my Value Over League Average stats (as well as Pythagorean Wins and DVOA Expected Wins), which also indicates they will be better in 2007. Improvements in passing offenses will lead to better records for Miami and Detroit, which might be just enough to push them into the playoffs.

8-27-07: Took out paragraph about Green Bay and Chicago because it wasn't particularly relevant, and when I went back to check the projection, I found I had mixed up the order.

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