Last week, Neil had a fascinating post on how each team’s win probability has varied by quarter over the last 35 years. The 2004 Pittsburgh Steelers were the poster child for wins added during the 4th quarter and overtime. Pittsburgh went 15-1, which means they exceeded the league average by 7 wins (the average team, of course, goes 8-8). So how did Pittsburgh go about getting those extra 7 wins?

The table below lists all 16 regular season games for the Steelers. The fifth column shows the point spread before the game, and the sixth column assumes that the home team has a 57.9% chance of winning every game. Of course, that’s going to be modified by the actual point spread, so the next column shows the win probability added based on the Vegas line. This is neutral of the home field WP, and the “wpa bg” column shows the total win probability of the team before the game. So when the Steelers hosted the Raiders in week 1, they were a 3.5-point home favorite, which meant they had a 60% chance of winning. The next four columns show how much win probability was added by the end of each quarter.

Wk | Opp | PF | PA | Line | wpa_loc | wpa_veg | wpa bg | wpa_1st | wpa_2nd | wpa_3rd | wpa_4th | wpa_tot |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | rai | 24 | 21 | -3.5 | 7.9% | 2.1% | 60.0% | 18.9% | 2.5% | 14.3% | 4.4% | 100.0% |

2 | rav | 13 | 30 | 4 | -7.9% | -3.5% | 38.7% | -18.4% | -13.9% | -6.2% | -0.1% | 0.0% |

3 | mia | 13 | 3 | 2.5 | -7.9% | 0.7% | 42.8% | 10.9% | 3.3% | 21.0% | 22.0% | 100.0% |

4 | cin | 28 | 17 | -4 | 7.9% | 3.5% | 61.3% | -1.5% | 13.1% | -34.3% | 61.3% | 100.0% |

5 | cle | 34 | 23 | -4.5 | 7.9% | 4.9% | 62.7% | 10.3% | 22.1% | 4.6% | 0.3% | 100.0% |

6 | dal | 24 | 20 | 3 | -7.9% | -0.7% | 41.4% | 1.1% | 1.4% | -37.8% | 93.9% | 100.0% |

8 | nwe | 34 | 20 | 3 | 7.9% | -16.4% | 41.4% | 49.1% | -0.6% | 10.0% | 0.2% | 100.0% |

9 | phi | 27 | 3 | 1.5 | 7.9% | -12.2% | 45.7% | 40.1% | 10.3% | 3.8% | 0.1% | 100.0% |

10 | cle | 24 | 10 | -3.5 | -7.9% | 17.8% | 60.0% | 11.0% | 19.4% | 5.3% | 4.4% | 100.0% |

11 | cin | 19 | 14 | -4 | -7.9% | 19.2% | 61.3% | -14.7% | -4.8% | 29.8% | 28.2% | 100.0% |

12 | was | 16 | 7 | -10 | 7.9% | 18.6% | 76.5% | 4.4% | 15.8% | -7.7% | 11.1% | 100.0% |

13 | jax | 17 | 16 | -3 | -7.9% | 16.4% | 58.6% | -1.1% | 23.3% | -20.7% | 40.1% | 100.0% |

14 | nyj | 17 | 6 | -4.5 | 7.9% | 4.9% | 62.7% | 7.5% | 0.2% | -13.9% | 43.6% | 100.0% |

15 | nyg | 33 | 30 | -10 | -7.9% | 34.3% | 76.5% | -15.0% | 25.4% | -28.3% | 41.5% | 100.0% |

16 | rav | 20 | 7 | -5 | 7.9% | 6.2% | 64.1% | -1.8% | 9.0% | 23.5% | 5.3% | 100.0% |

17 | buf | 29 | 24 | 9.5 | -7.9% | -17.5% | 24.7% | 11.9% | 18.5% | -23.7% | 68.6% | 100.0% |

Total | 0.0 | 0.8 | 8.8 | 1.1 | 1.4 | -0.6 | 4.2 | 15.0 |

For a 15-1 team, the Steelers were rarely heavy favorites; in fact, based on the point-spread in each game, Vegas would have expected Pittsburgh to win only 8.8 games. And while the Steelers played well in the first half, the main reason they achieved their lofty record was their 4th quarter performance. In fact, over half of their wins over average could be attributed to their great 4th quarter play. To put it another way, if you turned off every Pittsburgh game in 2004 right at the end of the 4th quarter, you would have guessed that the Steelers would win only 11.8 games.

That may not mean much in the abstract, but let’s compare the Steelers to the other teams with 15+ wins in NFL history:

tmyr | wpa_pre | wpa_1st | wpa_2nd | wpa_3rd | wpa_4th | wpa_tot |
---|---|---|---|---|---|---|

nwe2007 | 4.97 | 0.98 | 0.04 | 0.03 | 1.98 | 8 |

gnb2011 | 3.57 | 0.49 | 0.50 | 1.33 | 1.10 | 7 |

sfo1984 | 3.10 | 1.26 | 0.93 | -0.46 | 2.17 | 7 |

min1998 | 3.08 | 1.29 | 0.35 | 2.53 | -0.25 | 7 |

chi1985 | 2.77 | 0.02 | 0.68 | 1.84 | 1.69 | 7 |

pit2004 | 0.78 | 1.13 | 1.45 | -0.61 | 4.25 | 7 |

As you can see, the Steelers were somewhat of an outlier as far as 15-1 teams go. They weren’t expected to be that great based on the pre-game lines, and pulled out a lot of close games in the 4th quarter.

Fourth quarter play is certainly important, but the leverage associated with that quarter is clearly much more significant than it is in any other quarter. This made me wonder: if we completely ignored 4th quarter play, would that make our predictions better?^{1}

I looked at 780 pairs of team-seasons and noted how the team performed in Year N and how many games they won in Year N+1.^{2} If you look only at Year N records, the best-fit formula to predicting Year N+1 records is 5.11 + 0.36*Year N wins. The correlation coefficient is 0.36, indicating a mild relationship.

Now, what if we use both “Win Probability Through Three Quarters” and “Wins” as our Year N Inputs? In that case, the correlation coefficient is 0.38, but the key here are the p-values. The “WP T3Q” variable is extremely significant statistically, while the “Wins” variable is right on the border of being statistically significant with a p-value of 0.08.^{3} The best-fit formula becomes:

Year N+1 Wins = 4.41 + 0.33*WP-T3Q + 0.12*Wins

This is consistent with all other studies I’ve done showing that how a team performs in close games has very little predictive value. Listed below are the projected 2012 wins for each team based on their 2011 performance:

tm | wpa_veg | wpa_1st | wpa_2nd | wpa_3rd | wpa_4th | wpa_ot | WP-T3Q | WPA_4Q/OT | WINS | 2012 PROJ |
---|---|---|---|---|---|---|---|---|---|---|

gnb | 3.57 | 0.49 | 0.5 | 1.33 | 1.1 | 0 | 13.9 | 1.1 | 15 | 10.82 |

nwe | 3.24 | -0.75 | 1.11 | 1.49 | -0.1 | 0 | 13.1 | -0.1 | 13 | 10.31 |

sfo | 1.32 | -0.17 | 1.92 | 1.18 | 1.25 | -0.5 | 12.25 | 0.75 | 13 | 10.03 |

nor | 2.74 | 0.02 | 0.47 | 0.2 | 1.07 | 0.5 | 11.43 | 1.57 | 13 | 9.77 |

pit | 2.31 | 0.23 | 0.49 | 0.12 | 0.84 | 0 | 11.16 | 0.84 | 12 | 9.55 |

rav | 2.68 | 0.47 | -0.07 | -0.33 | 1.25 | 0 | 10.75 | 1.25 | 12 | 9.42 |

phi | 1.55 | -0.12 | 1.44 | 0.98 | -3.86 | 0 | 11.86 | -3.86 | 8 | 9.29 |

htx | 1.18 | 1.55 | 0.13 | -0.24 | -0.62 | 0 | 10.62 | -0.62 | 10 | 9.13 |

sdg | 1 | -0.29 | -0.04 | 0.95 | -0.62 | -1 | 9.62 | -1.62 | 8 | 8.55 |

det | 0.97 | -0.58 | -1.16 | 1.43 | 0.84 | 0.5 | 8.66 | 1.34 | 10 | 8.49 |

atl | 1.11 | 1.57 | -0.98 | -1.35 | 2.16 | -0.5 | 8.34 | 1.66 | 10 | 8.38 |

oti | 0.45 | -0.3 | 0.92 | -0.53 | 0.46 | 0 | 8.54 | 0.46 | 9 | 8.32 |

dal | 1.24 | 0.2 | -0.37 | -0.65 | -0.92 | 0.5 | 8.42 | -0.42 | 8 | 8.16 |

rai | -0.7 | -0.81 | 1.95 | -0.26 | -0.68 | 0.5 | 8.18 | -0.18 | 8 | 8.08 |

cin | -0.17 | 0.98 | -2.22 | 1.02 | 1.38 | 0 | 7.62 | 1.38 | 9 | 8.02 |

mia | -1.05 | 1.03 | 0.18 | 0.54 | -2.19 | -0.5 | 8.69 | -2.69 | 6 | 8 |

car | -0.86 | 0.5 | 1.1 | -0.08 | -2.66 | 0 | 8.66 | -2.66 | 6 | 7.99 |

chi | -0.44 | 0.83 | 0.9 | -1.46 | 0.67 | -0.5 | 7.83 | 0.17 | 8 | 7.97 |

nyg | 0.16 | -0.07 | -0.5 | -0.3 | 1.7 | 0 | 7.3 | 1.7 | 9 | 7.92 |

sea | -1.71 | 0.27 | -0.51 | 1.71 | -0.26 | -0.5 | 7.76 | -0.76 | 7 | 7.82 |

nyj | 1.06 | -1.08 | 0.2 | -0.93 | 0.74 | 0 | 7.26 | 0.74 | 8 | 7.78 |

crd | -1.08 | -0.7 | -1.1 | 0.12 | 0.77 | 2 | 5.23 | 2.77 | 8 | 7.12 |

was | -1.22 | -0.74 | 0.74 | -0.45 | -0.83 | -0.5 | 6.33 | -1.33 | 5 | 7.11 |

jax | -2.34 | -0.48 | 0.89 | 0.12 | -1.19 | 0 | 6.19 | -1.19 | 5 | 7.06 |

buf | -1.03 | 0.78 | -0.81 | -1.16 | 0.23 | 0 | 5.77 | 0.23 | 6 | 7.04 |

kan | -2.05 | 0.19 | -0.79 | -0.1 | 1.74 | 0 | 5.26 | 1.74 | 7 | 7 |

den | -1.14 | 0.99 | -3.45 | 0.2 | 1.9 | 1.5 | 4.6 | 3.4 | 8 | 6.91 |

min | -1.6 | 0.75 | -0.22 | -1.16 | -2.26 | -0.5 | 5.76 | -2.76 | 3 | 6.67 |

cle | -1.66 | -1.09 | 0.41 | -0.37 | -0.79 | -0.5 | 5.29 | -1.29 | 4 | 6.64 |

tam | -1.43 | -1.81 | -1.27 | 0.09 | 0.42 | 0 | 3.58 | 0.42 | 4 | 6.08 |

clt | -3.12 | -1.08 | 0.07 | -0.37 | -1.5 | 0 | 3.5 | -1.5 | 2 | 5.81 |

ram | -2.98 | -0.8 | 0.07 | -1.76 | -0.03 | -0.5 | 2.53 | -0.53 | 2 | 5.49 |

For each team, I listed their cumulative win probability added from their 16 regular season games based on the line before the game and the performance each quarter. WP-T3Q is not win probability added, but the sum of the individual win probabilities for each team by the end of the third quarter of each game. The next column shows how much win probability was added in the fourth quarter and overtime, and the final column shows the team’s win projection for 2012.

The obvious outlier team is the Eagles, who ironically have been excellent in the 4th quarter of 2012 with three fourth quarter comeback wins in their first four games. Philadelphia had another comeback against the Steelers in week five, although Pittsburgh responded with their own game-winning drive to steal the game.

Of course, the obvious overachiever last year would be the Cardinals^{4}, who have largely continued their 4th-quarter comeback ways so far this season.

- One nice side effect of using win probability over other standard stats is that we don’t have to worry about garbage time stats when we talk about 4th quarter play. For example, when the Jets played the Bills in week 1, New York was up 41-7 in the 3rd quarter but the Bills ended up scoring 28 points. But that doesn’t matter here: the Jets win probability was 98.6% at half-time, 100% by the end of the third quarter, and 100% at the end of the game. All of the Bills’ garbage time stats did not impact the win probability. [↩]
- I used all pair of seasons starting from 1983 to 2010, but excluded 1986 and 1987 due to the strike. [↩]
- I also ran a regression using just the WP-T3Q variable as the only input; the CC was 0.37, and the best-fit formula was 4.36 + 0.46*WP-T3Q. [↩]
- I’m not counting the Broncos, since replacing Tim Tebow with Peyton Manning makes all of this moot [↩]