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[Today is a two-post day at Football Perspective. Check here for my week 2 power rankings, while Neil provides an innovative look at the biggest comebacks of the last 35 years in this post. — Chase

In my last post, I introduced a method of estimating the home team’s pre-game win probability in Excel using the Vegas spread:

p(W) = (1-NORMDIST(0.5,-(home_line),13.86,TRUE)) + 0.5*(NORMDIST(0.5,-(home_line),13.86,TRUE)-NORMDIST(-0.5,-(home_line),13.86,TRUE))

The Comeback ranks as the 2nd most impressive comeback after two quarters, but only 20th overall.

Let me explain the rationale behind the scary-looking equation. The first part represents the probability that the home team ends regulation time with a lead of 1 point or more, using Hal Stern’s finding that the home team’s final margin of victory can be approximated by a normal random variable with a mean of the Vegas line and a standard deviation of 13.86. The second part is the probability that regulation ends in a tie, multiplied by 0.5 (this assumes each team has roughly a 50-50 chance of winning in overtime).

With a small twist, we can also apply this formula within games, to the line-score data for every quarter. Within a game, the home team’s probability becomes:

p(W) = (1-NORMDIST(away_margin+0.5,-home_line*(minleft/60),13.86/SQRT(60/minleft),TRUE))+0.5*(NORMDIST(away_margin+0.5,-home_line*(minleft/60),13.86/SQRT(60/minleft),TRUE)-NORMDIST(away_margin-0.5,-home_line*(minleft/60),13.86/SQRT(60/minleft),TRUE))

This is the same equation as before, but we’re adding in Home_Margin (home team pts minus road team pts for the game, through the end of the quarter in question), reducing the effect of the home Vegas line linearly based on how much time remains in the game, and changing the standard deviation of scoring margin to become:

Stdev = 13.86 / sqrt(60 / n)

where n = the number of minutes remaining in the game.

These changes will help us estimate a team’s chances of winning at the end of each quarter. For instance, Monday night’s game — where the Falcons were a 3-point home favorite over the Broncos — goes from:

Team1st2nd3rd4thTotal
Atlanta10107027
Denver0701421

To this:

TeamPregameAfter 1stAt HalfAfter 3rdFinal
Atlanta58.6%84.6%93.0%99.9%100.0%
Denver41.4%15.4%7.0%0.1%0.0%

If you made it through all that, my hat’s off to you — and now let’s look at the real reason you’re here, the list of the biggest quarter-by-quarter comebacks since 1978. In each case, the columns represent the percentage likelihood of winning for the home team:

RankGamePregameAfter 1stAt HalfAfter 3rdAfter 4thFinalComeback
112/1/1985 – min 28 @ phi (-6.5) 2368.03%89.22%99.11%99.98%0.00%0.00%0.02%
211/8/1987 – tam 28 @ crd (-2.5) 3157.15%33.48%16.02%0.02%100.00%100.00%0.02%
310/23/2000 – mia 37 @ nyj (-3) 4058.56%10.98%6.98%0.07%50.00%100.00%0.07%
410/6/2003 – clt 38 @ tam (-4.5) 3562.72%92.60%99.11%99.93%50.00%0.00%0.07%
511/26/2006 – nyg 21 @ oti (3.5) 2440.04%21.15%1.02%0.08%100.00%100.00%0.08%
69/12/1999 – dal 41 @ was (-2.5) 3557.15%42.98%51.02%99.91%50.00%0.00%0.09%
710/4/1992 – was 24 @ crd (10) 2723.54%3.68%1.25%0.16%100.00%100.00%0.16%
810/21/1984 – nor 27 @ dal (-6) 3066.74%73.38%20.75%0.25%50.00%100.00%0.25%
99/26/1988 – rai 30 @ den (-6.5) 2768.03%83.85%99.73%95.29%50.00%0.00%0.27%
1012/4/2005 – buf 23 @ mia (-3) 2458.56%5.93%4.63%0.28%100.00%100.00%0.28%
1110/4/1992 – chi 20 @ min (-4) 2161.35%50.00%13.12%0.31%100.00%100.00%0.31%
1212/11/1993 – sfo 24 @ atl (8) 2728.20%30.87%7.68%0.31%100.00%100.00%0.31%
1312/5/2004 – cin 27 @ rav (-6.5) 2668.03%74.39%73.79%99.63%0.00%0.00%0.37%
1410/8/1995 – clt 27 @ mia (-10) 2476.46%96.32%99.60%99.12%50.00%0.00%0.40%
159/17/2006 – nyg 30 @ phi (-3) 2458.56%57.43%87.94%99.47%50.00%0.00%0.53%
1610/12/2003 – kan 40 @ gnb (-2.5) 3457.15%77.00%79.97%99.44%50.00%0.00%0.56%
1712/27/2009 – tam 20 @ nor (-14) 1784.36%97.93%98.38%99.41%50.00%0.00%0.59%
1812/7/1980 – nor 35 @ sfo (-7) 3869.31%23.32%0.63%3.89%50.00%100.00%0.63%
1912/6/1992 – ram 31 @ tam (-1) 2752.87%71.29%99.37%68.00%0.00%0.00%0.63%
201/3/1993 – oti 38 @ buf (-2) 4155.73%41.76%0.72%30.72%50.00%100.00%0.72%
2110/28/2001 – nor 34 @ ram (-12) 3180.65%95.20%99.28%28.24%0.00%0.00%0.72%
2212/11/1983 – clt 19 @ den (-8.5) 2173.00%61.06%11.56%0.76%100.00%100.00%0.76%
2312/21/1996 – nwe 23 @ nyg (8.5) 2227.00%35.79%96.48%99.24%0.00%0.00%0.76%
249/12/1982 – ram 23 @ gnb (1) 3547.13%18.54%0.83%9.15%100.00%100.00%0.83%
2512/24/1995 – min 24 @ cin (5) 2735.92%37.75%0.83%11.75%100.00%100.00%0.83%
2611/10/1996 – crd 37 @ was (-10.5) 3477.55%74.39%70.37%99.16%50.00%0.00%0.84%
2710/4/1998 – det 27 @ chi (-2) 3155.73%23.96%54.06%0.88%100.00%100.00%0.88%
2811/4/1990 – was 41 @ det (3) 3841.44%42.57%89.86%99.03%50.00%0.00%0.97%
298/31/1997 – crd 21 @ cin (-7.5) 2470.57%45.44%23.00%1.01%100.00%100.00%1.01%
3010/25/1987 – buf 34 @ mia (-9.5) 3175.33%96.07%98.98%82.06%50.00%0.00%1.02%
319/13/1981 – atl 31 @ gnb (4) 1738.65%63.04%88.93%98.94%0.00%0.00%1.06%
3211/24/1996 – jax 28 @ rav (-4) 2561.35%79.74%79.25%98.94%50.00%0.00%1.06%
3310/10/2004 – ram 33 @ sea (-8) 2771.80%86.04%98.38%98.94%50.00%0.00%1.06%
3412/19/2010 – phi 38 @ nyg (-3) 3158.56%77.93%98.91%98.31%0.00%0.00%1.09%
3511/18/1984 – mia 28 @ sdg (7) 3430.69%55.79%14.23%1.17%50.00%100.00%1.17%
3610/2/2011 – sfo 24 @ phi (-10) 2376.46%88.63%98.75%88.94%0.00%0.00%1.25%
3711/6/1988 – sfo 23 @ crd (-3) 2458.56%47.51%6.98%1.41%100.00%100.00%1.41%
381/5/2003 – nyg 38 @ sfo (-3) 3958.56%57.43%10.14%1.41%100.00%100.00%1.41%
3910/31/1993 – det 30 @ min (-4) 2761.35%59.86%72.95%98.46%0.00%0.00%1.54%
4012/30/2001 – pit 23 @ cin (8) 2628.20%4.80%13.12%1.54%50.00%100.00%1.54%
4110/23/1983 – atl 27 @ nyj (-3.5) 2159.96%58.65%81.37%98.39%0.00%0.00%1.61%
4211/28/1999 – kan 37 @ rai (-3.5) 3459.96%68.02%68.58%98.39%0.00%0.00%1.61%
4312/3/1979 – rai 42 @ nor (-3) 3558.56%34.63%94.29%98.31%0.00%0.00%1.69%
4411/27/1980 – chi 23 @ det (-3) 1758.56%66.89%80.68%98.31%50.00%0.00%1.69%
4511/21/1983 – nyj 31 @ nor (-3) 2858.56%77.93%56.07%98.31%0.00%0.00%1.69%
4610/27/1985 – buf 17 @ phi (-9) 2174.18%49.17%28.76%1.69%100.00%100.00%1.69%
471/4/1981 – dal 30 @ atl (-2.5) 2757.15%77.00%79.97%98.24%0.00%0.00%1.76%
489/12/1982 – was 37 @ phi (-6.5) 3468.03%89.22%59.07%98.24%50.00%0.00%1.76%
4911/19/2000 – sdg 37 @ den (-9.5) 3875.33%63.43%17.29%1.76%100.00%100.00%1.76%
5012/10/1995 – sea 31 @ den (-7) 2769.31%89.79%98.16%95.46%0.00%0.00%1.84%
5110/28/1984 – den 22 @ rai (-6) 1966.74%86.94%82.05%98.16%50.00%0.00%1.84%
529/10/2000 – rai 38 @ clt (-6.5) 3168.03%94.19%98.05%21.96%0.00%0.00%1.95%
5311/12/2006 – sdg 49 @ cin (1.5) 4145.69%95.10%98.05%91.70%0.00%0.00%1.95%
549/28/1980 – nor 16 @ mia (-7) 2169.31%66.89%28.76%2.01%100.00%100.00%2.01%
5510/21/1984 – pit 16 @ clt (5) 1735.92%28.71%5.71%2.01%100.00%100.00%2.01%
569/13/1987 – ram 16 @ oti (5) 2035.92%20.85%10.14%2.01%100.00%100.00%2.01%
5711/26/1989 – ram 20 @ nor (0) 1750.00%71.99%76.22%97.80%50.00%0.00%2.20%
589/20/1992 – cin 23 @ gnb (0) 2450.00%50.00%23.78%2.20%100.00%100.00%2.20%
5911/3/1996 – cin 24 @ rav (-3.5) 2159.96%78.85%97.79%95.63%0.00%0.00%2.21%
609/16/1990 – crd 23 @ phi (-13.5) 2183.48%97.77%91.94%93.23%0.00%0.00%2.23%
6111/12/1978 – oti 26 @ nwe (-7) 2369.31%82.55%97.65%93.91%0.00%0.00%2.35%
6210/5/1980 – buf 26 @ sdg (-7) 2469.31%77.93%80.68%97.61%0.00%0.00%2.39%
6311/9/1980 – kan 31 @ sea (-3) 3058.56%47.51%94.29%97.61%0.00%0.00%2.39%
6410/6/1991 – phi 13 @ tam (3) 1441.44%42.57%43.93%2.39%100.00%100.00%2.39%
6511/1/1992 – oti 20 @ pit (3) 2141.44%33.11%47.97%2.39%100.00%100.00%2.39%
669/19/1993 – cle 19 @ rai (-3) 1658.56%84.61%93.02%97.61%0.00%0.00%2.39%
679/29/1996 – ram 28 @ crd (-1) 3152.87%30.14%25.39%2.39%50.00%100.00%2.39%
6812/29/2002 – sea 31 @ sdg (-3) 2858.56%34.63%67.67%97.61%50.00%0.00%2.39%
6912/11/1983 – crd 34 @ rai (-9) 2474.18%97.60%80.68%45.70%0.00%0.00%2.40%
709/5/1983 – dal 31 @ was (1.5) 3045.69%77.00%97.51%79.09%0.00%0.00%2.49%
719/17/1989 – nor 34 @ gnb (4.5) 3537.28%7.40%2.49%27.64%100.00%100.00%2.49%
7211/27/2005 – ram 33 @ htx (3.5) 2740.04%64.21%97.51%97.06%50.00%0.00%2.49%
7312/26/2010 – htx 23 @ den (2.5) 2442.85%23.00%3.15%2.49%100.00%100.00%2.49%
7410/2/2011 – det 34 @ dal (-2.5) 3057.15%77.00%96.85%97.51%0.00%0.00%2.49%
7512/11/1989 – sfo 30 @ ram (2) 2744.27%90.15%72.95%97.40%0.00%0.00%2.60%
769/10/1995 – clt 27 @ nyj (2) 2444.27%85.09%90.74%97.40%50.00%0.00%2.60%
7711/26/1995 – nwe 35 @ buf (-6) 2566.74%64.60%88.93%97.40%0.00%0.00%2.60%
7812/30/2002 – sfo 20 @ ram (-2) 3155.73%45.03%5.15%2.60%100.00%100.00%2.60%
7911/20/1983 – det 23 @ gnb (-4) 2061.35%71.99%97.36%87.52%50.00%0.00%2.64%
8011/21/2010 – buf 49 @ cin (-4) 3161.35%59.86%97.36%71.76%0.00%0.00%2.64%
8112/8/1991 – buf 30 @ rai (-1.5) 2754.31%63.43%75.42%97.29%50.00%0.00%2.71%
8210/31/1999 – nyg 23 @ phi (2.5) 1742.85%43.80%90.31%97.29%50.00%0.00%2.71%
8312/14/1997 – sea 22 @ rai (-1.5) 2154.31%89.60%97.20%91.14%0.00%0.00%2.80%
849/19/1999 – clt 28 @ nwe (-4.5) 3162.72%18.82%2.80%3.19%100.00%100.00%2.80%
8510/1/1989 – atl 21 @ gnb (-7) 2369.31%44.21%32.33%2.83%100.00%100.00%2.83%
8610/6/1991 – min 20 @ det (-3) 2458.56%34.63%16.65%2.83%100.00%100.00%2.83%
8712/15/1991 – mia 30 @ sdg (1) 3847.13%37.75%47.97%2.83%100.00%100.00%2.83%
8810/25/1981 – kan 28 @ rai (-3) 1758.56%77.93%97.03%93.91%0.00%0.00%2.97%
8912/1/1986 – nyg 21 @ sfo (-3) 1758.56%66.89%97.03%32.00%0.00%0.00%2.97%
9011/8/1992 – cin 31 @ chi (-9) 2874.18%71.29%97.03%90.85%50.00%0.00%2.97%
9110/14/2001 – mia 17 @ nyj (3) 2141.44%22.07%2.97%29.47%100.00%100.00%2.97%
929/25/2011 – det 26 @ min (3) 2341.44%62.25%97.03%90.85%50.00%0.00%2.97%
9311/29/1981 – rai 32 @ sea (0) 3150.00%50.00%76.22%96.93%0.00%0.00%3.07%
9412/21/1986 – was 21 @ phi (4) 1438.65%82.01%88.93%96.93%0.00%0.00%3.07%
9510/13/1991 – rai 23 @ sea (-2.5) 2057.15%65.76%96.85%93.69%50.00%0.00%3.15%
9611/13/1994 – min 20 @ nwe (2.5) 2642.85%16.15%3.15%6.31%50.00%100.00%3.15%
9712/27/1997 – min 23 @ nyg (-4.5) 2262.72%78.24%96.85%92.75%0.00%0.00%3.15%
9811/4/2001 – cle 21 @ chi (-4.5) 2762.72%38.14%59.07%3.19%50.00%100.00%3.19%
9910/5/2003 – rai 21 @ chi (3.5) 2440.04%23.64%4.39%3.19%100.00%100.00%3.19%
10010/26/1980 – pit 26 @ cle (3) 2741.44%15.39%22.24%3.32%100.00%100.00%3.32%

(“Comeback” lists the lowest probability that the winning team had at the end of any quarter.)

And just for fun, here’s a table of QBs since ’78 who led a comeback team in attempts during the game in question, ranked by the sum of their career “comeback points” (100% minus the comeback scores listed above):

RkQuarterbackComeback PtsBiggest ComebackScore
1Brett Favre90.649/20/1992 - gnb 24, cin 2397.80%
2Dan Marino76.841/5/1991 - mia 17, kan 1696.26%
3John Elway75.1112/11/1983 - den 21, clt 1999.24%
4Peyton Manning67.7610/6/2003 - clt 38, tam 3599.93%
5Tom Brady61.1912/2/2001 - nwe 17, nyj 1693.02%
6Joe Montana60.3512/7/1980 - sfo 38, nor 3599.37%
7Vinny Testaverde56.6510/23/2000 - nyj 40, mia 3799.93%
8Warren Moon54.829/13/1987 - oti 20, ram 1697.99%
9Drew Bledsoe53.2812/21/1996 - nwe 23, nyg 2299.24%
10Dave Krieg53.249/17/1995 - crd 20, det 1796.54%
11Jim Kelly51.2010/25/1987 - buf 34, mia 3198.98%
12Donovan McNabb49.7710/10/2010 - was 16, gnb 1393.91%
13Phil Simms48.9512/1/1986 - nyg 21, sfo 1797.03%
14Steve McNair47.849/8/2002 - oti 27, phi 2493.46%
15Kerry Collins47.3312/17/1995 - car 21, atl 1792.15%
16Drew Brees47.3311/17/2002 - sdg 20, sfo 1793.69%
17Boomer Esiason44.8411/10/1996 - crd 37, was 3499.16%
18Randall Cunningham43.6912/27/1997 - min 23, nyg 2296.85%
19Eli Manning42.269/17/2006 - nyg 30, phi 2499.47%
20Mark Brunell41.9911/24/1996 - jax 28, rav 2598.94%
21Ben Roethlisberger41.8110/17/2004 - pit 24, dal 2093.91%
22Matt Hasselbeck41.7412/29/2002 - sea 31, sdg 2897.61%
23Troy Aikman41.349/12/1999 - dal 41, was 3599.91%
24Brad Johnson40.6610/8/2006 - min 26, det 1796.40%
25Jake Plummer39.499/12/1999 - crd 25, phi 2495.37%
26Dan Fouts37.5811/18/1984 - sdg 34, mia 2898.83%
27Rich Gannon37.3910/4/1992 - min 21, chi 2099.69%
28Ron Jaworski37.2210/27/1985 - phi 21, buf 1798.31%
29Chris Chandler36.8910/4/1992 - crd 27, was 2499.84%
30Jim Harbaugh36.6910/8/1995 - clt 27, mia 2499.60%
31Jim Everett36.2712/6/1992 - ram 31, tam 2799.37%
32Joe Theismann36.219/12/1982 - was 37, phi 3498.24%
33Jim McMahon34.1510/25/1987 - chi 27, tam 2691.42%
34Steve Young34.0511/15/1992 - sfo 21, nor 2095.11%
35Steve DeBerg34.0111/13/1988 - kan 31, cin 2893.69%
36Jay Schroeder33.349/26/1988 - rai 30, den 2799.73%
37Trent Dilfer33.1411/17/1996 - tam 25, sdg 1791.19%
38Kurt Warner32.819/30/2007 - crd 21, pit 1483.35%
39Jake Delhomme32.7611/14/2004 - car 37, sfo 2793.36%
40Danny White31.6110/21/1984 - dal 30, nor 2799.75%
41Steve Bartkowski31.419/13/1981 - atl 31, gnb 1798.94%
42Jeff Garcia30.991/5/2003 - sfo 39, nyg 3898.59%
43Neil O'Donnell30.2911/1/1992 - pit 21, oti 2097.61%
44Bobby Hebert30.0712/11/1993 - atl 27, sfo 2499.69%
45Philip Rivers29.7611/12/2006 - sdg 49, cin 4198.05%
46Jon Kitna29.6912/30/2001 - cin 26, pit 2398.46%
47Steve Grogan29.529/24/1978 - nwe 21, rai 1494.19%
48Tommy Kramer29.1312/14/1980 - min 28, cle 2393.02%
49Michael Vick29.0812/19/2010 - phi 38, nyg 3198.91%
50Doug Williams29.0512/4/1988 - was 20, phi 1992.24%
51Trent Green28.4110/12/2003 - kan 40, gnb 3499.44%
52Steve Beuerlein28.3011/5/2000 - car 27, ram 2494.92%
53Joe Ferguson28.2910/5/1980 - buf 26, sdg 2497.61%
54Neil Lomax28.2711/8/1987 - crd 31, tam 2899.98%
55Ken O'Brien27.859/24/1989 - nyj 40, mia 3395.79%
56Bernie Kosar27.2710/26/1986 - cle 23, min 2094.85%
57Gus Frerotte27.1111/19/2000 - den 38, sdg 3798.24%
58Carson Palmer26.4812/5/2004 - cin 27, rav 2699.63%
59Kordell Stewart26.4010/5/2003 - chi 24, rai 2196.81%
60Rodney Peete26.2310/31/1993 - det 30, min 2798.46%
61Jeff George26.1811/10/1991 - clt 28, nyj 2792.30%
62Richard Todd25.7811/21/1983 - nyj 31, nor 2898.31%
63Stan Humphries25.7211/13/1994 - sdg 14, kan 1393.02%
64Jeff Hostetler25.711/2/1994 - rai 33, den 3090.85%
65Jeff Blake25.1712/24/1995 - cin 27, min 2499.17%
66Jim Zorn24.5111/8/1981 - sea 24, pit 2196.11%
67Aaron Brooks24.1510/28/2001 - nor 34, ram 3199.28%
68Brian Sipe23.9810/26/1980 - cle 27, pit 2696.68%
69Tony Romo23.7810/29/2006 - dal 35, car 1493.43%
70Mark Rypien23.7712/17/1989 - was 31, atl 3091.55%
71Jim Plunkett22.9811/22/1982 - rai 28, sdg 2495.37%
72Chad Pennington22.9511/9/2003 - nyj 27, rai 2492.99%
73Terry Bradshaw22.759/16/1979 - pit 24, crd 2196.40%
74Jay Cutler22.7111/6/2008 - den 34, cle 3093.91%
75Ken Stabler22.6812/3/1979 - rai 42, nor 3598.31%
76David Garrard22.3512/4/2005 - jax 20, cle 1483.35%
77Brian Griese22.0811/23/2003 - mia 24, was 2394.73%
78Elvis Grbac21.9811/28/1999 - kan 37, rai 3498.39%
79Daunte Culpepper21.7310/23/2005 - min 23, gnb 2094.85%
80Marc Bulger21.6610/10/2004 - ram 33, sea 2798.94%
81Bill Kenney21.3510/25/1981 - kan 28, rai 1797.03%
82Joe Flacco21.3110/30/2011 - rav 30, crd 2789.40%
83Lynn Dickey21.319/12/1982 - gnb 35, ram 2399.17%
84Matt Ryan20.829/18/2011 - atl 35, phi 3193.69%
85Tony Banks20.639/10/2000 - rav 39, jax 3693.02%
86Doug Flutie20.4312/15/1986 - chi 16, det 1386.38%
87Bubby Brister20.4311/26/1989 - pit 34, mia 1494.88%
88Jay Fiedler20.2312/30/2000 - mia 23, clt 1793.36%
89Mike Tomczak19.6110/25/1992 - cle 19, nwe 1783.88%
90Erik Kramer19.5610/4/1998 - chi 31, det 2799.12%
91Wade Wilson19.3112/1/1985 - min 28, phi 2399.98%
92Marc Wilson19.2711/29/1981 - rai 32, sea 3196.93%
93Alex Smith19.0510/2/2011 - sfo 24, phi 2398.75%
94Chris Miller18.679/18/1988 - atl 34, sfo 1786.94%
95Aaron Rodgers18.381/15/2011 - gnb 48, atl 2175.06%
96Jason Campbell18.3110/5/2008 - was 23, phi 1794.19%
97Kyle Orton18.0510/11/2009 - den 20, nwe 1787.94%
98Ken Anderson17.9912/11/1978 - cin 20, ram 1993.16%
99David Woodley17.5111/8/1981 - mia 30, nwe 2789.86%
100Matt Schaub17.399/19/2010 - htx 30, was 2790.85%
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