[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:
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).
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))
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:
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:
[table id=161 /]
(“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):
[table id=162 /]