A couple weeks ago, that long-held record got broken kind of like Michael Johnson broke the 200-meter record in the Atlanta Olympics. Malcolm Butler’s pick obliterated the old mark. My estimate has the Butler interception as increasing the Patriots’ chances of winning by 0.87. There is no doubt that what some have called the Immaculate Interception is on an island by itself as the most influential play in NFL history.

To get that change in win probability from Butler’s play, I am going to assume that the Seahawks would have run on third and fourth down. I am going to give a run from the one a 60% chance of working. That might seem high, but the Patriots were the worst team in football in stuffing the run in important short-yardage situations either on third or fourth down, or down by the goal line. And their limited success mostly came against terrible running teams. It is not a huge sample, but against teams outside the worst quarter of rushing teams by DVOA, the Patriots had allowed opponents to convert 16 of 17 times with two yards or less to go for a first down or touchdown. If we add the playoffs, they actually had three more stops against good running teams (Baltimore and Seattle), albeit in games where the opponent had a good amount of success on the ground. ^[2]Note that the stop against Baltimore should not even count. In an otherwise great game for Gary Kubiak, he called for a reverse to Michael Campanaro on third-and-1 in the second quarter. The run was … Continue reading With Seattle being the best rushing team in football by a mile and the Patriots being at best not great in run defense in that situation, it seems hard to think that Seattle had anything less than a 0.60 chance of scoring on a run.

Here are my other assumptions:

• Give Seattle a 2% chance of throwing an interception on the slant. ^[3]You could argue this is too high. It’s not going to make a big difference, but I do think the chance of the pick on that route is higher with Russell Wilson height making it even a little more … Continue reading
• Give Seattle a 0.5% chance of fumbling on a running play.
• The slant had a 55% chance of scoring a touchdown.
• The Patriots have a 5% chance of winning if the second down play scored the touchdown with a snap at 0:26, 3% if it was second down, and 1% if fourth down. ^[4]Really think these might be a little high, if anything.

Under those assumptions, the Seahawks’ win probability at the snap―taking the slant call as given―was 0.87. ^[5]There’s just one thing to add here. You would want to account for the possibility of a run losing yardage. To keep things not too complicated, I have not done that here. But my other assumptions … Continue reading

Prob (Score 2^nd down)*Prob (Win if Score) + Prob (3^rd down happens)*Prob (Score 3^rd down)*Prob (Win if Score) + Prob (4^th down happens)*Prob (Score 4^th down)*Prob (Win if Score) =

0.55*0.95 + 0.43*0.60*0.97 + 0.17*0.60*0.99 = 0.874

One interesting thing to note is that Pete Carroll’s seemingly odd explanation about wasting a play is not quite that crazy. If the Seahawks had just thrown the ball away on second down to waste some time, but leave them the timeout to run twice, their win probability was 0.82. That fall is small in part because the Patriots’ chances of winning after a Seattle score get even lower if they score on a later down. It’s still not a great idea because Marshawn Lynch’s chances of scoring on third or fourth down are not 100%, but Carroll may have been thinking along these lines. ^[6]Chase note: It’s also crazy because the “not wasting a play” idea was self-inflicted.  Seattle chose to snap the ball with 26 seconds left, which makes me think that Carroll is … Continue reading

Two other plays from this postseason deserve special note. First, the Jermaine Kearse Manna-from-Heaven catch could have been a top five most-influential play in NFL history. Under my rules, it does not get on the list because a game can only have one play on the list and the team that it hurts has to not win the Super Bowl in the end. But if Marshawn Lynch ran it in and the Seahawks won, the Kearse catch would have been the play that hurt the Patriots more than any other. Brian Burke’s Win Probability Calculator assigns the Patriots a 62% chance of winning at the snap and a 25% chance of winning after the completion. So the calculator estimates that the Kearse catch lowered the Patriots’ chances by 37%, eerily similar to the 39% hit the Patriots took from the Helmet Catch.

While that play does not make the cut because the Immaculate Interception wiped it out, another play from this postseason almost did squeeze onto the expanded list. The onside kick recovery by Seattle in the NFC Championship game, according to my estimates, lowered the Packers’ chances of winning the Super Bowl by about 14 percentage points. Here are the ingredients for that calculation:

• Give Green Bay a 0.8 chance of recovering the onside kick
• Green Bay has a 0.95 chance of winning if they recover
• Green Bay has a 0.55 chance of winning if they don’t recover ^[7]Burke’s calculator estimates this as 0.64. That seems too low to me, so I am adjusting that number a bit.
• Green Bay would have had 0.45 chance of beating the Patriots in the Super Bowl.

So, before the onside kick, the Packers’ chances of winning the Super Bowl were:

[Prob(Recover onside kick)*Prob(Beat Seattle if recover) + Prob(Don’t Recover)*Prob(Beat Seattle if don’t)]*Prob(Beat New England) = (0.8*0.95 + 0.2*0.55) * 0.45 = 0.39

After the onside kick, the Packers’ chances of winning the Super Bowl were:

Prob(Beat Seattle after not recovering) * Prob (Beat New England) = 0.55*0.45 = 0.25

So the failure to recover the onside kick lowered the Packers’ chances of winning the Super Bowl by 14 percentage points, leaving the Brandon Bostick botched recovery just off the list.

Below is the updated and expanded-to-25-plays list of the most influential plays in NFL history. The full set of ground rules can be found in last year’s post. The SBD, or Super Bowl Delta, value refers to the change in the probability of winning the Super Bowl for the team on the short end of the play. Since Norwood’s miss lowered the Bills’ chances of winning the Super Bowl by 45 percentage points, I assign an SBD value of 45 to that play.

On this updated list, Butler’s pick looks like Tiger Woods’s -12 on top of the scoreboard at the 2000 U.S. Open. The Immaculate Interception stands alone, almost twice as influential as any other play in the Super Bowl era.

Despite being an unorthodox decision, most fans approved of the move. I do as well. Against arguably the best team in the league and your division rival, on the road, why not take the gamble? Is 1-8-1 that much better than 1-9, because punting in that situation is clearly playing for the tie. However, I think it’s important to make a clear distinction here, because stats guys are always recommending teams to go for it more frequently on fourth down.

This was *not* one of those cases. The numbers say this was a bad move. That’s exactly why this decision should be characterized as a a gamble. It’s okay to be risky for riskiness’ sake, but it’s important to recognize that that’s the reason. You’re playing for the variance here, not for the expected value. According to Brian Burke, Jacksonville would have needed a 55% chance of converting to make going for it the smart play. Over time, 4th and 10 plays are converted at roughly a 35% rate, and I don’t think that’s going to be higher when it’s Chad Henne against one of the best defenses in the league, regardless of how the rest of the game unfolded.

An incomplete pass, and your win probably decreases to 30% (never mind what happens on a sack or potential interception return). Give Houston the ball at say, their 14 following a punt, and you have a 60% chance of winning (this counts a tie as half a win). If you convert, you have a 76% chance of winning. Assuming a 35% rate, your win probably if you go for it is just 46% compared to 60% if you punt.

So the numbers don’t say going for it was the smart play. This was a gamble in every sense of the word. When statistical analysts argue that teams should go for it more often on 4th and 1, we’re not advocating risky moves; we’re advocating smart ones. This was risk for risk’s sake — which, given the situation, was probably appropriate.