Feb 09 2017

The Super Bowl and Hindsight Bias

Brady SB51Full disclosure – I have been a Patriots fan since in the 1980s. I suffered through a couple long decades of rooting for a mediocre team, including the worst (at the time) Super Bowl defeat at the hands of the Bears. Then along came Belichick and Brady, and it has been a wild ride as a fan.

Super Bowl LI was perhaps the pinnacle – the Patriots came back from a 25 point deficit to tie the game and then win in sudden-death overtime. I feel genuinely bad for Falcons fans, but perhaps worse for those who stopped watching the game in the third quarter because they thought it was over. Those who stayed through to the end were rewarded with historically epic football.

(As an aside, I am a fan simply because it is fun to have a team to root for. Don’t read too much into it.)

What is interesting, from a critical thinking perspective, about the game is the way in which we construct narratives to explain random events, or at least events that have an element of randomness or “luck” involved. At half-time the Falcons were up 21-3 and the discussion among the commentators was all about how well the Falcons were playing and everything the Patriots were doing wrong. The Falcons had “momentum” and the Patriots had to figure out a way to steal this elusive “momentum” back.

Part way through the third quarter the Patriots started scoring, and the Falcons could not sustain a scoring drive. The Patriots ended up scoring 31 unanswered points. Clearly they got their mojo back, and were destined to win the whole time. The narrative then shifted to how Brady was perhaps the best quarterback of all time and Belichick is clearly magic, or perhaps made a deal with the devil. More seriously, some disgruntled fans were convinced the game was “rigged.” How else could you explain such a dramatic reversal of fortune?

But here’s the thing – I don’t think momentum in NFL football really even exists. Momentum is like a winning or losing “streak,” it is an illusion of the drunkards walk, applied only in hindsight to explain what happened. When statisticians examine professional sports they find little evidence for a “hot hands” effect in basketball or any other phenomenon that deviates outcomes from a statistically random pattern. I know there is still some debate about whether or not a tiny effect can be teased from the data, but there is certainly no dramatic effect. If not all of the streaks in┬áprofessional sports are random, then they are mostly random.

If a basketball player scores on 50% of their shots on the basket, then any given shot has a 50% chance of hitting, regardless of whether the last three shots hit or missed.

Baseball pitchers occasionally pitch a perfect game, without a single batter on the other team getting on base. If you calculate from average batting averages how often this should happen purely from chance, that is how often perfect games occur. There was nothing special about those games. It wasn’t the pitcher’s lucky underwear, or the home field advantage, or anything else. It was just a statistical streak.

I say this of professional sports because at that level the players are the best in the world. They are highly skilled and professional, which means minimizing the effects of variables like not making a strong effort, being distracted, or other psychological effects. Such factors become too small to detect, at least statistically.

In football there are some real factors to consider. Injuries may reduce a team’s effectiveness throughout a game, and the Falcons did lose a few players by the end of the game. There is also a chess-like competition between coaches, with each side making adjustments to counter the other’s strategy, and trying to outwit the other team. Belichick has a reputation for being exceptional at working the game, analyzing the match-up and making adjustments. Brady also deserves credit for never giving up, even when they were down by 25 points and their odds of winning were close to zero.

But a large part of the epic comeback was just chance. In the first half of the game the breaks just went against New England. Two turn-overs resulted in two of the Falcon’s three touchdowns. Little differences, or just a couple of quirky plays, can have a big different on the scoreboard. What’s interesting is that the commentators often base their narrative not on overall play, but on the scoreboard.

While I agree the Falcons were playing better than New England in the first half, that does not fully explain the 28-3 lead they held in the third quarter, which makes the Patriot’s come back seem more amazing. In reality, the Patriots were the same team in the first half, the dice were just not falling their way. The second half was mostly regression to the mean.

The Patriots also got lucky in the fourth quarter. One of their touchdowns was helped by three holding calls against the Falcons that led to Patriot first downs. It is possible that if not for one holding call the Patriots would have lost the game, then the narrative would have been very different. Instead of talking about how Brady was the best quarterback of all time, commentators might be saying that his career is over – because of one holding call.

I also think there is an interesting analogy to the recent presidential election. Hindsight bias causes us to look for explanations and invent narratives to explain quirky or close outcomes. Trump won the electoral vote because of narrow victories in three close states. Just like in football, small differences in total voting had a magnified effect on the “score.” If only 80 thousand votes had gone the other way, Clinton could have won.

But the narrative after the election treated the outcome as inevitable. Everything Trump did “worked,” it’s a sign of the times, and there were numerous explanations for Clinton’s failure. Flip a small percentage of votes and the narrative would also have flipped.

There were very real factors affecting the outcome of the election, but the pitfall is in overinterpreting narrow outcomes as if they were inevitable.

Super Bowl LI was a statistical outlier. Prior to this game, the three Super Bowl games which involved a team winning after being down by 10 points were the greatest comebacks. Now that number has risen to 25 points, and this record will likely stand for a long time. That such a comeback occurred in one game out of 51 (and probably will not be replicated for another 50 games) is consistent with randomness. It is epic because it is rare, but even rare events statistically should happen at a rate proportional to their rareness.

It is OK to have fun reveling in a statistically rare event, especially when the dice roll your way. Just don’t buy into the narratives people invent to impose a comforting order on the chaos.

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