Sunday, November 25, 2012

The difference between winning and losing

Oklahoma football coach Bob Stoops likes to say, "there's a big difference between winning and losing." Generally this in invoked after a narrow victory especially when the opponent was supposedly over matched. Here is an example from the 2002 season describing the 37-27 victory over Alabama where OU had blown a 20-point lead. And here is an example from the 2004 season describing the 42-35 victory over Texas A&M. But here is an example from this season where he is seemingly contradicting the often repeated mantra. Last night's thrilling Bedlam game gave Stoops another chance to claim that the difference between winning and losing is a vast gulf. So far, I don't believe he has.

I am not aiming to indict Bob Stoops for this common but nonetheless faulty reasoning. Many coaches in many sports have said the same. But I do want to take this opportunity to dispute the idea that a narrow victory is a substantial victory, and I will be using OU as my example. I had planned this blog post before last night's game. What an interesting coincidence that the game was a perfect example for the case I will make.

Missed it by that much

Stoops, et al. have it backwards. There is actually a very little difference between winning and losing in general in life and especially in college football. College football outcomes, like in the NFL, are surprisingly largely driven by random chance. For the NFL, Brian Burke estimates that over 50% of the outcome is random. I've made similar calculations to those of Brian to come up with a 60%-70% share of college football outcomes attributable to random chance. That alone should give us pause. If there is a lot of randomness (a large error term) in football outcomes, how much or little credit can we attribute to everything else?

Let's think about the difficulty in evaluating performances ex post without letting the actual outcome bias the appraisal. Consider a comeback against a lesser opponent that falls short versus one that succeeds. Suppose the game ends up being decided by a last second field goal attempted by the team favored to win. Make the field goal, and the commentators will look back on a splendid series of gritty plays that made the difference. Miss it, and the same commentators will describe how inept was the entire performance. This isn't consistent. All of the performance was the same up until that one single play.

So it turns out that a "brilliant" throw by a quarterback threading the needle between two defenders for a touchdown and the same throw being "ill advised" when intercepted can impact both the outcome of a game greatly as well as how we feel about that outcome. The random factors that govern the success of such a high impact, high sensitivity event are probably the critical factors, and they can cut either way. It seems there really is a fine line between stupid and clever.

OU was close, very close, to winning the BCS National Championship in the 2003 and 2008 seasons. A handful of plays against LSU and Florida, respectively, went a long way to determining those championship games' outcomes. But it would be inconsistent to hold that view about those seasons and games while clinging to the Big Difference theory. If the Big Difference is true, OU was a long way away from holding the crystal ball. Similarly, the Sooners were able to ever so narrowly escape numerous tight situations in their 2000 title run. Oklahoma State was a few fingertips away on a last-second, touchdown pass to ending the dream season. But for a few heroics at Texas A&M two weeks before the OSU game and in the Big XII title game against Kansas State, OU would have been out of the hunt. In the championship game itself Florida State came very close to winning.

Here are the lessons to draw from this:
  • It is not the actual outcome of specific close events that matter so much as the entire volume of evidence. 
  • As distasteful to some as it is, margin of victory matters. Prediction models for college football among others are significantly enhanced when margin of victory is included rather than just win-loss results.
  • Whether declaring the strength of the mandate a close election has created for a winning candidate or trumpeting a narrow victory on the gridiron, the logic is flawed. We need to be humble and reasonable in our assessments. That includes working hard to not let the outcome bias the assessment. 
Congratulations to both the Sooners and the Cowboys on a great game filled with wonderful excitement. As a fan I can write that more easily because my team prevailed. I know that my joy is not equal to the pain felt by Cowboy fans, and, perverse as it is, my joy is enhanced knowing they suffer and what that suffering feels like--I've been on the other side. I am very happy the Sooners won. I'm not sure if I wish they could have won 51-0 rather than 51-48, but I am sure a 51-0 outcome would mean a lot more.

Update: edited to correct a few grammatical mistakes.