In the NFL, where every decision is micro-analyzed by dozens of talking heads, very few of whom have had training in probability and statistics, coaches feel the heat of media scrutiny every time taking a risk fails, regardless of whether or not the risk was a good decision. The result is that coaches end up being extremely risk-averse in their play calling, often to the detriment of their team.
But isn’t it better to be safe than sorry? Well, it depends on what you’re trying to do. If coaches’ goals are to avoid media scrutiny then by all means don’t take the risk of going for it on fourth down or going for two.
But my assumption is that NFL coaches are trying to win football games. In order to win, decisions should be made so that their team’s chances of winning increase. Notice that decisions should not be evaluated on the outcome, as that would be outcome bias rather than analysis of the decision itself.
AdvancedNFLStats.com has a fantastic win probability calculator, based on empirical evidence (read: “recent history of actual teams playing actual games”). This can demonstrate the risks and payoffs of certain decisions. For example, during the 4th quarter of the 2013 AFC Championship game, the Ravens scored a touchdown making it 20-13 in the beginning of the 4th quarter. John Harbaugh is then faced with a choice to either kick the extra point of go for two. That gives us these scenarios with 14:49 left in the 4th quarter
Scenario Outcome Payoff
Go for 2 1. Convert 22-13, Chance of winning = 87%
2. Don’t Convert 20-13, Chance of winning = 82%
Extra Point 3. Kick is good 21-13, Chance of winning = 85%
I’m assuming the chance of a missed extra point is negligible and assuming that the Patriots would get the ball 1st and 10 at the 16 in the hypothetical scenarios, like they did in the actual scenario. It’s also important to note that because these percentages are averages based on recent league history, they view the Patriots and Ravens as average NFL teams, not accounting for whether one or the other is particularly good at keeping a lead or coming back because, for example, one has an exceptional no-huddle offense.
What about a motivated Patriots defense? What about a fired-up Ravens squad? Doesn’t that factor into the decision-making? You decide – with the help of some basic algebra:
Let x = chance of converting the two point conversion and let the probability of outcome 1 (convert) times the payoff from outcome 1 (87% chance of winning) + the probability of outcome 2 (don’t convert) times the payoff from outcome two (82%) = the payoff (85%) from outcome 3 (kick). This equalizes the payoffs from going for two and kicking the extra point.
.87x + .82(1-x) = .85
Solve and x = 0.6 so the chance of converting the two has to be exactly 60% to equalize the payoffs from kicking and going for two
Therefore, if you feel the Ravens were on a roll and had more than a 60% chance of converting, Harbaugh should have gone for 2. If you feel the Patriots defense had something to prove and the Ravens had less than a 60% chance of converting, Harbaugh made the right move to kick the extra point.
This shows the power of simple math for risk taking in the context of an NFL game.
Georgetown University Class of 2016