Published: 30 November 2014
Up 30-27 with 2:27 left in the fourth quarter, the Baltimore Ravens faced a 4th-and-4 from the San Diego Chargers 13-yard line. Both teams had one timeout remaining so a first down would mean the Chargers could get the ball back with 24 seconds left, assuming the Ravens did not score or convert a second new set of downs. With a field goal, the Ravens would be up only six points, meaning a touchdown would all but win the game for the Chargers. Avid football analytics readers know that in some situations, being up four to six points is worse than being up three points. This is because opposing offenses are forced to be more aggressive, and as a result, more efficient by passing the ball, rather than settling for a long, game-tying field goal (a.k.a. The Jason Garrett).
With a successful conversion, the Ravens' win probability would jump to 97.3%; a failure means 77.6% chance to win. The probability of converting on 4th-and-4 is roughly 43.6%.
E[WPGo-For-It] = 86.2%
A 31-yard field goal converts at 94.0% (probably higher for Tucker), resulting in a win probability of 82.1%; a miss means the Ravens would have a 77.1% chance to win. Tucker has only missed one field goal under 40 yards in his career, so let's be generous and say there is a 98.0% chance he makes the field goal.
E[WPField Goal] = 82.0%
That makes the break-even point a 22.5% conversion rate on fourth down - essentially half of the actual league-wide conversion rate.
Brian's original win probability model has it as an even greater difference, so much so that there is no break-even point (although his field goal success rate is admittedly low):
After the field goal, Philip Rivers led the Chargers on an eight-play eighty-yard touchdown drive, culminating in the game-winning score to Eddie Royal. The Chargers actually scored touchdowns on each of their final three drives.
The fact that the Ravens ultimately lost is not grounds for criticizing John Harbaugh's decision to kick the field goal - it is the process that is important, not the result. And, to be fair, many different factors can sway these probabilities in game. That being said, the league baselines are a great place to start the analysis and there is such an enormous gap in expected win probability that the Ravens likely made the incorrect decision.