Game Theory in Goal Line Situations
Every week in the NFL, coaches face a hard decision when on their opponent’s goal line. Should they trust their running back and run the ball or should they have their quarterback pass for a touchdown? Recently, with two minutes left in the game, the Giants decided to pass three times in a row against the Patriots. This decision eventually lost them the game as they settled for a field goal, giving Tom Brady time to drive down the field and set up a 54 yard field goal. According to Tom Rock, a writer for Newsday, Tom Coughlin, the Giants’ coach, defended his play calling, saying that he maximized their chances at scoring given the defense that was presented. Giants fans believed the opposite, claiming that he should have run the ball to run down the clock and force the Patriots to use their last timeout.
Game theory can help sort out this dilemma. To fully describe the situation, the Patriots had six defensive backs on the field, a formation that is used to defend against the run. 2:06 minutes remained in the fourth quarter, the Patriots had one timeout, and the Giants had 1st down and goal at the Patriots’ 5-yard line. Strictly speaking pass versus rush, Coughlin was correct. According to Pro Football Reference, from 1994 – 2015, 29.6% of rush plays called between the opponent’s 5-yard line and their end zone have resulted in a touchdown when less than three minutes remained in the fourth quarter. Under the same conditions, 36.1% of pass plays resulted in a touchdown. Multiplying those percentages by the points that they yield reveals the payoff for each option. Pass plays result in a payoff of 2.52 points per play while run plays result in 2.0 points per play. Historically, pass plays have been somewhat more effective than run plays inside of the opponent’s 5-yard line.
Why might this be? It seems illogical that pass plays should be more successful in intense, short-yardage situations. Justin Wolfers’ explanation of Pete Carroll’s infamous call for a pass in the final seconds of the last Super Bowl gives some clarification. According to Wolfers, game theory dictates that coaches should approach the red zone with a mixed strategy. Common sense indicates that a run play would be more effective in short yardage situations but opposing defensive coordinators know this and may plan to defend against the run, minimizing the payoff of a running play and increasing the payoff of a passing play. When coaches are deciding between running and passing, they should abandon their dominant strategy, running the ball, and approach it with a mixed strategy. According to Football Outsiders, mixing running and passing plays from a first down on the opponent’s 5-yard line increases the percentage of scoring a touchdown on a per down basis to 70.7%. Mixed strategies work well because the opposing defenses don’t know what to defend against; by defying common sense, teams maximize their payoffs.
The idea of a mixed strategy clarifies the issue with Coughlin’s play calling in the final minutes of the Giants/Patriots game. The first and second pass plays were acceptable since the Patriots were defending against the run but, by the third, his pass-heavy strategy was exposed and the defense was prepared for another pass, sacking Eli Manning for a six yard loss. Essentially, the Giants took the idea of defying the dominant strategy too far. The Patriots recognized his new strategy and were prepared for it. If Coughlin had offered a mixed strategy and called a run play to throw the defense off, he would have had a statistically better chance of scoring a touchdown and defeating the Patriots.
This discussion relates to Networks because of the discussion of payoff, game theory, dominant strategies and mixed strategies.
Links:
http://www.footballoutsiders.com/stat-analysis/2013/closer-look-touchdowns-red-zone
http://www.pro-football-reference.com/play-index/play_finder.cgi