Theory

Sports professionals are often faced with a significant amount of strategy.  For example, in the National Football League, a contest between two teams is essentially a chess match between two coaches.  The strategy encompasses play-calling, substitutions, game plan, and much more.  The coaches may be exhibiting the minimax strategy of game theory to best improve their chances of winning the game.

The “minimax” strategy in game theory states that, in a head-to-head match up, players should follow two rules: be unpredictable; secondly, minimize the gain of your opponent to the best of your ability.  Many players do not follow the strategy to the T, however.  In reality, the use of such a strategy may not seem conducive to winning, which is the ultimate goal of any professional sports player.

Author Steven Levitt and Ken Kovash of Mozilla recently worked together to find out whether professional athletes indeed follow the strategy of minimax.  Using statistics gathered from Major League Baseball and the National Football League, the two determined that professional sports athletes could better utilize the game theory strategy to win more games in their respective sport.

For example, they found that in professional baseball, pitchers could use different types of pitches to increase their chances of success.  They studied over 3 million pitches and related each pitch to the opposing batter’s likeliness to get a hit or reach base.  In their findings, they found that when pitchers threw fastballs, the opposing batter’s likelihood to be successful increased by 20% over curveballs.  Each hitter has a different preference of balls to hit, however, and this is consider in their strategy.  Too often a pitcher will choose a different type of pitch to avoid predictability, when in fact the change may be more predictable than a lack of change.  That is, a hitter may expect a breaking ball pitch if he has just seen a fastball.

In professional football, the two factors shifted from fastball/curveball to running the football and passing the football.  They found that passing the football yielded more yards and better field position than running the football.  This conclusion may be skewed, however, as many coaches choose the strategy of running the ball for more reasons than just field position and yards gained.  For example, running the ball may wear down the other team’s defense and control the time of possession in a game.

Game theory plays a big part in the strategy found in professional sports.  Whether the coaches and players are conscious of these theories is not of importance.  The minimax strategy brings a few more strategies that may benefit sports teams to mind:

1.  Stacking Theory

In a 7 match tennis match, there are often 4 singles matches and 3 doubles matches.  The stacking strategy involves strategically positioning the potential match ups in a way that improves your chances of winning the overall match.  This is common in professional baseball as well, where it is common knowledge that the pitching rotation is a representation of the skills of each pitcher on your team.

2.  Randomization

Randomization is professional sports is the best way to be unpredictable.  For example, a poker player may have a randomly generated to decide when to buff and when to call.  In another example, football coaches would undoubtedly need to throw the football in certain run-obvious situations to keep the defense honest.  Randomization may be an important strategy in sport that has yet to be fully utilized.

3.  Risk vs. Reward

The typical game theory of risk vs reward is a prevalent strategy in sport.  Using risky behavior at the opportune time may turn the tide for one player or team.  For example, a football coach may choose to fake a punt or a field-goal in hopes of obtaining a first down and continuing a drive.  There is heavy risk involved in “going for it” on 4th down, but in some cases the coach may decide that the possible reward is worth the risk.