The Prisoner's Dilemma

Nate Silver at Baseball Prospectus wrote in his “Unfiltered” post on December 23 that clubhouse chemistry in baseball is quite different than clubhouse chemistry in basketball or football. Silver used the example of the Chicago Bulls, citing that their coach, Phil Jackson, had to maximize the best interests of the team, which were often in conflict with the best interests of each individual. Each player stood to gain by scoring; the Bulls, as a team, stood to gain if the player who had the highest probability of scoring took the shot.

This can be translated into football as well, as Silver mentions. Again, there is high potential for a conflict between the team’s best interest and the individual’s best interest on that team. Every time a quarterback passes the ball to receiver A, receivers B, C, and D have no chance to add to their statistics. Every time the coach calls a running play, the quarterback has no chance to pad his statistics, etc.

Here we see illustrated a fundamental problem of groups in all of human society, not just sports. If each person within a group of people maximizes their own best interest---a fundamental tenet of the individualistic American society where each person is encouraged to try to “get ahead”----the group’s interest is often thwarted, which thus trickles down to the individuals of the group.

Philosophically speaking, there is a hypothetical situation called the “Prisoner’s Dilemma.” If you’ve ever taken a philosophy, ethics or economics class, you’ve probably heard of this, in some variation.

The idea is this: two people are arrested for a crime which the police have insufficient evidence to convict them of. They are sequestered and each given the following proposal: “If you confess to this crime, and your partner stays silent, you will go free and your partner will receive 20 years in jail. If you both confess, you will both receive 5 years in jail.” If neither partner confesses, however, they will both only be jailed for one year on a minor charge.

However, each criminal knows that their partner is receiving the same offer. Thus, there are four possible outcomes:

1) Neither confesses; they each receive one year of jail time

2) Prison A confesses, but Prisoner B does not; A goes free, B receives 20 years

3) Prison B confesses, but Prisoner A does not; B goes free, A receives 20 years

4) Both confess; both receive 5 years

Because each prisoner has to make the decision without knowing what decision their partner makes, the logical choice for both prisoners it to confess (assuming their goal is to get the smallest amount of time in jail as possible). Here’s why:

From the point of view of Prisoner A, if his partner confesses, his best move would be to confess as well, that way he’d receive only 5 years instead of 20. However, if his partner does not confess, Prisoner A’s best move would still be to confess---that way, he’d receive 0 years instead of 1.

From Prisoner A’s point of view:

1) Assuming my partner confesses, I can either:

a. Confess and receive 5 years

b. Not confess and receive 20 years

2) Assuming the partner does NOT confess, I can either:

a. Confess and receive 0 years

b. Not confess and receive 1 year

As you can see, regardless of what my partner does, it makes sense for me to confess. This also applies to my partner, who is going through the exact same calculations. Thus, it is logical for both to confess, and each receives 5 years. However, this is not the optimal outcome for the prisoners---had they both trusted the other and opted to stay quiet, they could have each gotten away with only 1 year. The logic of the individual leads to a sub-optimal outcome for the “group.”

To translate this to sports, it would be optimal if each player on a team performed their given duty or task in order to maximize the team’s performance; this would increase the chances of the team being successful. Role players are necessary for basketball teams to win games---someone needs to set picks, be a defensive specialist, and other things which benefit the team but do not show up in the boxscore.

However, each individual player is concerned with themselves as well---the more points a basketball player averages, the larger his next contract; the more rebounds he grabs, the bigger his payday. Thus, what is beneficial to each individual on a particular team may not be beneficial to the team as a whole. Furthermore, each player attempting to make the best decisions for themselves could lead to a sub-optimal outcome for the team.

This can have a detrimental effect on the team, as you can imagine. This can also lead to tension within the locker-room, as players may be upset with one another over the decisions they have made, because these decisions affect both the team’s ability to win and the individual’s ability to maximize his statistics. NBA Player A could be angry at NBA Player B because he thinks Player B is taking ill-advised shots in an effort to boost his own scoring totals. Furthermore, Player A could be upset because every shot Player B takes is one less shot that Player A can take in an attempt to boost his own scoring totals.

Additionally, because basketball and football players depend on one another directly within the game itself in order to achieve both personal and team success, a personal dislike of another player or a conflict with another player can directly affect team performance. If Player A doesn’t like Player B, he might choose to pass the ball to him less. This would both irritate Player B and lessen the team’s chances of being successful, because the player’s decision-making would be clouded by a subjective opinion of a teammate, rather than an objective analysis of best way to score.

If Point Guard A doesn’t like to pass, he’s probably hurting the team’s chances of scoring as well as irritating other players on the team, who would then be less likely to pass to Point Guard A, and so forth. In basketball and football, locker-room chemistry is essential; it’s not that guys have to like each other, but they have to not let personal feelings get in the way of their playing with each other, because this could hurt the team (and, by extension, the individuals themselves).

In baseball, this is not the case, at least not nearly to the same extent as in basketball and football. This stems from the very nature of the sport itself. As Silver writes, “baseball isn’t like basketball – or other major team sports – in this important way: baseball players don’t make decisions, by and large, that affect the statistics or opportunities of their of their teammates.” Baseball is not the same kind of “team” sport that basketball and football are. Certainly it is a team sport in the sense that baseball games are won and lost by a team. However, the game of baseball consists of a series of individual events within one game. Often times these individual events are related and in a quick succession, and thus can seem to be “team” oriented. However, they are distinctly different from events which make up a basketball or football game.

In basketball, for example, the point is to shoot the ball into the basket. However, there is only one ball, and only one player can score at once for his team. Furthermore, one player’s scoring prevents another player from scoring on that possession. This is not true in baseball, at least not to the extent that it would be in another sport. My hitting a home run does not prevent you from hitting a home run.

You are likely now thinking of the various plays in baseball where my doing something does prevent you from achieving something, such as a run-batted-in. If I do not get on base, you cannot drive me in. If I’m on base and am caught stealing, you cannot drive me in; if I’m on base and steal second base, it’s easier for you to drive me in. This is all true (and is the basic argument for why RBIs are a relatively meaningless stat, because they are so dependent on others). However, there are few of these scenarios in baseball; and even within these scenarios the events are individual, uninfluenced by teammates’ conscious decisions. If I fail to reach base, it is not in an attempt to prevent you from driving me in. Similar logic applies to my getting caught stealing. Occasionally you will hear someone moan about a player attempting to pad his stolen base totals; however, this is very rare, as many steals are called by the manager or a coach.

Let’s examine how baseball consists of a series of individual events, even within one “play.” First of all, we have the matchup of batter versus pitcher. Obviously this is not “individual” in the sense that it involves only one player; however, the players are competing against each other, and no one on either team can influence whether the pitcher or batter performs well.

Scoring runs in baseball is about the accumulation of independent individual at-bats. Scoring the ball in basketball is about the accumulation of dependent series of events. Larry Hughes getting open for a three-pointer depends on LeBron James getting double-teamed, Hughes moving without the ball, James’ vision and ability to pass and find the open man, the defense’s inability to rotate fast enough. Much of Hughes’s open shot depends on his teammates---James’s ability to pass and choice to pass to Hughes or pass at all, a teammate setting a pick freeing Hughes from his defender, positioning and location of other Cavaliers players. Once Hughes gets the ball, he makes the decision whether or not to shoot it, and this decision has a direct impact on all of his teammates on the court, because if Hughes chooses to shoot, no one else is going to be able to shoot.

In baseball, each event leading to scoring runs---each at-bat---is completely independent from the previous and next at-bat. While scoring runs is dependent on the situation---you need runners on base in order to score---the actual scoring still depends on an individual at-bat, and the succession of individual outcomes leads to scoring runs. If a player fails to add to his statistics, it is because of his own failure, not because of a decision his teammates have made.

If you look at the correct stats in baseball, you can isolate one player’s contribution to his team in a way that you cannot isolate it in basketball, because a player’s contribution in basketball is so dependent on his teammates. This means that if you take Player A out of the Cleveland Cavaliers’s lineup and drop him in Detroit Pistons’s lineup in basketball, he may not contribute in the same way because he is playing with different guys in a different system. However, if you take Player B out of the Cleveland Indians’s lineup and drop him in the Detroit Tigers’s lineup he will contribute the exact same amount as he did in Cleveland.

For example, an at-bat in baseball is one large dependent event---it’s batter vs pitcher, but also depends on the fielders. If the pitcher induces a ground-ball, he depends on his infields to turn this into an out. If the pitcher does his part (gets the hitter to hit the ball on the ground), but the infielders fail to do theirs (field the ball and throw the batter out at first), the pitching team will not have achieve its goal, to retire the batter. However, each individual involved in the play---the pitcher, fielder, and first baseman---benefits individually from making the play which would also benefit the team. There is no Prisoner’s Dilemma here. Additionally, none of these events depends on players making an active decision one way or another.

In basketball, a player can decide not to pass the ball to another player; in baseball, if a player fails to field a ground-ball, it is not because he actively decided he was going to fail to field the ball. Thus, while a teammate could be upset at another for his inability to perform his job, any personal strife with the teammate, conflict of personalities or “clubhouse tension” will have no bearing the plays within the game, because plays within the game are made only by individuals, and because there is no conflict between one individual’s best interest and another’s, nor between an individual’s best interest and the team’s best interest.

Thus, in baseball players rarely make intentional decisions which directly affect another player’s ability to maximize his own interests. If a batter fails to get a hit, it’s likely not for lack of effort. If an outfielder fails to catch a fly ball, it’s not because he dislikes the pitcher. In basketball and football, events are dependent upon choices made by players during the game, such as whether or not to pass the ball. However, in baseball, one large event consists of several small independent events which combine into a large dependent event.