Streaks and perceptions

I want to address a topic that lies in a similar realm as the gambler’s fallacy: the idea of streaks and, more importantly, our perceptions of them.

Even the most casual sports fan has heard, at some point, of Joe DiMaggio’s 56-game hitting streak during the summer of 1941. This feat is so prominent, that Stephen Jay Gould referred to it as “the most extraordinary thing that ever happened in American sports”.

Intuitively, this record may seem like one of myth and fairy tale, since in my lifetime (starting in 1981), various records in various sports have been shattered. But during this time, the closest any player has been to DiMaggio’s streak has been a relatively meager 39 games by Paul Molitor in 1987—and I have absolutely no recollection of this ever happening. In fact, no one in the history of Major League Baseball has come that close to matching the record of hitting safely in 56 consecutive games (the closest was 45 games by Willie Keeler in 1896/1897). So I suppose I can understand why this particular record has been held on such a high pedestal. But is this record really so “mythical” and “extraordinary”?

Samuel Arbesman and Steven Strogatz of Cornell University published a paper that showed that while DiMaggio’s streak is amazing, it was not entirely unlikely. In fact, their analyses showed that upon simulating the history of baseball 10,000 times over, 42 percent of these baseball universes included streaks of DiMaggio’s length or longer. Taking it one step further, their analyses showed that a 56-game streak should have occurred long before 1941.

What about other streaks, ones we hear about on a day-to-day basis? Consider the game of basketball. We constantly hear announcers refer to a player as being “on fire” or “in the zone”. And I’m sure many of you have heard someone say that a team needs to get the ball to the “hot hand”. What do you think? Are players really “on fire” and do they really have a “hot hand”?

These phrases and descriptions all imply that if a player’s performance is subject to hot and cold shooting, it should be more likely that the player will make a shot after making his previous shot than after missing his previous shot. The further implication of such phrases is that a player’s makes and misses will cluster together far more than what chance would dictate.

Let’s run a quick experiment. Take a look at this player’s shot sequence (the X’s represent makes and the O’s represent misses):

O X X X O X X X O X X O O O X O O X X O O

Do you think this sequence constitutes streak shooting?

If you answered “yes”, well, you’re wrong but you’re not alone. In his book, How We Know What Isn’t So, Thomas Gilovich posed this exact same sequence to a group of basketball fans, and a majority of them (62 percent) thought it represented streak shooting. However, this sequence is perfectly random in that the number of adjacent shots with the same outcome (i.e. XX or OO) is equal to the number of adjacent shots with different outcomes (i.e. XO or OX). Now, this doesn’t mean that streaks don’t occur; it just means that our interpretation of what we see tends to be flawed.

A player like Carlos Beltran has a reputation of being a streaky hitter, and he seems to be chastised by fans for his so-called “streakiness”. Living in the New England area, I’ve heard many complaints about how he only hit .248 last July and can’t come up with clutch hits (though that is an entirely different topic). But is such a reputation really warranted? After all, a month is simply an arbitrary split of time. And Beltran also carries a career .281 average, so a .248 average in any given month really isn’t that far off from what is expected.

Meanwhile, on the other end of this spectrum is Justin Morneau, who is slowly building a reputation as being a consistent hitter. But despite being so “consistent”, he only hit .243 this past September. In four full seasons at the major league level, Morneau boasts a .284 average, similar to Beltran, but you never quite hear complaints of inconsistency or streakiness.

I bring up these two players in particular because in one of my leagues last year, a manager purposely avoided Beltran in the second round, claiming that Beltran “was too inconsistent”. In another league, a manager drafted Morneau ahead of Berkman because he liked the “consistency” that Morneau brought to his team.

There are other variables and issues involved with these particular decisions, but I think it is very clear that there is a problem with this line of thinking. The basketball dilemma posed by Gilovich showed that, theoretically, the outcome of a shot is independent of the outcome of the shot that occurred before it. That same idea can be applied to baseball—the outcome of any given at-bat for a player is independent of the outcome of his last at-bat. Obviously there are other variables involved (e.g. player’s psyche, pitcher’s adaptation and changes in pitch type, etc.), but the real point is that we, as observers, tend to misidentify streaks and incorrectly interpret them. Whether it be by coaxing a fellow manager into trading a “streaky” Beltran or by simply not falling into the trap ourselves, we, as managers, can exploit those who fail to recognize their faulty perceptions and misinterpretations of these events that are merely random.