Fooled By Randomness

In my last post I discussed the myth of the SI jinx. Here is a brief recap. Athletes and teams are usually on the cover of SI for extraordinary performances. Almost always, an extraordinary performance is followed by an ordinary performance. So the SI jinx is easily explained by athletes and teams that have regressed back to their normal performance level. Contrary to popular belief, therefore, Sport Illustrated is not actually causing an athlete or team to play worse. However, people have a difficult time understanding this, and this is largely due to their inability to perceive and understand randomness. In this post, I want to build off of this point by illustrating just how bad we are with randomness. Let’s start with ipods.

When Apple first sold the ipod shuffle, users complained that it was not random enough. Though the engineers at Apple had programmed the ipod shuffles to be random, people were convinced that they were not. The problem was that “the randomness didn’t appear random, since some songs were occasionally repeated.” I took to the Apple blogosphere to see if this was true and on the Google’s first hit I found the following two posts:

User 1: There are 2800 songs in my ipod, I found that the Shuffle Songs function is not random enough, it always picks up the songs which I had played in the last one or two days.

User 2: It is random, which is why it’s not paying attention to whether or not you’ve played the songs lately.

User 2 is right, the ipod shuffle is random, making it entirely possible for a song to be played two days in a row, or two times in a row for that matter. The mistake made by User 1, is that people perceive streaks and patterns as indications that sequences are not random, even though random sequences inherently contain streaks and patterns.

Our tendency to misinterpret randomness is exemplified by the gambler’s fallacy, which describes our intuition’s habit of believing that the odds of something with a fixed probability are influenced by recent occurrences. For example, we think that the more times a coin lands on heads the more chances it has of landing on tails. In reality though, if a coin landed on heads one hundred times in a row it would still have a 50/50 chance of landing on heads the 101st time.

We make the same mistake when we watch sports. In 1985 Cornell psychologist Thomas Gilovich published a paper that “investigated the origin and the validity of common beliefs regarding the ‘hot hand’ and ‘streak shooting’ in the game of basketball.” His study was motivated by the common belief shared by fans, coaches, and players that a player’s chance of hitting a shot are greater following a hit as opposed to a miss. To see if basketball players actually “heat up,” Gilovich collected shooting stats from the Philadelphia 76ers 1980-81 season. He found that the chance a basketball player has of making a shot is actually unrelated to the outcome of his previous shot. In his words:

Contrary to the expectations expressed by our sample of fans, players were not more likely to make a shot after making their last one, two, or three shots than after missing their last one, two, or three shots. In fact, there was a slight tendency for players to shoot better after missing their last shot… the data flatly contradicts the notion that “success breeds success” in basketball and that hits tend to follow hits and misses tend to follow misses (1991, p. 12).

Gilovich’s conclusion comes as a surprise to most people. For some reason, our intuition tells us that a basketball player’s field goal percentage is influenced by his previous shots. This is why we want a player who is shooting well to continue to shoot, and vice versa.

Similar results have been found with baseball players and baseball teams. Michigan State University psychologist Gordon Wood demonstrated that the probability of an MLB team winning after a win, or losing after a loss, was fifty percent after analyzing the outcomes of all 1988 Major League Baseball games (26 teams & 160 games). Likewise, Indiana University statistician Christian Albright found the same with batters. He states that, “The behavior of all players examined… does not differ significantly from what would be expected under a model of randomness.” Like the outcome of a basketball shot, an MLB game and at bat were unaffected by past performance

None of these studies are denying that streaks exist; but they are saying that our intuition does a poor job of understanding and perceiving randomness – we mistakenly “see” patterns amongst randomness.

There are powers and perils to this cognitive bias. If you bet your life savings on a falsely perceived streak in the stock market, you could easily lose a life’s savings. Likewise in gambling, if you have gotten lucky on a slot machine you will want to keep going thinking that you have found a “hot” slot (in the end, of course, you will most likely have less than you started). On the other hand, our tendency to see order amongst random-chance events is an incredibly useful survival technique. Think what it would be like if you perceived the world as a series of random events; imagine that headache. With this in mind (not the headache), it seems awfully useful that we can “see” patterns that aren’t actually there.

• Thanks Nassim Taleb for the title of the post.
• The ipod shuffle discussion can be found here.