On Coin Flips, Hot Streaks and the MLB Playoffs

When I was in college, I once set up the following experiment for an independent study I did in psychology and economics:

A coin flipping contest with a prize of $10.

There were 128 students involved in the contest. It's pretty easy to get college kids to flip coins for free pizza and a chance at enough money for 4 beers at the local college dive bar. It was set up NCAA Bracket style such that there were 7 rounds, with each round half the pool being eliminated until we had a final champion. One person got to flip the coin and the other person got to call it. Who got to do what was determined by drawing straws. The coin had to go at least 7 feet in the air and hit the ground.

Now the tournament was completely uninteresting and actually wasn't the focus of the study. What the students said after the tournament was what I was trying to get at.

Coin flips are obviously luck, especially when the coin flips more than a couple of times and even more so when different people are flipping the coin each time. You'd have to be borderline crazy to ascribe victory in this sort of tournament to anything other than luck.

However, in talking to the winner, and even those that had made it to the last few rounds, they all described a feeling that they could predict the coin flip. The winner going so far to say that he was basically 100% confident he was going to win the final matchup. Those who had won several rounds all ascribed their winnings to something other than pure luck usually "getting a feel for how the coin would flip and how to flip if it I was the one doing the toss." The winner actually said "how could you call that luck? I picked the correct side seven straight times, what are the chances of that happening?" Well, he's right that it is extremely unlikely that a given person picks correctly seven straight times in a coin flipping contest, there is less than a 1% chance of that happening. In fact the chances are exactly 1/128.

However, the problem is that we had 128 students and a contest set up such that somebody had to win. Stepping away from an individual in the coin flipping contest's point of view, it was clear that somebody had to be lucky and it just happened to be him. But our brain doesn't like that explanation. Our brain is designed so that, as much as possible, we don't ascribe unlikely events to dumb luck. The winner earnestly believed he had some sort of skill in predicting those coin flips.

In his career Barry Bonds came to the plate 12,606 times. In his career he reached base 44.4% of the time and got a base hit 29.8% of the times he didn't walk, sacrifice or get hit by a pitch.

Imagine a time when Barry Bonds reeled off seven consecutive hits. What do you think the announcers were saying? They were probably saying something along the lines of "wow, Barry is just completely locked in right now! That baseball must seem as big as a watermelon to him!" His manager would be elated and thinking about the carnage his zoned in slugger would be doing against that day's pitcher. Not only was it Barry Bonds, but it was Barry Bonds on a torid hot streak. Now, the fact is that while seven straight hits is highly unlikely, for a player who gets a hit 29.8% of the time and had just under 10,000 ABs, you'd expect it to happen right around 7 times. So while it was unlikely for it to be happening at any given point in time, by just pure dumb luck, you'd expect it to happen seven times over his career. Yet do players, managers, fans or announcers ascribe these sorts of streaks to luck? No, they ascribe them to being hot and skill.

Now imagine we flip the script and Barry Bonds has just had back to back 0-4 days, zero for his last eight. The announced would be talking about how Barry needed to make x adjustment, that his timing was off, that he wasn't seeing the ball. His hitting coach might even suggest some sort of change. He would be cold. Except for he wouldn't. When a player doesn't get a hit 70% of the time, there's roughly a 5% chance that he will go a couple of games without getting a hit. in a full season, you'd expect that to happen several times, just by pure, dumb, bad luck. Yet, we almost always view it as the hitter is cold and may actually need to make some sort of adjustment to his swing.

To be sure, skill or lack of it has something to do with it. A player who gets a hit 35% of the time is much more likely to have a long hitting streak than a player who gets a hit just 25% of the time. But the majority of it is luck. You can think of it this way, if you do something (come to bat) enough times, highly improbable things (really long hitting streaks, really ice cold streaks) end up being likely to happen at some point.

Going back to my coin flipping contest, let's imagine a sport where the absolute best teams in the league win just 60% of their games. Now let's imagine we created a tournament where we took only those teams that already didn't win all that much more than half the time, and had them play only other similarly good teams (that won between 55% and 60% of their games) in one five game series to open and then seven game series subsequently.

Think about that for a second, we are only pitting teams that win between 55% and 60% of their games against one another in relatively short playoff series. You'd expect the best teams to have very slightly better odds, but mostly it would just be luck. Teams that are that closely matched would take several hundred games of playing one another to really sort out which team was actually better. Yet, you can bet, just like the coin flip participants, that those that went out early would be called chokers, and the champion would have put together a magical run and earned their way alongside the greats of the sport. Nobody would characterize the World Series winner (oops, did I let that slip) as just lucky, they would have ridden dominant pitching and "clutch hitting" all the way to glory. Because that's how our brains work. While it's risky to bet on any given winner, it's a virtually guaranteed bet that the winner, and especially the winner's fans, won't think the win was pure luck. When betting on chance, the only certainty is that people won't believe they're betting on chance.