Probability Matching Madness!

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Now that it’s been a few weeks since the men’s NCAA tournament ended, I’m already missing college basketball, so I thought I’d create my first Science in Society blog about filling out your tourney bracket and what it has to do with…probability and psychology.

Every March, thousands (millions?) of people, some of whom know a lot about college basketball (e.g., me) and some of whom know little to nothing about college basketball (e.g., whoever probably won your bracket pool), fill out brackets.

People choose the winners of each game by various methods.  I try to go with the “basketball IQ” method, using statistics, tendencies, strengths and weaknesses of the matchups, observations from having seen teams play, etc., to make my picks.  (There's one notable exception – I always choose my alma matter, Notre Dame, as the champion. This has not proven an effective strategy.  Hence I actually do better in my bracket pools in the unfortunate years that ND doesn’t make the tourney.)  Other methods include picking teams based which team’s colors you like better, if you like the cities they are in, or my personal favorite alternate strategy: picking the winner based on which team’s mascot would win in a fight.

So what strategy do most people choose?  Most people don’t use any of those strategies above, at least not purely. Instead, most use probability matching, as reported in a recent paper in the Journal of Applied Social Psychology.  What this means is that for a given matchup – say a 4-seed versus a 13-seed – people predict upsets at the same frequency that they’ve happened in the past.  Historically, a 13-seed will beat a 4-seed just over 20% of the time. Therefore, when people fill out their brackets, they tend to pick one of the four 4-vs-13 matchups as an upset – thus they match their predictions to the observed probability.

Let’s see what happened if you were a “typical” person and probability matched for the 4-13 matchups in this year’s tourney.  The four matchups were #4 Maryland vs. #13 Houston, #4 Vanderbilt vs. #13 Murray St, #4 Wisconsin vs. #13 Wofford, and #4 Purdue vs. #13 Sienna.  Probability matching means you pick one of these as upsets.  You could pick one randomly – or based on team color or mascot or whatever – or even try to use basketball IQ like I did.  Purdue lost its best player to injury late in the regular season, and Sienna was a very well-coached, overachieving team, so that was my upset pick for 4-vs-13.

It turns out that Purdue won – so I picked that game wrong – but there was in fact one 4-13 upset: Vandy lost to Murray St.  So let’s look at the outcomes of probability matching based on which upset you picked (no matter how you picked it).  Let’s say you and three friends each picked a different upset.  The three people who picked Houston, Wofford, or Sienna to upset each correctly picked only 2 of 4 games.  If you picked Murray St, you correctly picked all 4 games – good for you, and thanks for probably beating me in my pool.  However, since three people got 2 right and one person got 4 right, a probability matcher will correctly pick only 2.5 out of 4 games, on average. Turns out probability matching is NOT the optimal strategy to maximize the number of games picked correctly.

So what strategy is optimal?  It’s a simple one, disparagingly called “chalk," in which you just pick the better seeded team. So pick all the 4 seeds to win. You know you will probably miss one game – the upset – but you don’t care.  You still know you are going to get 3 out of 4 games right.

Why do people persist in probability matching?  First, going “chalk” is boring and your friends will ridicule you for your cowardice.  Upsets are fun!  Second, by going “chalk,” you’re only going to do as well as those who seeded the teams did.  So you definitely won’t get embarrassed in your pool, since they are usually right.  But you won’t win it. The person who wins is one who does probability match – and who is lucky enough to pick all or most of the upsets correctly.  So it’s that person you hate who probably picked Murray St AND also picked #14 Ohio to beat #3 Georgetown.

So what’s the take-home message here?  Picking chalk will prevent you from embarrassing yourself.  But I recommend you persist in your probability-matching habits and picking upsets by whatever method you choose. Maybe you’ll finish in last, but maybe you’ll win your pool.  But either way, you’ll have more fun than “that guy” who just chooses the smaller number.

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