David R. Henderson  

NCAA Outcomes: Margins and Randomness

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The outcomes so far in the NCAA men's basketball games have surprised most people. The biggest surprise is Virginia Commonwealth University (VCU) beating the mighty Kansas, President Obama's choice to win the whole thing. VCU's wins are surprising. But it, and some of other outcomes, illustrate two principles, one in economics and the other in statistical reality.

The economic principal is the idea that the margin matters. Think of how some of the outcomes would have changed had a few little things changed. I'm thinking, for example, of the close University of Arizona game against U Conn. (U Conn won 65-63.) What if Arizona's star, Derrick Williams, hadn't been called for just one touch foul? Then he would have been on the floor longer and Arizona might have won. Or, in some of the other games, what if two of a team's 3-point attempts had been a few inches shorter or longer and gone in? Again a different outcome. Margins can matter a lot.

And the statistical principle, which is related to the above, is how much randomness there is. One team can be a little off its game for most of a half and, although it is a better team generally than the team it's playing against, this can make a difference. There's always randomness. So much that happens in the world is random. So the moral of the story is that the degree of certainty otherwise-intelligent people have about their bracket choices is just not justified.

A related moral is that when you play a lot of games and win enough to get to be one of the 20 or so top picks in the choice of 68 teams, you've done a good job. What happens from then on is a mix of skill and randomness. My favorite two stories are ones that illustrate a team official who understood and a pair of owners who didn't.

The team official I have in mind is Billy Beane, general manager of the Oakland A's. In his book, Moneyball, which is one of the best applied economics books of the first decade of the 2000s, Michael Lewis tells how, once Billy Beane gets his A's to the playoffs (162 games is enough to wipe out a lot of randomness), who wins is random and so he doesn't bother watching.

The owners I have in mind in the other direction are the Maloof brothers, who own the Sacramento Kings. Coach Rick Adelman brought this small market team to the playoffs every year he was coach (1999-2006.) In 2002, Adelman took the Kings to the Western Conference championship where they lost in 7 games to the Los Angeles Lakers. And what did the Maloofs do in 2006? They fired Adelman.


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COMMENTS (15 to date)
John Goodman writes:

I had no idea that you knew so much about sports. What a surprise.

Eric writes:

There seem to be an exceptionally large number of "toss-up" games this year. Butler/Pitt is the obvious one but I'm thinking of #1 Ohio State vs. Kentucky. OSU missed a hurried three point shot with about 2 seconds left and Kentucky won 62-60. The CBS analysts had gone 2-1 for Kentucky prior to the game and were acting afterwards as though they had been fantastic analysts and the game was a foregone conclusion. From my perspective, the game was a coin-flip and the analysts could just as easily have been explaining why OSU was the better team.

dcpi writes:

This post asks for a definition of "random". Certainly, even the Kansas City Royals or VCU would defeat a time of little leaguers every time. So victory is based on skill not luck. What the "upsets" underscore is the eveness of the talent in the tourney.

There really is no "luck" in high level sports unless one defines luck as the residue of skill. I have participated in a international sport as a relatively poorly skilled participant. Upsets come from many factors, one of the most important of which in my experience is motivation and desire in the moment. If both opponents are highly motivated and desirous, the more skilled will win nearly every time. Team sports are harder to predict because no one athlete controls the entire game and skills and desire vary across the team.

So what is random? What is luck?

Jeremy writes:

And then there's the small-school coaches who make it to the Sweet 16 (or more) on randomness, and subsequently get tagged as a great coach and get recruited to a bigger school. One simple make or miss by one of a coach's players can be the difference between a career at small schools and millions of dollars more at a big school. These schools are making a similar mistake as the Maloof brothers, but in reverse.

I don't 100% agree with you on the Adelman thing. Larry Bird vowed to only coach for 3 years because he said players stop listening to a coach after 3 years. I'm sure losing hastens that. I don't remember the circumstances for Adelman, but a team could fire a coach even though they think he's a great coach if they think the players have started tuning the coach out. Of course, they should change players then, but it's the coach they'll get rid of.

Floccina writes:

The 3 point shot has made basketball outcomes much more random. I think that they should eliminate the 3 point shot. IMO it adds too much randomness.

Bob Murphy writes:

David, I nitpick only because I care. But this sentence was a kick in the kidney for me:

The biggest surprise is Virginia Commonwealth University (VCU) beating the mighty Kansas, President Obama's choice to win the whole thing.

It astounds me when the American media, say, report on the rescue of the Chilean coal miners, and 95% of the story is how President Obama feels about it.

I think it would be an interesting analysis if you tried to remember what made you list President Obama's choice as if that should be relevant. (Note, I'm not being sarcastic. Maybe it's because the president by definition will pick the "obvious" choice in something like this, so as to curry favor with people while not alienating those who disagree.)

But it's still interesting that you used Obama, instead of Bobby Knight's bracket or something.

David R. Henderson writes:

@Bob Murphy,
I used it because I remember when Obama reported his brackets the degree of certainty he communicated. So he's an example of someone who doesn't seem to get randomness. Also, to be completely honest, I got delight from the fact that his favored pick didn't win.

Chris T writes:

Ah, "What If?", the bane and pleasure of every sports fan. Randomness is a part of every sport, the best teams or individuals are the ones that can overcome it.

drobviousso writes:

dcpi - While I don't doubt for a second your first hand knowledge, there is extensive literature out there on luck in sports. You are, I'm sure unintentionally, performing a reductio ad absurdum on the concept of luck in sports.

Marking up the outcome of an incredibly chaotic set of interconnected events to one simple factor (motivation/desire) is, I believe, a form of confirmation bias. The MLB is farther along in recognizing this than many other US sports leagues (NFL is probably the worst).

If you are into baseball, Moneyball is probably a good first book to read. I'm not into baseball, so I haven't read that, but I do like football, and I would recommend The Hidden Game of Football as a primer.

Bob Murphy writes:

@David, ah, OK, I take it back then. I would have no problem if NPR had said, after the Chilean miners were rescued, "I guess our president is dumb, since he thought the rescue would take longer." :)

Mark writes:

The baseball playoffs aren't totally random. A team with 3 really good starting pitchers is in better shape then a team with an unusually good fifth starter who is more valuable when there are multiple back to back games. Actually, the whole bullpen may be less valuable. I would add back up catchers and maybe all bench players too but I haven't done any research into the topic. I am getting crushed in my ESPN bracket, but oddly enough I am crushing Dick Vitale who keeps on talking about his eye ball test. If you watch the last ten games of 60 or so tournament teams it comes to over 1000 hours of eye ball testing!
There are a couple of systems RPI, Sagarin that try to be objective and should really be used
more by NCAA but the systems are flawed and everyone thinks they are an expert already. It is odd that the basketball tournament is seen as the model for college football when we may watch a team win it all this year that shouldn't even be in the tournament according to some people, not me. Basically agree with you on the role of randomness and chance but I also think that many teams alternate from being a top 10, to top 40, to top 5 team all in the same year which is different then randomness but may be obscured by it.

Pat writes:

Billy Beane only says that because his teams fail in the playoffs. His teams are built around walks and playoff pitchers throw strikes. He's omitting a variable in his analysis - pitchers on playoff teams are better than those not in the playoffs.

dcpi writes:

drobviousso: Thanks for the recommendation. I have read MoneyBall and even have autographed copies from both Billy Beane and Michael Lewis. Both are very smart men. In the case of baseball playoffs, I would posit that the playoff structure (more off days, no need to "save" players), means that the outcome is more determined more by the core players on the roster and that in turn means that a shallower team with a few dominent players has an advantage. Beane's teams are built for the long haul of the season, not for the playoff format.

My question is really about the definition of luck. An athlete without skills cannot defeat one with them (with the exception of improbable events such as injury). The illusion of luck comes from the fact that in most competitive events the variance in skill amongst competitors is very small. In many cases, the relevant factors cannot even be measured or are not understood, even by the competitors themselves. There are also different components: skill and technique, physical endurance and strength, mental stamina and will, strategy and the ability to adapt to ones opponent quickly.

None of the above are luck, but most of the above cannot now be modeled ahead of a contest. So, it looks like luck, or random chance, to observers. Really, what people here are calling luck is just the lack of knowledge. Beane, of course, relies on better modeling to remove more "luck" from the equation.

Joseph K writes:

When you're talking about the randomness, it reminded of something I was thinking when watching the World Cup last year. I really like sports that are really high scoring because the preponderance of points makes it considerably less likely that a game will be decided by randomness. Tennis is the same way. One player might get a few lucky points, but with the sheer number of points played, the probability is high that both players will get about an equal number of lucky points. The randomness only starts to make a difference when they're really close. Same with basketball; the team that's clearly better virtually always wins. You can just just look at the score in a basketball game or tennis match and know how close it is. But it's not in the case in soccer, where many games are decided by only one or two points. If the score is like 4-0, you know that probably one team dominated, but if you see it's 2-1, it might have been not nearly as close as the score indicates. The low scores makes randomness more prominent. I've watched so many soccer games where one team was clearly dominant but didn't manage to win because they just missed a shot, or a goalie got an amazing save, or a ref made a bad call. In basketball, randomness definitely plays a part, but the preponderance of shots and plays and points tends to lead neither team to be favored by luck more than the other.

dcpi writes:

@Josephk

I think you understand my point. Life is the same way, only a lot more so.

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