Category: Sports

Lance Armstrong Game Theorist

Armstrong’s victory in the Tour de France is a testament to his awesome physical skills but he and his team should also be credited with a sound understanding of game theory. Game theory arises in the tour because it’s important to take advantage of the draft created by riders in front. The dynamics of draft alone are fairly simple but add to this that the leader is not necessarily winning, the use of teams, the many stages, the different terrain etc. and you have a very complex strategic space. Correspondent Stephen Tuel writes about one episode of strategic biking:

The 18th stage was an excellent example of game theory at work. Lance Armstrong and the peloton were a few minutes back of a breakaway group of 6 riders (none of whom were a threat to the top of the overall standings since all were over 1 hour behind). Reading the various news reports and between the lines it appears that Armstrong’s team, US Postal, was doing all the work at the front of the peloton and the team of the closest competitors, T-Mobile, were loafing. (The crucial strategic variable in bicycling appears to be the effect of wind resistance, especially on the flat and on downhills–whoever is at the front has to work harder, and whoever is following can choose to conserve energy or share the effort.)

Armstrong and another rider (also over 1 hour behind in the overall standings) left the peloton, caught up with the group of 6, and helped them build a bigger lead. Once the lead started stretching, the T-Mobile team moved back to the front of the peloton and started taking their turns at the lead to help catch the breakaway group. Armstrong and his collaborator then relaxed, let the group of 6 go on (one eventually won the stage) and rejoined the peloton. By moving up with the breakaway group, Armstrong changed the payoffs which were letting the T-Mobile team slack off. Presumably, the continuing threat kept them working their share through the rest of the race.

See also this paper on strategic driving in NASCAR.

Addendum: Educated Guesswork and Evolution Will be Blogged chime in with another theory, Armstrong wanted to punish another cyclist for extra-curricular reasons. Interesting.

Look who’s scalping now

Recently, two major league baseball teams decided if they couldn’t beat scalpers, they would join them. The Chicago Cubs’ parent company established a corporation with the sole purpose of scalping Cubs tickets. The Seattle Mariners took a different, though similarly nefarious, approach. The team began facilitating the scalping of tickets on its website (where the team could charge a commission on the transactions) even as it hired off-duty police officers to enforce a local antiscalping law on the competition–the good old-fashioned freelance ticket broker…

It remains a puzzle why baseball teams ever prohibited scalping of tickets. Arguably they wanted to prevent their game from becoming seen as the province of the rich, which would have limited TV revenues in the longer run. Clearly the tide is turning toward more scalping and market-clearing prices. Why? Perhaps enough people are wealthy today that the reputational constraints are being relaxed.

Here is the full story, and thanks to Eric Crampton for the pointer.

Bartering the Big Kahuna?

For reasons mostly involving ego, Shaq and Kobe no longer wish to play together. The economic question is why two superstars can’t seem to get along on the same team. L.A., arguably America’s largest sports market, is the value-maximizing place to play ball, but pride, envy, and relative status seem to have won out.

And what would the Lakers get? Butler, a small forward/guard, can start on most teams in the NBA. Odom and Grant give them a plausible front line. The idea is that Kobe and Odom will be the new Jordan and Pippen. Unlikely, but the Dallas Mavericks were not offering anyone who could play defense.

Shaq is 32, has played twelve seasons (mostly long and tough), and no longer has stellar games on a back-to-back basis without a few days’ rest. He doesn’t try very hard throughout most of the regular season, which is poison for team morale, and he is on the verge of being a defensive liability. Miami may make the Eastern finals, but if the Lakers can’t get through Detroit I bet Miami won’t either. Miami already made the second round of the playoffs this year. In two years what will they have left?

The Lakers would be taking on risks too. If Odom is caught smoking pot again, he has to sit out an entire year. And how about this bit?

“Even though his scoring average dropped from 15.2 to 9.2 points last season, [Caron] Butler has great potential.

Butler also has a checkered past, being arrested 15 times before age 15. He spent a year in jail for bringing a gun and cocaine to school.”

Here is the analysis of the ever-smart Marty Burns on the pending deal. Tony Kornheiser agrees.

The bottom line? This would be one of the biggest deals in NBA history. But oddly neither team is giving up or getting very much.

And oh yes, this guy could stop the deal.

NBA economics

Read Mark Cuban’s thoughts on the Detroit Pistons, and why the Lakers lost. Mark Cuban, in case you don’t already know, is the owner of the NBA’s Dallas Mavericks. His blog pretends to be about basketball but like so much of the best sports writing it concerns personnel management, human motivation, and how to measure achievement. I loved this line from yesterday: “Believe it or not, even in the NBA [trade] discussions start based off of what we read in the newspapers.”

Why so many perfect games in baseball?

…in the first 60 years of the 20th century, there were 4 perfect games in baseball, a game where a pitcher pitches a complete game and no one on the other team reaches first base. In the next 45 years, there have been 11, so the rate of perfection has roughly quadrupled.

Of course Randy Johnson just pitched a perfect game this last week.

Michael Coffey, of The New York Times, claims that higher returns to celebrity have increased the returns to extraordinary performances. But the more general fact is one of declining variance across athletic performances. Wilt Chamberlain dominated his contemporaries (one year he averaged fifty points and twenty-eight rebounds per game), but now basketball talent is more tightly clustered. Many runners can do a four-minute mile, and so on. So I doubt the Coffey explanation. It is now harder to stand out from the crowd, especially as we consider longer time frames of achievement.

Nor can you argue that pitchers are gaining on hitters across the board. Home run totals have skyrocketed. Russ Roberts makes a good point; he cites better fielding, which boosts the chance for a perfect game but doesn’t stop home runs. And of course we are simply playing more games of professional baseball [Richard Squire tells me about twice as many].

Or consider a statistical explanation. Yes, more excellent performers will mean that overall achievement is more tightly bunched. But at the same time, the flow of one-time “outlier performances” can rise. You have more “perfect game capable” pitchers trying to pitch perfect games than ever before. No one of them will achieve the lifetime dominance of Cy Young, but today’s best pitch or best pitched inning is better than Cy Young’s. This holds, even though batters have improved as well. We are dealing with the extremes of the distributions, not the bunching of the means as calculated across lifetime achievement. So we get more perfect pitches today than we did eighty years ago. Now just inch up the temporal unit from “pitch” to “game” and you can get to the required result…

What really impresses me:

A perfect game, nah. A sherpa just made it up Mount Everest in less than thirteen hours; even very good climbers can require at least four days.

Mind over Muscle or Where is Fatigue?

The old theory, taught to me in high school, is that muscles become fatigued when they run out of fuel/oxygen or they become suffused with lactic acid, an unpleasant byproduct of work. But if this is so, why do athletes almost always manage to go their fastest in the last mile of a race when their muscles should be closest to exhaustion? An article in New Scientist, (“Running on Empty,” by Rick Lovett, 20 March, 04, p.42-45, a copy is here) based on the work of Timothy Noakes and others, raises some more puzzles and offers a new theory.

If fatigue is based in the muscles then without more fuel, oxygen or less lactic acid you should not be able to improve performance. Yet, amphetamines and drugs like Ecstasy do allow athletes and clubbers to work and play harder (sometimes to dangerous effect). Measurements of the input factors also show that (absent unusual factors) fatigued muscles don’t in fact run out of critical factors.

The common sense response to these puzzles is that runners speed up in the last mile because they know it is the last mile and are willing to push themselves to their limits. Similarly, drugs fool the brain into thinking that the muscles are less fatigued than they are. If one thinks seriously about this common sense notion, as has Thomas Noakes, it provides a quite different view of fatigue than the old theory. The brain in this view is a central regulator that monitors the muscles and sends out messages of fatigue, quite possibly long before the muscles are truly spent as a sort of insurance policy. The central regulator theory doesn’t say that fuel and oxygen are unimportant only that the relation between fuel and fatigue is mediated by the brain.

The central regulator may have rational expectations. Experienced runners apparently report that the first mile of a 10k race is easier than the first mile of a 5k race. Makes no sense on the old theory but if you think about the central regulator meting out a fatigue budget in advance then everything becomes clear.

How then to improve performance? Try convincing yourself that you are running a 10k instead of a 5k (hypnosis may work). Also, Noakes suggests interval training, interspersed bouts of high intensity workouts with recovery breaks. The idea here is to the teach the central regulator that going faster won’t do you any harm.

Is it just my imagination?

Kevin Garnett recently won the MVP award in the NBA after a stellar and very consistent season. He was awarded the trophy in a ceremony before last night’s playoff game, and then had a subpar performance. I recall this same pattern holding in the past when other players receive the award before games. The example of David Robinson comes to mind; he received the trophy and was promptly outplayed by Hakeem Olajuwon. I suspect the lesson is that approbational incentives always matter at the margin, and an MVP trophy makes it harder to motivate oneself for the single basketball game to follow the trophy award. A lesson for life lies therein. If nothing else, try to isolate your awards, triumphs, and conquests from your subsequent performance.

Addendum: Here is another quantitative method of measuring the marginal product of basketball players, the best I have seen yet. Kevin Garnett comes out as number one.

Sports economics puzzle of the day

I very much enjoyed my visit this week to the University of Western Ontario. I had an especially good time trading micro puzzles with one of my hosts John Palmer. John is an economist, an artist, and founder of the Philistine Liberation Organization.

We quickly hit upon the old sports chestnut: why is soccer not a major professional sport in America?

It seems easy enough to add commercials when the ball goes out of bounds. And we have plenty of land for soccer fields. Maybe soccer is too boring on television, but hey (no brickbats please) what about baseball? Could it be that soccer is too hard to describe on radio, noting that this medium drove the initial popularity of baseball?
I have the vague intuition that soccer is too “working class” for the non-unionized United States, but it is hard to go far with this hypothesis.

My best shot at an answer was the following: Americans prefer professional sports where they know (or feel) that they are the best in the world. This applies to baseball, football, and basketball, the major professional sports in the United States. At tennis we are no joke. Chess became massively popular, but only briefly, when Bobby Fischer defeated Boris Spassky.

The implicit prediction, of course, is that basketball will decline in popularity.

Addendum: Perhaps a country can only fit so many sports. Thanks to Scott Cunningham for the pointer. In another direction, Bob Crosby writes the following:

“Both soccer and hockey have problems gaining US audiences for similar reasons.

Both games make it very difficult for the best players to fully exploit their skills. Put differently, they are games where the difference between the great players and the mediocre players is minimized.

In hockey, (a) the unwillingness of the refs to call hooking, slashing and holding penalties and (b) the ridiculously small size of modern rinks mean that the value of speed and skill is reduced. The wide disparities in skill levels that naturally exist are reduced or eliminated.

In soccer, the off-sides rule has the same effect. It acts as a speed break. And speed breaks help slower, less talented players.

In short, the difference between the best players and the worst players is structurally minimized in those sports.

Football, basketball, baseball or golf do not have similar problems. In those sports, wide disparities in talent are encouraged and immediately and easily discernable by fans.”

Celebrity misbehavior

Celebrities appear to engage in more anti-social behavior than the rest of us. What might be some reasons for this?

1. Famous people are simply crazy.

2. Rich people can get away with more.

3. Stars seek publicity, even “bad” publicity, to boost their celebrity.

4. Many celebrities are young and thus immature.

5. Celebrities are stressed, lack privacy, and are out of touch with the real world.

6. Celebrities get away with more because they can. You cannot substitute for them very easily.

Some of these propositions receive explicit tests from Todd Kendall of Clemson University. Kendall looks at technical fouls in the NBA; this penalty is assigned when a player hits another, screams at the referee, or engages in other forms of unsportsmanlike conduct. We learn the following:

a) Technical fouls are positively correlated with bad behavior off the court.

b) The more dominant a player is on a team, the more likely he commits technical fouls. Remember this guy?

c) Youth does not predict a player’s propensity to commit technical fouls. In fact older players commit more technical fouls. (Note to self: counterexample)

d) Committing technical fouls, adjusting for other variables, is not associated with higher income (this goes against number three above.

e) On a given team, technical fouls are not “contagious.”

f) Much of bad behavior is not predicted by any particular variable and thus can be thought of as idiosyncratic.

My take: The worst offenders are frustrated, spoiled brats who hate losing, can’t stand their teammates, but carry their teams on their backs.

Addendum: It is not easy to get your parents to sue you, read this update from the world of tennis.

The marginal product of NBA players

Most of you have read Moneyball by now, so why not measure the marginal products of NBA players as well? After all, playoff time and the MVP award are just around the corner. Wayne Winston, professor of decision sciences at Indiana University, has tried to crack the numbers:

“Basketball’s a team sport, and lots of things aren’t tracked,” Winston says. “Like taking the charge, going through a screen, tipping a ball to your teammate, saving a ball from going out of bounds. That’s where our system comes in. All these little things should translate into points.”
One problem: Traditional plus-minus systems tend to overrate average players on good teams and underrate good players on lousy ones. After all, a zero plus-minus rating on the Los Angeles Lakers is not the same as a zero rating on the Los Angeles Clippers, mostly because one team has Kobe Bryant and Shaquille O’Neal and the other has Marko Jaric and Chris Kaman.
To compensate, Winval’s ratings are weighted to take into account every other player on the floor. For every time segment a player is in a game, the system tracks the other nine players on the floor, the length of the segment and the score at the start and end of the segment.”

In other words, he tries to measure marginal product in terms of points, adjusting for the values of the other players. The system is called Winval, here is the article, the paper version has more information. And who comes out on top? Please sit down, the five best players in the NBA, according to this measure are:

1. Hedo Turkoglu (who? he plays for San Antonio but doesn’t even start)
2. Vince Carter (a well-known star, but universally considered soft and a choker)
3. Kevin Garnett (the likely MVP for this year)
4. Brad Miller (very good player, but not elite)
5. Manu Ginobili (very good player, perhaps headed toward elite status)

Shaq, Kobe, and Tim Duncan are not in the top ten. None of the five, except for Garnett, crack a recent USA Today straw poll for NBA mvp. (By the way, here is last year’s Winval list.) Now maybe these rankings are right and conventional wisdom is all wet. Marginal product is, well…marginal product. But what are some other options?

1. A player with a high rank could have a really bad replacement, thus boosting his measured marginal impact.
2. Some players are “momentum” players, they are put in when the tide is turning.
3. Some players are wonderful for the time they play but could not keep it up for the whole game. They look great when you see them, but they are not worth very much overall.
4. The econometric model is somehow misspecified, but of course you can always say this.

The bottom line: I’m still puzzled by how much the measurements diverge from common sense. The NBA offers gobs and gobs of measurable information. Yet intuition remains indispensable when we try to estimate marginal product. By the way, Winval predicts that Mitchell Butler (who?, 13.4 minutes per game) is the best Washington Wizard.

Stadium Construction and Broken Windows

USA Today reports on a study by University of Dayton economists Marc Poitras and Larry Hadley: privately financed sports stadiums pay for themselves. Tax dollars aren’t necessary to make them viable. Somehow I doubt that the study will slow the pace of publicly financed sports stadiums. While it may make it more embarrassing for franchise owners to ask for public handouts, what’s a little stigma among friends? The success of the begging strategy is mainly due to the threat of exit–owners demand public financing as a way of extracting money from cities fearful that teams will leave. There isn’t free entry into sports leagues–leagues tightly control new entrants–so cities are always vulnerable to the threat of a team leaving.

The claim that sports teams and new stadiums are good for the economy is a classic case of the “broken window fallacy” of Bastiat. The benefits are seen–the jobs building the stadium, the fans who spend money at the restaurants near the stadium. Unseen are the jobs lost elsewhere and the restaurants on the other side of town that lose business. Roger Noll and Andrew Zimbalist found that the net benefit of public stadiums is basically zero–there’s no stimulus to the local economy worth talking about. Their conclusion:

In our forthcoming Brookings book, Sports, Jobs, and Taxes, we and 15 collaborators examine the local economic development argument from all angles: case studies of the effect of specific facilities, as well as comparisons among cities and even neighborhoods that have and have not sunk hundreds of millions of dollars into sports development. In every case, the conclusions are the same. A new sports facility has an extremely small (perhaps even negative) effect on overall economic activity and employment. No recent facility appears to have earned anything approaching a reasonable return on investment. No recent facility has been self-financing in terms of its impact on net tax revenues. Regardless of whether the unit of analysis is a local neighborhood, a city, or an entire metropolitan area, the economic benefits of sports facilities are de minimus.

The U of Dayton study is here.

You can find the entire Noll and Zimbalist book online here.