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Star Michigan guard Trey Burke collected two personal fouls in the early minutes of the National Championship game against Louisville and he was promptly benched and sat out most of the remaining first half. The announcers didn’t bother to say why because its common wisdom that you don’t want your best players fouling out early.
But the common wisdom requires some scrutiny because on its surface it actually looks absurd. You fear your best player fouling out because then his playing time might be limited. So in response you guarantee his playing time will be limited by benching him. Jonathon Weinstein once made this point.
But just because basketball commentators, and probably even basketball coaches, don’t properly understand the rationale for the strategy doesn’t mean the strategy is unsound. In fact it follows from a very basic strategic idea: information is valuable.
Suppose the other team is scoring points at some random rate. If they are lucky they score a lot and if they are less lucky they score fewer. If the other team scores a lot your team should start shooting threes and go for short possessions to catch up. If the other team scores fewer you should go for safer shots and run down the clock. But you only know which of these you should do at the end of the game. If your best players are on the bench at that time you cannot capitalize on this information.
In our paper, Alex Frankel, Emir Kamenica and I argue that soccer is among the most suspenseful sports according to our theoretical measure. Now, via Matt Dickenson, comes an empirical validation of this finding using German cardiac arrest data:
The red line shows the spike in heart attacks on the dates of 2006 World Cup matches involving the German national team. Note that point 7 is the third place match against Portugal after Germany had been eliminated in their semi-final match against Italy (point 6.)
Here I am on the podcast Hang Up And Listen with hosts Stefan Fatsis, Mike Pesca and Josh Levin. Its a sports oriented podcast and I am talking about Purple Pricing. They had some very good questions. I come in at about the 25 minute mark.
Professional soccer leagues tend to be dominated year after year by a small number of top teams. Major League Baseball on the other hand, has seen World Series appearances by the Detroit Tigers, the Texas Rangers, the Philadelphia Phillies, the Tampa Bay Rays, etc. It seems like any team can assemble a champion.
These two sports have very different production functions. A baseball team is basically a collection of individuals. Among team sports its the closest thing to an individual sport. A team’s output is basically the sum of individual outputs with very little complementarity. In baseball there is very little talk of one player making his teammates better. The production function is additive and, offensively, players are perfectly substitutable.
Soccer is at the other extreme where players are highly complementary. Scoring a goal is a total team effort. Even the best striker needs good chances. In soccer, the best players are more productive when there are other good players on the team. The production function is closer to Leontif.
These differences in production explain the differences in market structure. Consider competitive bidding for a top player in the two sports. In baseball that player’s marginal product is the same on any team he would play for so many teams will compete and any team could land him. In soccer that player’s marginal value is highest for the team that is already the best. The competition is going to be very weak and he is likely to sign with the best team.
In baseball competition levels the playing field. In soccer it tilts it even further.
Dear Northwestern Economics community. I was among the first to submit my bracket and I have already chosen all 16 teams seeded #1 through #4 to be eliminated in the first round of the NCAA tournament. In case you don’t believe me:
Now that i got that out of the way, consider the following complete information strategic-form game. Someone will throw a biased coin which comes up heads with probability 5/8. Two people simultaneously make guesses. A pot of money will be divided equally among those who correctly guessed how the coin would land. (Somebody else gets the money if both guess incorrectly.)
In a symmetric equilibrium of this game the two players will randomize their guesses in such a way that each earns the same expected payoff. But now suppose that player 1 can publicly announce his guess before player 2 moves. Player 1 will choose heads and player 2′s best reply is to choose tails. By making this announcement, player 1 has increased his payoff to a 5/8 chance of winning the pot of money.
This principle applies to just about any variety of bracket-picking game, hence my announcement. In fact in the psychotic version we play in our department, the twisted-brain child of Scott Ogawa, each matchup in the bracket is worth 1000 points to be divided among all who correctly guess the winner, and the overall winner is the one with the most points. Now that all of my colleagues know that the upsets enumerated above have already been taken by me their best responses are to pick the favorites and sure they will be correct with high probability on each, but they will split the 1000 points with everyone else and I will get the full 1000 on the inevitable one or two upsets that will come from that group.
this a screenshot, from a few minutes ago (ed: last week), of bwin.com. the bets here are on goals in regular time of the barcelona-milan to be played in a little while. barcelona lost 2-0 in milan so barcelona needs at least 2 goals to force extra-time/penalty kicks. this is for the champions league.
as you can see from the screenshot barcelona winning 1-0 pays 10, 2-0 pays 7.5, 3-0 pays 8.75, while 4-0 pays 12.
what can we learn from this non-monotonicity? gamblers anticipate that barcelona’s extra incentives to score the 2-0 goal make it a more likely event than the 1-0 result (even though they have to score an extra goal!). once they have scored the 2-0, those extra incentives vanish so we are back to the intuition that a result with more goals is less likely.
How could this effect play out in real time? Here’s a model. It takes effort to increase the probability of scoring a goal. An immediate implication is that if the score is 0-0 with little time left, Barcelona will stop spending effort and the game will end 0-0. Too late in the game and it becomes so unlikely they can score two goals that the effort cost isn’t worth it. But if the score is 1-0 they will continue to spend effort beyond that point. So there is some interval near the end of the game where the conditional probability of scoring a goal is positive if the score is 1-0 but close to zero if the score is 0-0.
I would be interested in seeing some numbers calibrated to generated the betting odds above. We need three parameters. The first two are the probability of scoring a goal in a given minute of game time when Barcelona spends effort, and when it does not. The second is Barcelona’s rate of substitution between effort and win-probability. This could be expressed as follows. Over the course of a minute of play what is the minimum increase in win probability that would give Barcelona sufficient incentive to spend effort. These three parameters will determine when Barcelona stops spending effort in the 1-0 versus 0-0 scenarios and given this will then determine the probabilities of 1-0, 2-0, 3-0 etc. scores.
Consider a team selling tickets for its upcoming baseball season. Before the season begins it offers a bundle of tickets for every game. Some of these games however are certain to have very low attendance (games on a Tuesday, games against poor opponents, etc.) The tickets for these games will be placed on the secondary market at very low prices. Indeed one of the biggest problems for teams is the inability to prevent those secondary market prices from falling so low that they cannibalize single-game box office sales. The problem is so severe that many baseball teams are making arrangements with StubHub to enforce a price floor on that exchange.
The problem has a much simpler solution: stop selling season tickets. The team should instead offer the following type of bundle: you may purchase tickets for all of the predictably high-demand games at the usual season ticket discount.Then you may add to that bundle any subset of the low-demand games you desire but each at a price equal to the face value of the ticket.
This arrangement will make both season ticket holders and the team better off. Season ticket holders will opt not to add the low demand games (unless the opponent is a team they really like for example) and since they weren’t going to those games anyway they are saving money.
The team will increase revenue: supply of tickets to low demand games will be controlled. Secondary market tickets will be priced at or near face value because nobody will buy a ticket at face value for a lousy game unless they actually plan to use the tickets. This enables the team to hold prices at their desired (i.e. revenue maximizing) level without cannibalism.
What distinguishes a great mnemonist, I learned, is the ability to create lavish images on the fly, to paint in the mind a scene so unlike any other it cannot be forgotten. And to do it quickly. Many competitive mnemonists argue that their skills are less a feat of memory than of creativity. For example, one of the most popular techniques used to memorize playing cards involves associating every card with an image of a celebrity performing some sort of a ludicrous — and therefore memorable — action on a mundane object. When it comes time to remember the order of a series of cards, those memorized images are shuffled and recombined to form new and unforgettable scenes in the mind’s eye. Using this technique, Ed Cooke showed me how an entire deck can be quickly transformed into a comically surreal, and unforgettable, memory palace.
The author documents his training as a mental athlete and his US record breaking performance memorizing a deck of cards in 1 minute 40 seconds. I personally have a terrible memory, especially for names, but I don’t think this kind of active memorization is especially productive. The kind of memory enhancement we could all benefit from is the ability to call up more and more ideas/thoughts/experiences related to whatever is currently going on. We need more fluid relational memory, RAM not so much.
It was the way he treated last-second, buzzer-beating three-pointers. Not close shots at the end of a game or shot clock, but half-courters at the end of each of the first three quarters. He seemed to be purposely letting the ball go just a half-second after the buzzer went off, presumably in order to shield his shooting percentage from the one-in-100 shot he was attempting. If the shot missed, no harm all around. If it went in? Then the crowd would go nuts and he’d get a few slaps on the back, even if he wouldn’t earn three points for the scoreboard.
In Baseball, a sacrifice is not scored as an at-bat and this alleviates somewhat the player/team conflict of interest. The coaches should lobby for a separate shooting category “buzzer-beater prayers.” As an aside, check out Kevin Durant’s analysis:
“It depends on what I’m shooting from the field. First quarter if I’m 4-for-4, I let it go. Third quarter if I’m like 10-for-16, or 10-for-17, I might let it go. But if I’m like 8-for-19, I’m going to go ahead and dribble one more second and let that buzzer go off and then throw it up there. So it depends on how the game’s going.”
This seems backward. 100% (4-4) is much bigger than 80% (4/5) whereas the difference between 8 for 19 and 8 for 20 is just 2 percentage points.
We, Jeff and Sandeep, are working with Northwestern Sports to launch what we think is going to be a revolutionary way to sell tickets to sporting events (and someday theatre, concerts, and restaurants…). Starting today it is in effect for two upcoming Mens’ Basketball games: The February 28 game against Ohio State and the March 7 game against Penn State.
We are using a system which could roughly be described as a uniform price multi-unit Dutch Auction. In simpler terms we are setting an initial price and allowing prices to gradually fall until either the game sells out or we hit our target price. Thus we are implementing a form of dynamic pricing but unlike most systems used by other venues our prices are determined by demand not by some mysterious algorithm.
But here is the key feature of our pricing system: as prices fall, you are guaranteed to pay the lowest price you could have got by delaying your purchase. That is, regardless of what price is listed at the time you reserve your seat, the price you will actually pay is the final price.
What that means is that fans have no reason to wait around and watch the price changes and try to time their purchases to get the best possible deal. We take care of that for you.
It also removes another common gripe with dynamic pricing, different people paying different prices for the same seats. Our system is fair: since everyone pays the lowest price, everyone will be paying the same price.
We explain all of the details in the video below. If you have any questions please ask them in the comments and we will try to answer them.
And Go ‘Cats!
Update: Price alerts are now available. You may send email to email@example.com to be notified when prices fall. (And if you just want to know when prices reach some target p, put that in your message.)
Another good one from Scott Ogawa. It’s the Creampuff Dilemma. A college football coach has to set its pre-season non-conference schedule, thinking ahead to the end-of-season polling that decides Bowl Bids. A schedule stocked with creampuffs means lots of easy wins. But holding fixed the number of wins, a tough schedule will bolster your ranking.
Here’s Scott’s model. Each coach picks a number p between 0 and 1. He is successful (s=1) with probability p and unsuccessful (s=0) with probability 1-p. These probabilities are independent across players. (Think of these as the top teams in separate conferences. They will not be playing against each other.)
Highest s-p wins.
Check out the prices on Stub Hub for tickets to the upcoming Big10 basketball game between the Iowa Hawkeyes and the Wisconsin Badgers. Quite a few of them are significantly below the $24 face value of the tickets. This can happen because fans who buy season tickets for Badgers basketball are buying for the games against the conference powerhouses. For the games against cellar dwellers like Iowa they dump their tickets on the secondary market at whatever price they will fetch.
Coping with scalpers who buy tickets through the box office and resell them at inflated prices is one thing. You could have raised prices yourself but you chose not to. But what do you do when scalpers are undercutting your box office price?
You should buy the tickets back from the scalpers is what you should do. The fans who are going to buy from the scalper at the low price might also be willing to buy at box office prices. If you buy the cheap tickets on StubHub first then the box office is the only option left for them. And if they do buy from the box office you have made a profit because you bought low and sold high.
But there’s a chance those fans aren’t willing to pay box office prices and in that case you’re just losing money. So there’s a tradeoff. It means that you don’t want to buy secondary market tickets at prices just below your box office price but you definitely do want to buy the tickets priced so low that they are worth the risk. Indeed there is some optimal offer price that you should be prepared to repurchase tickets at.
In fact every venue’s box office should be both a buyer and seller of tickets with an optimally calculated spread between bid and ask prices.
Now you might wonder whether this only further encourages season ticket holders to dump their unwanted tickets. Indeed it does but that’s exactly what you want them to do. The tickets will be reallocated more efficiently and you will capture the gains from trade. Moreover, fans are now willing to pay higher prices for season tickets if they know they can easily resell their unwanted tickets. You can then raise season ticket prices to capture those gains.
I read this interesting post which talks about spectator sports and the gap between the excitement of watching in person versus on TV. The author ranks hockey as the sport with the largest gap: seeing hockey in person is way more fun than watching on TV. I think I agree with that and generally with the ranking given. (I would add one thing about American Football. With the advent of widescreen TVs the experience has improved a lot. But its still very dumb how they frame the shot to put the line of scrimmage down the center of the screen. The quarterback should be near the left edge of the screen at all times so that we can see who he is looking at downfield.)
But there was one off-hand comment that I think the author got completely wrong.
I think NBA basketball players might be the best at what they do in all of sports.
The thought experiment is to compare players across sports. I.e., are basketball players better at basketball than, say, snooker players are at playing snooker?
Unless you count being tall as one of the things NBA basketball players “do” I would say on the contrary that NBA basketball players must be among the worst at what they do in all of professional sports. The reason is simple: because height is so important in basketball, the NBA is drawing the top talent among a highly selected sub-population: those that are exceptionally tall. The skill distribution of the overall population, focusing on those skills that make a great basketball player like coordination, quickness, agility, accuracy; certainly dominate the distribution of the subpopulation from which the NBA draws its players.
Imagine that the basket was lowered by 1 foot and a height cap enforced so that in order to be eligible to play you must be 1 foot shorter than the current tallest NBA player (or you could scale proportionally if you prefer.) The best players in that league would be better at what they do than current NBA players. (Of course you need to allow equilibrium to be reached where young players currently too short to be NBA stars now make/receive the investments and training that the current elite do.)
Now you might ask why we should discard height as one of the bundle of attributes that we should say a player is “best” at. Aren’t speed, accuracy, etc. all talents that some people are born with and others are not, just like height? Definitely so, but ask yourself this question. If a guy stops playing basketball for a few years and then takes it up again, which of these attributes is he going to fall the farthest behind the cohort who continued to train uninterrupted? He’ll probably be a step slower and have lost a few points in shooting percentage. He won’t be any shorter than he would have been.
When you look at a competition where one of the inputs of the production function is an exogenously distributed characteristic, players with a high endowment on that dimension have a head start. This has two effects on the distribution of the (partially) acquired characteristics that enter the production function. First, there is the pure statistical effect I alluded to above. If success requires some minimum height then the pool of competitors excludes a large component of the population.
There is a second effect on endogenous acquisition of skills. Competition is less intense and they have less incentive to acquire skills in order to be competitive. So even current NBA players are less talented than they would be if competition was less exclusive.
So what are the sports whose athletes are the best at what they do? My ranking
- Table Tennis
The final seconds are ticking off the clock and the opposing team is lining up to kick a game winning field goal. There is no time for another play so the game is on the kicker’s foot. You have a timeout to use.
Calling the timeout causes the kicker to stand around for another minute pondering his fateful task. They call it “icing” the kicker because the common perception is that the extra time in the spotlight and the extra time to think about it will increase the chance that he chokes. On the other hand you might think that the extra time only works in the kickers favor. After all, up to this point he wasn’t sure if or when he was going to take the field and what distance he would be trying for. The timeout gives him a chance to line up the kick and mentally prepare.
What do the data say? According to this article in the Wall Street Journal, icing the kicker has almost no effect and if anything only backfires. Among all field goal attempts taken since the 2000 season when there were less than 2 minutes remaining, kickers made 77.3% of them when there was no timeout called and 79.7% when the kicker was “iced.”
So much for icing? No! Icing the kicker is a successful strategy because it keeps the kicker guessing as to when he will actually have to prepare himself to perform. The optimal use of the strategy is to randomize the decision whether to call a timeout in order to maximize uncertainty. We’ve all seen kickers, golfers, players of any type of finesse sport mentally and physically prepare themselves for a one-off performance. The mental focus required is a scarce resource. Randomizing the decision to ice the kicker forces the kicker to choose how to ration this resource between two potential moments when he will have to step up.
If you ice with probability zero he knows to focus all his attention when he first takes the field. If you ice with probability 1 he knows to save it all for the timeout. The optimal icing probability leaves him indifferent between allocating the marginal capacity of attention between the two moments and minimizes his overall probability of a successful field goal. (The overall probability is the probability of icing times the success probability conditional on icing plus the probability of not icing times the success probability conditional on icing.)
Indeed the simplest model would imply that the optimal icing strategy equalizes the kicker’s success probability conditional on icing and conditional on no icing. So the statistics quoted in the WSJ article are perfectly consistent with icing as part of an optimal strategy, properly understood.
But whatever you do, call the timeout before he gets a freebie practice kick.
It’s clear that lots of sports franchises suffer from suboptimal ticket-pricing schemes. Between games that feature many empty seats, games that sell out entirely, and the ability of scalpers to obtain profits on the secondary market, money is obviously being left on the table. The University of Minnesota is trying an interesting idea with its new Golden Ticket pricing concept that for $75 lets you attend all nine Big Ten men’s basketball matchups.
But with a catch.
The catch is that if you go to a game and Minnesota loses, then your pass expires.
Watching the Olympic Games this Summer I noticed that the volleyball competition has changed the scoring system from the old “sideout” system to what used to be called “quick score.” (This change may have happened a long time ago, I don’t watch much volleyball.) The traditional sideout scoring method increments the score only when the serving team wins a point. When the serving team loses the point the serve is awarded to the other team (a “sideout”) but the score is unchanged. This can lead to long drawn out games with repeated sideouts and little scoring. As a stopgap, in the old days, volleyball matches would switch to the quick score system after a certain amount of time has elapsed. In quick scoring a sideout earns a point for the team that gains the serve.
I always liked the sideout system, thinking of it as a characteristic volleyball rule that is compromised for expediency by the switch to quick score. Instinctively it seemed that the fact you could only score when you are serving played a big role in volleyball strategy. But when I was watching this summer it occurred to me that the two scoring systems are less different than it appeared at first.
The basic observation is that at any stage of the game sideout scores are just quick scores minus the number of sideouts. And sideouts necessarily alternate between teams so the number you are subtracting differs by at most one across the two teams. So I started to think if there was a way to characterize the mapping between scoring systems that would clarify precisely the strategic impact of the switch. And I think I figured it out.
Quick scoring is defined as follows. The team who wins a point has its score incremented by one, regardless of who was serving that point. (The serve switches when the receiving team wins a point just as in the sideout system.) The winner of the game is the first team to have a score of at least 15 (or 25 in other cases) and at least a 2 point lead. (I.e. the game continues past 15 if neither team has a two point lead.)
Quick scoring is equivalent to the following system: 28 points will be played. After 28 points (let’s call it regulation) if the score is tied (14-14) then they continue to play until some team has a 2 point advantage.
This is in turn equivalent to side-out scoring with the following amended rules. Lets refer to the team that receives serve in the first point of the game as the receiving team.
- A total of 28 ponts is played in regulation.
- At the end of play if either team is ahead by 2 points then that team wins except if
- the receiving team either scored the last point or earned a side-out in the last point and the receiving team is ahead by 1 point. In this case the receiving team wins.
If none of these conditions are met then the game continues past regulation. We define the team that has the serve in the first point past regulation as team 1 and the other team as team 2. The score is reset to 0-0. Play continues (with side-out scoring) until the first moment at which one of the following occurs.
- Team 1 has a 2 point lead, in which case team 1 is the winner.
- Team 2 has a 1 point lead, in which case team 2 is the winner.
The proof of this equivalence is below the jump. Here’s what it means. Quick scoring is not an innoccuous change in the rules to speed up play but its pretty close. Because a near identical outcome would obtain if instead of switching to quick score, we keep sideout scoring but cap the number of regulation points at 28. Its nearly, but not exactly identical because of the two scoring “epicycles” that have to be appended, namely #3 in regulation and #2 in overtime. Note that both of these wrinkles tend to benefit the receiving team. I don’t know the stats (anybody?) but it appears to me that the receiving team already has a large advantage in volleyball at the level of an individual point. You could say that an effect of sideout scoring is that it levels the playing field by giving a small overall advantage to the serving team. The switch to quick scoring eliminates that.
I wonder if there is a noticeable difference in the frequency with which the (initially) receiving team wins a volleyball game after the switch to quick scoring.
I’ve decided to lump speed together with all of these other (hypothesized) factors under the general heading of “Floor Stretch”. We’ll use it for an exercise in theoretical sports economics…Whatever it is that truly makes up “Floor Stretch”, it has to be sufficiently valuable that it offsets the lower raw productivity of the smaller players….
Floor Stretch, however, is really a relative function. Having 5 point guards on the floor only stretches the other team if they don’t also have 5 point guards playing. In this sense, what we really care about is the ratio of Floor Stretch between the two teams competing. Theoretically, the Floor Stretch ratio is what the raw productivity must be balanced against in order to determine the best mix of players. This, then, gets us into some classical Game Theory….
I’m too focussed on the election to digest fully. But I got this from Goolsbee’s Twitter feed today – he must be confident?
- Its socially valuable for the University of Michigan measure consumer confidence and announce it even if that is an irrelevant statistic. Because otherwise somebody with less neutral motives would invent it, manipulate it, and publicize it.
- Kids are not purely selfish. They like it when they get better stuff than their siblings. To such an extent that they often feel mistreated when they see a sibling get some goodies.
- Someone should develop a behavioral theory of how people play Rock, Scissors, Paper when its common knowledge that humans can’t generate random sequences.
- The shoulder is the kludgiest joint because there are infinitely many ways to do any one movement. Almost surely you have settled into a sub-optimal way.
- I go to a million different places for lunch but at each one I always order one dish.
Economists Andrew Healy, Neil Malhotra, and Cecilia Mo make this argument in afascinating article in the Proceedings of the National Academy of Science. They examined whether the outcomes of college football games on the eve of elections for presidents, senators, and governors affected the choices voters made. They found that a win by the local team, in the week before an election, raises the vote going to the incumbent by around 1.5 percentage points. When it comes to the 20 highest attendance teams—big athletic programs like the University of Michigan, Oklahoma, and Southern Cal—a victory on the eve of an election pushes the vote for the incumbent up by 3 percentage points. That’s a lot of votes, certainly more than the margin of victory in a tight race. And these results aren’t based on just a handful of games or political seasons; the data were taken from 62 big-time college teams from 1964 to 2008.
And Andrew Gelman signs off on it.
I took a look at the study (I felt obliged to, as it combined two of my interests) and it seemed reasonable to me. There certainly could be some big selection bias going on that the authors (and I) didn’t think of, but I saw no obvious problems. So for now I’ll take their result at face value and will assume a 2 percentage-point effect. I’ll assume that this would be +1% for the incumbent party and -1% for the other party, I assume.
Let’s try this:
- Incumbents have an advantage on average.
- Higher overall turnout therefore implies a bigger margin for the incumbent, again on average.
- In sports, the home team has an advantage on average.
- Conditions that increase overall scoring amplify the advantage of the home team.
- Good weather increases overall turnout in an election and overall scoring in a football game.
So what looks like football causes elections could really be just good weather causes both. Note well, I have not actually read the paper but I did search for the word weather and it appears nowhere.
A new joint paper with Alex Frankel and Emir Kamenica. The talk begins with tennis, the discussion of American Idol begins at 12:14, how to write a mystery novel is at 15:51, the M. Night Shamyalan dilemma is at 17:32, the ESPN Classic dilemma is at 18:50, and the optimal sporting contest is at 28:37.
I wrote about it here. I had a look at the video and it was the right call given the rule, but as I argued in the original post the rule is an unnecessary kludge. At best, it does nothing (in equilibrium.)
- Is it that women like to socialize more than men do or is it that everyone, men and women alike, prefers to socialize with women?
- A great way to test for strategic effort in sports would be to measure the decibel level of Maria Sharapova’s grunts at various points in a match.
- If you are browsing the New York Times and you are over your article limit for the month, hit the stop button just after the page renders but before the browser has a chance to load the “Please subscribe” overlay. This is easy on slow browsers like your phone.
- Given the Archimedes Principle why do we think that the sea level will rise when the Polar Caps melt?
The eternal Kevin Bryan writes to me:
Consider an NFL team down 15 who scores very late in the game, as happened twice this weekend. Everybody kicks the extra point in that situation instead of going for two, and is then down 8. But there is no conceivable “value of information” model that can account for this – you are just delaying the resolution of uncertainty (since you will go for two after the next touchdown). Strange indeed.
Let me restate his puzzle. If you are in a contest and success requires costly effort, you want to know the return on effort in order to make the most informed decision. In the situation he describes if you go for the 2-pointer after the first touchdown you will learn something about the return on future effort. If you make the 2 points you will know that another touchdown could win the game. If you fail you will know that you are better off saving your effort (avoiding the risk of injury, getting backups some playing time, etc.)
If instead you kick the extra point and wait until a second touchdown before going for two there is a chance that all that effort is wasted. Avoiding that wasted effort is the value of information.
The upshot is that a decision-maker always wants information to be revealed as soon as possible. But in football there is a separation between management and labor. The coach calls the plays but the players spend the effort. The coach internalizes some but not all of the players’ cost of effort. This can make the value of information negative.
Suppose that both the coach and the players want maximum effort whenever the probability of winning is above some threshold, and no effort when its below. Because the coach internalizes less of the cost of effort, his threshold is lower. That is, if the probability of winning falls into the intermediate range below the players’ threshold and above the coach’s threshold, the coach still wants effort from them but the players give up. Finally, suppose that after the first touchdown the probability of winning is above both thresholds.
Then the coach will optimally choose to delay the resolution of uncertainty. Because going for two is either going to move the probability up or down. Moving it up has no effect since the players are already giving maximum effort. Moving it down runs the risk of it landing in that intermediate area where the players and coach have conflicting incentives. Instead by taking the extra point the coach gets maximum effort for sure.
“I just crashed, I did it on purpose to get a restart, just to have the fastest ride. I did it. So it was all planned, really,” Hindes reportedly said immediately after the race. He modified his comments at the official news conference to say he lost control of his bike.”
The opposition took it in stride:
French officials did not formally complain about the British tactic.
“You have to make the most of the rules. You have to play with them in a competition and no one should complain about that,” the France team’s technical director, Isabelle Gautheron, told The Associated Press.
“He (Hindes) should not have told the truth,” Daniel Morelon, a Frenchman who coaches the China team, told the AP. “It’s part of the game, but you should not tell others.”
Eight female badminton players were disqualified from the Olympics on Wednesday for trying to lose matches the day before, the Badminton World Federation announced after a disciplinary hearing.
The players from China, South Korea and Indonesia were accused of playing to lose in order to face easier opponents in future matches, drawing boos from spectators and warnings from match officials Tuesday night.
All four pairs of players were charged with not doing their best to win a match and abusing or demeaning the sport.
Apparently the Badminton competition has the typical structure of a preliminary round followed by an elimination tournament. Performance in the preliminary round determines seeding in the elimination tournament. The Chinese and South Korean teams had already qualified for the elimination tournament but wanted to lose their final qualifying match in order to get a worse seeding in the elimination tournament. They must have expected to face easier competition with the worse seeding.
This widely-used system is not incentive-compatible. This is a problem with every sport that uses a seeded elimination tournament. Economist/Market Designers have fixed Public School Matching and Kidney Exchange, let’s fix tournament seeding. Here are two examples to illustrate the issue:
1. Suppose there are only three teams in the competition. Then the elimination tournament will have two teams play in a first elimination round and the remaining team will have a “bye” and face the winner in the final. This system is incentive compatible. Having the bye is unambiguously desirable so all teams will play their best in the qualifying to try and win the bye.
2. Now suppose there are four teams. The typical way to seed the elimination tournament is to put the top performing team against the worst-performing team in one match and the middle two teams in the other match. But what if the best team in the tournament has bad luck in the qualifying and will be seeded fourth. Then no team wants to win the top seed and there will be sandbagging.
As I see it the basic problem is that the seeding is too rigid. One way to try and improve the system is to give the teams some control over their seeding after the qualifying round is over. For example, we order the teams by their performance then we allow the top team to choose its seed, then the second team chooses, etc. The challenge in designing such a system is to make this seed-selection stage incentive-compatible. The risk is that the top team chooses a seed and then after all others have chosen theirs the top team regrets its choice and wants to switch. If the top team foresees this possibility it may not have a clear choice and this instability is not only problematic in itself but could ruin qualifying-round incentives again.
So that is the question. As far as I know there is no literature on this. Let’s us, the Cheap Talk community, solve this problem. Give your analysis in the comments and if we come up with a good answer we will all be co-authors.
UPDATE: It seems we have a mechanism which solves some problems but not all and a strong conjecture that no mechanism can do much better than ours. GM was the first to suggest that teams select their opponents with higher qualifiers selecting earlier and Will proposed the recursive version. (alex, AG, and Hanzhe Zhang had similar proposals) The mechanism, lets call it GMW, works like this:
The qualifiers are ranked in descending order of qualifying results. (In case the qualifying stage produces only a partial ranking, as is the case with the group stages in the FIFA World Cup, we complete the ranking by randomly ordering within classes.) In the first round of the elimination stage the top qualifier chooses his opponent. The second qualifier (if we was not chosen!) then chooses his opponent from the teams that remain. This continues until the teams are paired up. In the second round of elimination we pair teams via the same procedure again ordering the surviving teams according to their performance in the qualifying stage. This process repeats until the final.
It was pointed out by David Miller (also JWH with a concrete example, and afinetheorem) that GMW is not going to satisfy the strongest version of our incentive compatibility condition and indeed no mechanism can.
Let me try to formalize the positive and negative result. Let’s consider two versions of No Envy. They are strong and weak versions of a requirement that no team should want to have a lower ranking after qualifying.
Weak No Envy: Let P_k(r,h) be the pairing that results in stage k of the elimination procedure when the ordering of teams after the qualifying stage was r and the history of eliminations prior to stage k is given by h. Let r’ be the ordering obtained by altering r by moving team x to some lower position without altering the relative ordering of all other teams. We insist that for every r, k, h, and x, the pairing P_k(r,h) is preferred by team x to the pairing P_k(r’,h).
Strong No Envy: Let r’ be an ordering that obtains by moving team x to some lower position and possibly also altering the relative positions of other teams. We insist that for every r,k,h, and x, the pairing P_k(r,h) is preferred by team x to P_k(r’,h).
GMW satisfies Weak No Envy but no mechanism satisfies Strong No Envy. (The latter is not quite a formal statement because it could be that the teams pairing choices, which come from the exogenous relative strengths of teams, make Strong No Envy hold “by accident.” We really want No Envy to hold for every possible pattern of relative strengths.)
One could also weaken Strong No Envy and still get impossibility. The interesting impossibility result would find exactly the kind of reorderings r->r’ that cause problems.
Finally, we considered a second desideratum like strategy-proofness. We want the mechanism that determines the seedings to be solvable in dominant strategies. Note that this is not really an issue when the teams are strictly ordered in objective strength and this ordering is common knowledge. It becomes an issue when there is some incomplete information (an issue raised by AG, and maybe also when there are heterogeneous strengths and weaknesses, also mentioned by AG.)
Formalizing this may bring up some new issues but it appears that GMW is strategyproof even with incomplete information about teams strengths and weaknesses.
Finally, there are some interesting miscellaneous ideas brought up by Scott (you can unambiguously improve any existing system by allowing a team who wins a qualifying match to choose to be recorded as the loser of the match) and DRDR (you minimize sandbagging, although you don’t eliminate it, by having a group format for qualifiers and randomly pairing groups ex post to determine the elimination matchups, this was also suggested by Erik, ASt and SX.)
Sprinters Allyson Felix and Jeneba Tarmoh threw their bodies across the finish line so evenly matched that cameras recording 3,000 frames a second couldn’t tell who beat whom.
Both runners recorded precisely the same finishing time, down to thousandths of a second: 11.068 seconds.
Two women beat Felix and Tarmoh: Carmelita Jeter and Tianna Madison. Their first and second place finishes on Saturday give them the chance to represent the United States at the Olympics in London this summer.
But the photo finish leaves USA Track & Field with a dilemma: Who gets the third slot?
There appears to be no precedent for a dead heat at U.S. Olympic Team track and field trials, prompting the U.S. Olympic Committee to announce new rules Sunday.
One of the runners can give up her claim to a spot on the Olympic team.
If neither one takes that unlikely option, they’ll be asked if they want to run a tie-breaking race or flip a coin.
If they choose the same option, the committee will respect their wishes.
If they disagree, they’ll have to race for it.
And if both athletes refuse to declare a preference, officials will flip a coin — a U.S. quarter to be exact.
They certainly have given it some thought but they may want to consult the previous literature as it seems they might be slightly off track:
Leaving nothing to chance, other than the flip itself, the rules also detail who gets to pick heads or tails and how the coin should be flipped.
“The USATF representative shall bend his or her index finger at a 90-degree angle to his or her thumb, allowing the coin to rest on his or her thumb,” the rules say.
Because of runners’ high:
When people exercise aerobically, their bodies can actually make drugs — cannabinoids, the same kind of chemicals in marijuana. Raichlen wondered if other distance-running animals also produced those drugs. If so, maybe runner’s high is not some peculiar thing with humans. Maybe it’s an evolutionary payoff for doing something hard and painful, that also helps them survive better, be healthier, hunt better or have more offspring.
So he put dogs — also distance runners — on a treadmill. Also ferrets, but ferrets are not long-distance runners. The dogs produced the drug, but the ferrets did not. Says Raichlen: “It suggests some level of aerobic exercise was encouraged by natural selection, and it may be fairly deep in our evolutionary roots.”
This is a screenshot from an espn.com webstreaming replay of the French Open match between Maria Sharapova and Klara Zakapalova. As you can see Sharapova won the first set and now they are locked in a tight second set. But hmmm… something tells me that Zakapalova will be able to push it to three sets…
Courtesy of Emir Kamenica.
College sports. The NBA and the NFL, two of the most sought-after professional sports in the United States outsource the scouting and training of young talent to college athletics programs. And because the vast majority of professionals are recruited out of college the competition for professional placement continues four years longer than it would if there were no college sports.
The very best athletes play basketball and football in college, but only a tiny percentage of them will make it as professionals. If professionals were recruited out of high school then those that don’t make it would find out four years earlier than they do now. Many of them would look to other sports where they still have chances. Better athletes would go into soccer at earlier ages.
As long as college athletics programs serve as the unofficial farm teams for professional basketball and football, many top athletes won’t have enough incentive to try soccer as a career until it is already too late for them.