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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.
My 9 year-old daughter’s soccer games are often high-scoring affairs. Double-digit goal totals are not uncommon. So when her team went ahead 2-0 on Saturday someone on the sideline remarked that 2-0 is not the comfortable lead that you usually think it is in soccer.
But that got me thinking. Its more subtle than that. Suppose that the game is 2 minutes old and the score is 2-0. If these were professional teams you would say that 2-0 is a good lead but there are still 88 minutes to play and there is a decent chance that a 2-0 lead can be overcome.
But if these are 9 year old girls and you know only that the score is 2-0 after 2 minutes your most compelling inference is that there must be a huge difference in the quality of these two teams and the team that is leading 2-0 is very likely to be ahead 20-0 by the time the game is over.
The point is that competition at higher levels is different in two ways. First there is less scoring overall which tends to make a 2-0 lead more secure. But second there is also lower variance in team quality. So a 2-0 lead tells you less about the matchup than it does at lower levels.
Ok so a 2-0 lead is a more secure lead for 9 year olds when 95% of the game remains to be played (they play for 40 minutes). But when 5% of the game remains to be played a 2-0 lead is almost insurmountable at the professional level but can easily be upset in a game among 10 year olds.
So where is the flipping point? How much of the game must elapse so that a 2-0 lead leads to exactly the same conditional probability that the 9 year olds hold on to the lead and win as the professionals?
Next question. Let F be the fraction of the game remaining where the 2-0 lead flipping point occurs. Now suppose we have a 3-0 lead with F remaining. Who has the advantage now?
And of course we want to define F(k) to be the flipping point of a k-nil lead and we want to take the infinity-nil limit to find the flipping point F(infinity). Does it converge to zero or one, or does it stay in the interior?
Suppose you and I are playing a series of squash matches and we are playing best 2 out of 3. If I win the first match I have an advantage for two reasons. First is the obvious direct reason that I am only one match short of wrapping up the series while you need to win the next two. Second is the more subtle strategic reason, the discouragement effect. If I fight hard to win the next match my reward is that my job is done for the day, I can rest and of course bask in the glow of victory. As for you, your effort to win the second match is rewarded by even more hard work to do in the third match.
Because you are behind, you have less incentive than me to win the second match and so you are not going to fight as hard to win it. This is the discouragement effect. Many people are skeptical that it has any measurable effect on real competition. Well I found a new paper that demonstrates an interesting new empirical implication that could be used to test it.
Go back to our squash match and now lets suppose instead that it’s a team competition. We have three players on our teams and we will match them up according to strength and play a best two out of three team competition. Same competition as before but now each subsequent game is played by a different pair of players.
A new paper by Fu, Lu, and Pan called “Team Contests With Multiple Pairwise Battles” analyzes this kind of competition and shows that they exhibit no discouragement effect. The intuition is straightforward: if I win the second match, the additional effort that would have to be spent to win the third match will be spent not by me, but by my teammate. I internalize the benefits of winning because it increases the chance that my team wins the overall series but I do not internalize the costs of my teammate’s effort in the third match. This negative externality is actually good for team incentives.
The implied empirical prediction is the following. Comparing individual matches versus team matches, the probability of a comeback victory conditional on losing the first match will be larger in the team competition. A second prediction is about the very first match. Without the discouragement effect, the benefit from winning the first match is smaller. So there will be less effort in the first match in the team versus individual competition.
My son and I went to see the Cubs last week as we do every Spring.
The Cubs won 8-0 and Matt Garza was one out away from throwing a complete game shutout, a rarity for a Cub. The crowd was on its feet with full count to the would-be final batter who rolled the ball back to the mound for Garza to scoop up and throw him out. We were all ready to give a big congratulatory cheer and then this happened. This is a guy who was throwing flawless pitches to the plate for nine innings and here with all the pressure gone and an easy lob to first he made what could be the worst throw in the history of baseball and then headed for the showers. Cubs win!
But this Spring we weren’t so interested in the baseball out on the field as we were in the strategery down in the toilet. Remember a while back when I wrote about the urinal game? It seems like it was just last week (fuzzy vertical lines pixellating then unpixellating the screen to reveal the flashback:)
Consider a wall lined with 5 urinals. The subgame perfect equilibrium has the first gentleman take urinal 2 and the second caballero take urinal 5. These strategies are pre-emptive moves that induce subsequent monsieurs to opt for a stall instead out of privacy concerns. Thus urinals 1, 3, and 4 go unused.
So naturally we turn our attention to The Trough.
A continuous action space. Will the trough induce a more efficient outcome in equilibrium than the fixed array of separate urinals? This is what you come Cheap Talk to find out.
Let’s maintain the same basic parameters. Assume that the distance between the center of two adjacent urinals is d and let’s consider a trough of length 5d, i.e. the same length as a 5 side-by-side urinals (now with invincible pink mystery ice located invitingly at positions d/2 + kd for k = 1, 2, 3, 4.) The assumption in the original problem was that a gentleman pees if and only if there is nobody in a urinal adjacent to him. We need to parametrize that assumption for the continuos trough. It means that there is a constant r such that he refuses to pee in a spot in which someone is currently peeing less than a distance r from him. The assumption from before implies that d < r < 2d. Moreover the greater the distance to the nearest reliever the better.
The first thing to notice is that the equilibrium spacing from the original urinal game is no longer a subgame-perfect equilibrium. In our continuous trough model that spacing corresponds to gentlemen 1 and 2 locating themselves at positions d/2 and 7d/2 measured from the left boundary of the trough. Suppose r <= 3d/2. Then the third man can now utilize the convex action space and locate himself at position 2d where he will be a comfortable distance 3d/2>= r away from the other two. If instead r > 3d/2, then the third man is strictly deterred from intervening but this means that gentleman number 2 would increase his personal space by locating slightly farther to the right whilst still maintaining that deterrence.
So what does happen in equilibrium? I’ve got good news and bad news. The good news first. Suppose that r < 5d/4. Then in equilibrium 3 guys use the trough whereas only 2 of the arrayed urinals were used in the original equilibrium. In equilibrium the first guy parks at d/2 (to be consistent with the original setup we assume that he cannot squeeze himself any closer than that to the left edge of the trough without risking a splash on the shoes) the second guy at 9d/2 and the third guy right in the middle at 5d/2. They are a distance of 2d> r from one another, and there is no room for anybody else because anybody who came next would have to be standing at most a distance d< r from two of the incumbents. This is a subgame perfect equilibrium because the second guy knows that the third guy will pick the midpoint and so to keep a maximal distance he should move to the right edge. And foreseeing all of this the first guy moves to the left edge.
Note well that this is not a Pareto improvement. The increased usage is offset by reduced privacy.They are only 2d away from each other whereas the two urinal users were 3d away from each other.
Now the bad news when r >5d/4. In this case it is possible for the first two to keep the third out. For example suppose that 1 is at 5d/4 and 2 is at 15d/4. Then there is no place the third guy can stand and be more than 5d/4 away hence more than r from the others. In this case the equilibrium has the first two guys positioning themselves with a distance between them equal to exactly 2r, thus maximizing their privacy subject to the constraint that the third guy is deterred. (One such equilibrium is for the first two to be an equal distance from their respective edges, but there are other equilibria.)
The really bad news is that when r is not too large, the two guys even have less privacy than with the urinals. For example if r is just above 5d/4 then they are only 10d/4 away from each other which is less than the 3d distance from before. What’s happening is that the continuous trough gives more flexibility for the third guy to squeeze between so the first two must stand closer to one another to keep him away.
Instant honors thesis for any NU undergrad who can generalize the analysis to a trough of arbitrary length.
Bicycle “sprints.” This is worth 6 minutes of your time.
Thanks to Josh Knox for the link.
If you give them the chance, Northwestern PhD students will take a perfectly good game and turn it into a mad science experiment. First there was auction scrabble, now from the mind of Scott Ogawa we have the pari-mutuel NCAA bracket pool.
Here’s how it worked. Every game in the bracket was worth 1000 points. Those 1000 points will be shared among all of the participants who picked the winner of that game. These scores are added up for the entire bracket to determine the final standings. The winner is the person with the most points and he takes all the money wagered.
Intrigued, I entered the pool and submitted a bracket which picked every single underdog in every single game. Just to make a point.
Here’s the point. No matter how you score your NCAA pool you are going to create a game with the following property: assuming symmetric information and a large enough market, in equilibrium every possible bet will give exactly the same expected payoff. In other words an absurd bet like all underdogs will win is going to do just as well as any other, less absurd bet.
This is easy to see in simple example, like a horse race where pari-mutuel betting is most commonly used. Suppose A wins with twice the probability that B wins. This will attract bets on A until the number of bettors sharing in the purse when A wins is so large that B begins to be an attractive bet. In equilibrium there will be twice as much money in total bet on A as on B, equalizing the expected payoff from the two bets. One thing to keep in mind here is that the market must be large enough for these odds to equilibrate. (Without enough bettors the payoff on A may not be driven low enough to make B a viable bet.)
It’s a little more complicated though with a full 64 team tournament bracket. Because while each individual matchup has a pari-mutuel aspect, there is one key difference. If you want to have a horse in the second-round race, you need to pick a winner in the first round. So your incentive to pick a team in the first round must also take this into account. And indeed, the bet share in a first round game will not exactly offset the odds of winning as it would in a standalone horse race.
On top of that, you aren’t necessarily trying to maximize the expected number points. You just want to have the most points, and that’s a completely different incentive. Nevertheless the overall game has the equilibrium property mentioned above.
(Now keep in mind the assumptions of symmetric information and a large market. These are both likely to be violated in your office pool. But in Scott’s particular version of the game this only works in favor of betting longshots. First of all the people who enter basketball pools generally believe they have better information than they actually have so favorites are likely to be over-subscribed. Second, the scoring system heavily favors being the only one to pick the winner of a match which is possible in a small market. )
In fact, my bracket, 100% underdogs, Lehigh going all the way, finished just below the median in the pool. (Admittedly the market wasn’t nearly large enough for me to have been able to count on this. I benefited from an upset-laden first round.)
Proving that equilibrium of an NCAA bracket pool has this equilibrium property is a great prelim question.
In basketball the team benches are near the baskets on opposite sides of the half court line. The coaches roam their respective halves of the court shouting directions to their team.
As in other sports the teams switch sides at halftime but the benches stay where they were. That means that for half of the game the coaches are directing their defenses and for the other half they are directing their offenses.
If coaching helps then we should see more scoring in the half where the offenses are receiving direction.
This could easily be tested.
How can a guy who never misses a field goal miss an easy one at a crucial moment?
Still, a semiconsensus is developing among the most advanced scientists. In the typical fight-or-flight scenario, scary high-pressure moment X assaults the senses and is routed to the amygdala, aka the unconscious fear center. For well-trained athletes, that’s not a problem: A field goal kick, golf swing or free throw is for them an ingrained action stored in the striatum, the brain’s autopilot. The prefrontal cortex, our analytical thinker, doesn’t even need to show up. But under the gun, that super-smart part of the brain thinks it’s so great and tries to butt in. University of Maryland scientist Bradley Hatfield got expert dart throwers and marksmen to practice while wearing a cumbersome cap full of electrodes. Without an audience, their brains show very little chatter among regions. But in another study, when dart throwers were faced with a roomful of people, the pros’ neural activity began to resemble that of a novice, with more communication from the prefrontal cortex.
When I was in the 6th grade I won our school’s spelling bee going away. The next level was the district-wide spelling bee, televised on community access cable. My amygdala tried to insert an extra `u’ into the word tongue and I was out in the first round.
Let’s join Harvard Sports Analysis for the post-mortem:
But no one knew that his score would decide the game. Before he ran the ball in, the Giants had 0.94 win probability (per Advanced NFL Stats). After the play, the Giants’ win probability dropped to 0.85. Had he instead taken a Brian Westbrook or Maurice Jones-Drew-esque knee on the goal line, the Giants would have had a 0.96 win probability. Assuming the Patriots used their final time out, the Giants would have had 3rd and Goal from the 1-yard line with around 1:04 left to play. At this point, the Giants could either attempt to score a touchdown or take a knee. Assuming the touchdown try was unsuccessful or that Eli Manning kneeled, the Giants could have let the clock run all the way down to 0:25 before using the Giants’ final time out. With 4th and Goal from the 2 with 25 seconds left to play, the Giants would have a 0.92 win probability, 0.07 higher than after Bradshaw scored the touchdown of his life.
I am not sure about all this though. Shouldn’t Bradshaw have just stood there on the 1 (far away enough that he can’t be pushed in) and then cross over at the last second?
This is something I have wondered about for a long time.
When the muscle is stretched, so is the muscle spindle (see section Proprioceptors). The muscle spindle records the change in length (and how fast) and sends signals to the spine which convey this information. This triggers the stretch reflex (also called themyotatic reflex) which attempts to resist the change in muscle length by causing the stretched muscle to contract. The more sudden the change in muscle length, the stronger the muscle contractions will be (plyometric, or “jump”, training is based on this fact). This basic function of the muscle spindle helps to maintain muscle tone and to protect the body from injury.
One of the reasons for holding a stretch for a prolonged period of time is that as you hold the muscle in a stretched position, the muscle spindle habituates (becomes accustomed to the new length) and reduces its signaling. Gradually, you can train your stretch receptors to allow greater lengthening of the muscles.
Some sources suggest that with extensive training, the stretch reflex of certain muscles can be controlled so that there is little or no reflex contraction in response to a sudden stretch. While this type of control provides the opportunity for the greatest gains in flexibility, it also provides the greatest risk of injury if used improperly. Only consummate professional athletes and dancers at the top of their sport (or art) are believed to actually possess this level of muscular control.
This clarified a lot for me.
In many situations, such reinforcement learning is an essential strategy, allowing people to optimize behavior to fit a constantly changing situation. However, the Israeli scientists discovered that it was a terrible approach in basketball, as learning and performance are “anticorrelated.” In other words, players who have just made a three-point shot are much more likely to take another one, but much less likely to make it:
What is the effect of the change in behaviour on players’ performance? Intuitively, increasing the frequency of attempting a 3pt after made 3pts and decreasing it after missed 3pts makes sense if a made/missed 3pts predicted a higher/lower 3pt percentage on the next 3pt attempt. Surprizingly [sic], our data show that the opposite is true. The 3pt percentage immediately after a made 3pt was 6% lower than after a missed 3pt. Moreover, the difference between 3pt percentages following a streak of made 3pts and a streak of missed 3pts increased with the length of the streak. These results indicate that the outcomes of consecutive 3pts are anticorrelated.
This anticorrelation works in both directions. as players who missed a previous three-pointer were more likely to score on their next attempt. A brick was a blessing in disguise.
The underlying study, showing a “failure of reinforcement learning” is here.
Suppose you just hit a 3-pointer and now you are holding the ball on the next possession. You are an experienced player (they used NBA data), so you know if you are truly on a hot streak or if that last make was just a fluke. The defense doesn’t. What the defense does know is that you just made that last 3-pointer and therefore you are more likely to be on a hot streak and hence more likely than average to make the next 3-pointer if you take it. Likewise, if you had just missed the last one, you are less likely to be on a hot streak, but again only you would know for sure. Even when you are feeling it you might still miss a few.
That means that the defense guards against the three-pointer more when you just made one than when you didn’t. Now, back to you. You are only going to shoot the three pointer again if you are really feeling it. That’s correlated with the success of your last shot, but not perfectly. Thus, the data will show the autocorrelation in your 3-point shooting.
Furthermore, when the defense is defending the three-pointer you are less likely to make it, other things equal. Since the defense is correlated with your last shot, your likelihood of making the 3-pointer is also correlated with your last shot. But inversely this time: if you made the last shot the defense is more aggressive so conditional on truly being on a hot streak and therefore taking the next shot, you are less likely to make it.
(Let me make the comparison perfectly clear: you take the next shot if you know you are hot, but the defense defends it only if you made the last shot. So conditional on taking the next shot you are more likely to make it when the defense is not guarding against it, i.e. when you missed the last one.)
You shoot more often and miss more often conditional on a previous make. Your private information about your make probability coupled with the strategic behavior of the defense removes the paradox. It’s not possible to “arbitrage” away this wedge because whether or not you are “feeling it” is exogenous.
I write all the time about strategic behavior in athletic competitions. A racer who is behind can be expected to ease off and conserve on effort since effort is less likely to pay off at the margin. Hence so will the racer who is ahead, etc. There is evidence that professional golfers exhibit such strategic behavior, this is the Tiger Woods effect.
We may wonder whether other animals are as strategically sophisticated as we are. There have been experiments in which monkeys play simple games of strategy against one another, but since we are not even sure humans can figure those out, that doesn’t seem to be the best place to start looking.
I would like to compare how humans and other animals behave in a pure physical contest like a race. Suppose the animals are conditioned to believe that they will get a reward if and only if they win a race. Will they run at maximum speed throughout regardless of their position along the way? Of course “maximum speed” is hard to define, but a simple test is whether the animal’s speed at a given point in the race is independent of whether they are ahead or behind and by how much.
And if the animals learn that one of them is especially fast, do they ease off when racing against her? Do the animals exhibit a tiger Woods effect?
There are of course horse-racing data. That’s not ideal because the jockey is human. Still there’s something we can learn from horse racing. The jockey does not internalize 100% of the cost of the horse’s effort. Thus there should be less strategic behavior in horse racing than in races between humans or between jockey-less animals. Dog racing? Does that actually exist?
And what if a dog races against a human, what happens then?
I hadn’t watched American football in many years but around Christmas time I watched a little bit with my son who is getting old enough to pay attention to it. What struck me was how many pointless rules there are in football. I asked myself which of the many pointless rules is the most pointless. Some candidate
1.Holding
2. Illegal motion
These two are basically rules that establish a conventional way to play the game. If you dropped these rules you would still have a game that makes sense but aesthetically you could argue the game is less attractive. Players grabbing each others uniforms, offensive players running around before the snap. It’s a matter of taste but the deadweight loss is the subjective element of enforcement. Bottom line: artificial rules but not totally pointless.
3. Intentional grounding. This rule has a point but its a stupid point. The quarterback can’t throw the ball just anywhere, he has to throw it near somebody who could legally catch it. Or he can throw it out of bounds, it seems. But if he can’t do any of those he has to get mowed down by a charging defender.
But here’s the most pointless rule I could come up with:
4. Ineligible Receiver Downfield. There are only certain players on the offense who are designated as eligible to catch a pass. If anybody else catches a pass then it doesn’t count. Now that by itself is pretty artificial. Those players, and their counterparts on the defense are basically added to the game just to offset one another. You could remove them from both sides and it would be a wash. But even more pointless: an ineligible player is not allowed to advance down the field when a pass is thrown, even if it is thrown to somebody else. These rules essentially provide job security for giant, immobile humanoids whose only function is to stand in the way of somebody else. They take away the possibility of having a team of 10 perfectly substitutable athletes plus a quarterback. I can’t see how that would not be a more interesting game.
Is there any more pointless rule than that?
From the great blog Mind Hacks:
Because of this, the new study looked at volleyball where the players are separated by a net and play from different sides of the court. Additionally, players rotate position after every rally, meaning its more difficult to ‘clamp down’ on players from the opposing team if they seem to be doing well.
The research first established the belief in the ‘hot hand’ was common in volleyball players, coaches and fans, and then looked to see if scoring patterns support it – to see if scoring a point made a player more likely to score another.
It turns out that over half the players in Germany’s first-division volleyball league show the ‘hot hand’ effect – streaks of inspiration were common and points were not scored in an independent ‘coin toss’ manner.
Via Vinnie Bergl, here is a post which examines pitch sequences in Major League Baseball, looking for serial correlation in the pitch quality, i.e. fastball, changeup, curve, etc. The motivating puzzle is the typical baseball lore that. e.g. the changeup “sets up” the fastball. If that were true then the batter knows he is going to face a fastball next and this reduces the pitcher’s advantage. If the pitcher benefits from being unpredictable then there should be no serial correlation. The linked post gives a cursory look at the data which shows in fact the opposite of the conventional lore: changeups are followed by changeups.
There is a problem however with the simple analysis which groups together all pitch sequences from all pitchers. Not every pitcher throws a changeup. Conditional on the first pitch being a changeup, the probability increases that the next pitch will be a changeup simply because we learn from the first pitch that we are looking at a pitcher who has a changeup in his arsenal. To correct for this the analysis would have to be carried out at the individual level.
Should we expect serial independence? If the game was perfectly stationary, yes. But suppose that after throwing the first curveball the pitcher gets a better feel for the pitch and is temporarily better at throwing a curveball. If pitches were serially independent, then the batter would not update his beliefs about the next pitch, the curveball would have just as much surprise but now slightly more raw effectiveness. That would mean that the pitcher will certainly throw a curveball again.
That’s a contradiction so there cannot be serial independence. To find the new equilibrium we need to remember that as long as the pitcher is randomizing his pitch sequence, he must be indifferent among all pitches he throws with positive probability. So we need to offset the temporary advantage of a curveball this is achieved by the batter looking for a curveball. That can only happen in equilibrium if the pitcher is indeed more likely to throw a curveball.
Thus, positive serial correlation is to be expected. Now this ignores the batter’s temporary advantage in spotting the curveball. It may be that the surprise power of a breaking pitch is reduced when the batter gets an earlier read on the rotation. After seeing the first curveball he may know what to look for next and this may in fact make a subsequent curveball less effective, ceteris paribus. This model would then imply negative serial correlation: other pitches are temporarily more effective than the curveball so the batter should be expecting something else.
That would bring us back to the conventional account. But note that the route to “setting up the fastball” was not that it makes the fastball more effective in absolute terms, but that it makes it more effective in relative terms because the curveball has become temporarily less effective.
The latter hypothesis could be tested by the following comparison. Look at curveballs that end the at bat but not the inning. The next batter will not have had the advantage of seeing the curveball up close but the pitcher still has the advantage of having thrown one. We should see positive serial correlation here, that is the first pitch to the new batter should be more likely (than average) to be a curveball. If in the data we see negative correlation overall but positive correlation in this scenario then it is evidence of the batter-experience effect.
(Update: the Fangraphs blog has re-done the analysis at the individual level and it looks like the positive correlation survives. One might still worry about batter-specific fixed effects. Maybe certain batters are more vulnerable to the junk pitches and so the first junk pitch signals that we are looking at a confrontation with such a batter.)
This article in The New Yorker about Federer’s loss to Djokovic in the US Open Semi-final is absolutely worth a read. You don’t have to care about tennis as long as you have a personal stake in the deep question of what style of perfection really wins.
http://www.newyorker.com/online/blogs/sportingscene/2011/09/roger-federer-novak-djokovic.html
But I have a slightly different take.
All Fed-Heads knew right away when he won the second set to go up 2-0 that nevertheless was going to lose the match. The tragedy of that match, and of Roger Federer in general is not that perfection failed. He was never perfect or anything close to it. The irony is that, by comparison to Nadal and Djokovic, especially Nadal, Roger Federer is so much more like the rest of us mortals.
Nadal has pure animal fighting spirit branded onto his DNA. Yes, his tennis is wrong, but that doesn’t matter because he is the one who has the aura of invincibility, not Federer. You can count on Roger to make impeccable shots. To play like an artist. But you can count on Nadal to win.
Federer is not like a superhero who just effortlessly deploys his superpower and watches the results roll in. When you watch him long enough you start to see how tightly wound he is at every moment, mustering every ounce of concentration to keep himself in that groove. If he is a master of anything he is a master of trying.
What you learn from watching his matches the last year is just how unstable that groove is. And what makes his decline so depressing is how it reminds us that if you have to try you are not a master. He carried the banner for all of us who have nothing going for us except the will to try, and even he The Master Tryer, the man who tried so hard that he was Perfect, can’t beat those guys whose strokes are hacker strokes next to his, but who were born winners.
And that is why this particular match was really his most tragic. Match point against Djokovic. After tanking sets 3 and 4 and then pulling himself together to go up a break and serve for the match in the fifth set, we still knew he was going to lose. It was just a matter of how.
Djokovic is not Nadal. He does not win by sheer will. A lot of trying went in to his streak this year. And to Federer fans, Djokovic is something of an interloper. You look at his game and there is no real reason he should be pushing Roger out of the top 2. He is super solid. But we want our iconic battle between Mr. Made-Perfect against Mr. Passion. Djokovic doesn’t belong.
But when Federer had Djokovic match point down, Djokovic did something that made a total mockery of everything about Federer’s game. He took a blind swing on a service return and hit it for a stinging winner. He became Nadal for a single shot. You are not supposed to be able to become Nadal. That is not something you can try to do. And indeed there was no trying involved whatsoever. He just did it.
Federer could never, ever do that.
If you think about pain as an incentive mechanism to stop you from hurting yourself there are some properties that would follow from that.
When I was pierced by a stingray, the pain was outrageous. The puncture went deep into my foot and that of course hurts but the real pain came from the venom-laden sheath that is left behind when the barb is removed. Funny thing about the venom is that it is protein based and it can be neutralized by denaturing the protein, essentially changing its structure by “cooking” it as you would a raw egg.
How do you cook the venom when it is inside your foot? You don’t pee on it unless you are making a joke on a sitcom (and that’s a jellyfish anyway.) What you do is plunge your foot is scalding hot water raising the internal temperature enough to denature the venom inside. Here’s what happens when you do that. Immediately you feel dramatic relief from the pain. But not long after that you begin to notice that your foot is submerged in scalding hot water and that is bloody painful.
So you take it out. Then you feel the nerve-numbing pain from the venom return to the fore. Back in. Relief, burning hot water, back out. Etc. Over and over again until you have cooked all the venom and you are done. In all about 4 hours of soaking.
A good incentive scheme is reference-dependent. There’s no absolute zero. Zero is whatever baseline you are currently at and rewards/penalties incentivize improvement relative to the baseline. When the venom was the most dangerous thing, the scalding hot water was painless. Once the danger from the venom was reduced, the hot water became the focus of pain. And back and forth.
Second Observation. After three weeks of surfing (minus a couple of days robbed by my stingray friend) I came away with a sore shoulder. Rotator cuff injuries are common among surfers, especially over the hill surfers who don’t exercise enough the other 11 months of the year. The interesting thing about a rotator cuff injury is that the pain is felt in the upper shoulder, not at the site of the injury which is more in the area of the shoulder blade. It’s referred pain.
In a moral hazard framework the principal decides which signals to use to trigger rewards and penalties. Direct signals of success or failure are not necessarily the optimal ones to use because success and failure can happen by accident too. The optimal signal is the one that is most informative that the agent took the appropriate effort. Referred pain must be based on a similar principle. Rotator cuff injuries occur because of poor alignment in the shoulder resulting in an inefficient mix of muscles doing the work. Even though its the rotator cuff that is injured, the use of the upper shoulder is a strong signal that you are going to worsen the injury. It may be optimal to penalize that directly rather than associate the pain with the underlying injury.
(Drawing: Scale Up Machine Fail, from www.f1me.net.)
Usain Bolt was disqualified in the final of the 100 meters at the World Championships due to a false start. Under current rules, in place since January 2010, a single false start results in disqualification. By contrast, prior to 2003 each racer who jumped the gun would be given a warning and then disqualified after a second false start. In 2003 the rules were changed so that the entire field would receive a warning after a false start by any racer and all subsequent false starts would lead to disqualification.
Let’s start with the premise that an indispensible requirement of sprint competition is that all racers must start simultaneously. That is, a sprint is not a time trial but a head-to-head competition in which each competitor can assess his standing at any instant by comparing his and his competitors’ distance to a fixed finished line.
Then there must be penalty for a false start. The question is how to design that penalty. Our presumed edict rules out marginally penalizing the pre-empter by adding to his time, so there’s not much else to consider other than disqualification. An implicit presumption in the pre-2010 rules was that accidental false starts are inevitable and there is a trade-off between the incentive effects of disqualification and the social loss of disqualifying a racer who made an error despite competing in good faith.
(Indeed this trade-off is especially acute in high-level competitions where the definition of a false start is any racer who leaves less than 0.10 seconds after the report of the gun. It is assumed to be impossible to react that fast. But now we have a continuous variable to play with. How much more impossible is it to react within .10 seconds than to react within .11 seconds? When you admit that there is a probability p>0, increasing in the threshold, that a racer is gifted enough to reach within that threshold, the optimal incentive mechanisn picks the threshold that balances type I and type II errors. The maximum penalty is exacted when the threshold is violated.)
Any system involving warnings invites racers to try and anticipate the gun, increasing the number of false starts. But the pre- and post-2003 rules play out differently when you think strategically. Think of the costs and benefits of trying to get a slightly faster start. The warning means that the costs of a potential false start are reduced. Instead of being disqualified you are given a second chance but are placed in the dangerous position of being disqualified if you false start again. In that sense, your private incentives to time the gun are identical whether the warning applies only to you or to the entire field. But the difference lies in your treatment relative to the rest of the field. In the post-2003 system that penalty will be applied to all racers so your false start does not place you at a disadvantage.
Thus, both systems encourage quick starts but the post 2003 system encouraged them even more. Indeed there is an equilibrium in which false starts occur with probability close to 1, and after that all racers are warned. (Everyone expects everyone else to be going early, so there’s little loss from going early yourself. You’ll be subject to the warning either way.) After that ceremonial false start the race becomes identical to the current, post 2010, rule in which a single false start leads to disqualification. My reading is that equilibrium did indeed obtain and this was the reason for the rule change. You could argue that the pre 2003 system was even worse because it led to a random number of false starts and so racers had to train for two types of competition: one in which quick starts were a relevant strategy and one in which they were not.
Is there any better system? Here’s a suggestion. Go back to the 2003-2009 system with a single warning for the entire field. The problem with that system was that the penalty for being the first to false start was so low that when you expected everyone else to be timing the gun your best response was to time the gun as well. So my proposal is to modify that system slightly to mitigate this problem. Now, if racer B is the first to false start then in the restart if there is a second false start by, say racer C, then racer C and racer B are disqualified. (In subsequent restarts you can either clear the warning and start from scratch or keep the warning in place for all racers.)
Here’s a second suggestion. The racers start by pushing off the blocks. Engineer the blocks so that they slide freely along their tracks and only become fixed in place at the precise moment that the gun is fired.
(For the vapor mill, here are empirical predictions about the effect of previous rule-regimes on race outcomes:
- Comparing pre-2003, under the 2003-2009 you should see more races with at least one false start but far fewer total false starts per race. The current rules should have the least false starts.
- Controlling for trend (people get faster over time) if you consider races where there was no false start, race times should be faster 2003-2009 than pre-2003. That ranking reverses when you consider races in which there was at least one false start. Controlling for Usain Bolt, times should be unambiguously slower under current rules.)
The weather in Chicago sucks but at least there are real seasons (there’s only one in SoCal where I am from.) Here’s a thought about seasons.
Everything gets old after a while. No matter how much you love it at first, after a while you are bored. So you stop doing it. But then after time passes and you haven’t done it for a while it gets some novelty back and you are willing to do it again. So you tend to go through on-off phases with your hobbies and activities.
But some activities can only be fun if enough other people are doing it too. Say going to the park for a pickup soccer game. There’s not going to be a game if nobody is there.
We could start with everyone doing it and that’s fun, but like everything else it starts to get old for some people and they cut back and before long its not much of a pickup game.
Now, unlike your solo hobbies, when the novelty comes back you go out to the field but nobody is there. This happens at random times for each person until we reach a state where everybody is keen for a regular pickup game again but there’s no game. What’s needed is a coordination device to get everyone out on the field again.
Seasons are a coordination device. At the beginning of summer everyone gets out and does that thing that they have been waiting since last year to do. Sure, by the end of the season it gets old but that’s ok summer is over. The beginning of next summer is the coordination device that gets us all out doing it again.
On Tuesday, in the sixth round of the MLB Draft, the San Diego Padres selectedoutfielder Kyle Gaedele (who the Tampa Bay Rays had previously drafted in the 32nd round of the 2008 draft). Gaedele plays center field and shows good signs of hitting for power, but what most writers, sports fans, and guys named Bradley talk about is Gaedele’s great uncle.
Casual fans probably do not know about Kyle’s great uncle, Eddie Gaedel (who removed the e off his last name for show-business purposes). We nerds can forgive the casual fan for forgetting a player who outdid, in his career, only the great Otto Neu. Gaedel took a single at-bat, walked to first, and then left for a pinch runner.
What makes Eddie Gaedel a unique and important part of baseball history, however, is not his statistics, per se, but his stature. Gaedel stood 3’7″ tall, almost half the height of his great nephew. Gaedel was the first and last little person to play in Major League Baseball, and the time has come for that to change.
In baseball, the strike zone (effectively the target that a pitcher must aim for) is defined relative to the size of the hitter. A very small player has a very small strike zone, so small that many pitchers will have a hard time throwing strikes. Insert such a batter at a key moment, he walks to first base and then you replace him with a fast runner. Why doesn’t every team have such a player on their roster?
Cap Clutch: Vinnie Bergl.
Via Marginal Revolution, an essay exploring the psychology of watching a sporting event after the fact on your DVR. Is it less enjoyable than watching the same game live when it happens? I love this question and I love the answers he gives. Strangely though, he divides his reasons into the “rational” and the “irrational” and with only one exception I would give the opposite classification. Here are his rational ones:
- Removing commercials reduces drama. I suppose he calls this rational because he thinks that its true and perfectly sensible. The unavoidable delay before action resumes builds suspense. But even though I agree with that, I call this an irrational reason because of course I can always watch the commercials or just sit around for 2 minutes if I’d rather not see yet another Jacob’s Creek wine commercial. If in fact I don’t do that, then that’s irrational.
- If you know it has already happened then it is less interesting. Again, this may be true for many people, but to make it into the rational category it has to be squared with the fact that we watch movies, TV dramas, even reality TV shows whose outcomes we know are already determined.
- Recording gives me too much control. Same as #1.
Now for the irrational ones:
- I don’t get to believe that my personal involvement will affect the game. This one I agree with. Many people are under this illusion and it would be hard to call it rational for someone to think they are any less in control when the event is already over.
- If this were a really exciting game I would have found out about it independently by now no matter how hard I tried to avoid it. I would call this the one truly rational reason and I think its a big problem for most major sports. If something really exciting happened that information is going to find you one way or another. So if you are sitting down to watch a taped event and the information didn’t find you, then you know it can only be so good. Even worse, if the game reaches a state where it would take a dramatic comeback to change the outcome, you know that comeback isn’t going to happen.
I would add two of my own, one rational and one irrational. First, you don’t watch a DVR’d sporting event with friends. The whole point of recording it is to pick the optimal time to watch it and that’s not going to be your friend’s optimal time. Plus he probably already saw it, plus who is going to control the fast-forward? Watching with friends adds a dimension to just about anything, especially sports so DVR’d events are going to be less interesting just for the lack of social dimension having nothing to do with the tape delay.
Second, there is something very strange about hoping for something to happen when in fact it has either already happened or already not. Now, this is irrelevant for people who easily suspend disbelief watching movies. Those people can yell at the fictitious characters on the screen and feel elation and despair when their pre-destined fate is played out. But people who can’t find the same suspense in fiction look to sports for the source of it. For those people too many existential questions get in the way of enjoying a tape-delayed broadcast.
A reader, Kanishka Kacker, writes to me about Cricket:
Now, very often, there are certain decisions to be made regarding whether a given batter was out or not, where it is very hard for the umpire to decide. In situations like this, some players are known to walk off the field if they know they are “out” without waiting for the umpire’s decision. Other players don’t, waiting to see the umpire’s decision.
Here is a reason given by one former Australian batsman, Michael Slater, as to why “walking” is irrational:
(this is from Mukul Kesavan’s excellent book “Men in White”)
“The pragmatic argument against walking was concisely stated by former Australian batsman Michael Slater. If you walk every time you’re out and are also given out a few times when you’re not (as is likely to happen for any career of a respectable length), things don’t even out. So, in a competitive team game, walking is, at the very least, irrational behavior. Secondarily, there is a strong likelihood that your opponents don’t walk, so every time you do, you put yourself or your team at risk.”
What do you think?
Let me begin by saying that the only thing I know about Cricket is that “Ricky Ponting” was either the right or the wrong answer to the final question in Slumdog Millionaire. Nevertheless, I will venture some answers because there are general principles at work here.
- First of all, it would be wrong to completely discount plain old honor. Kids have sportsmanship drilled into their heads from the first time they start playing, and anyone good enough to play professionally started at a time when he or she was young enough to believe that honor means something. That can be a hard doctrine to shake. Plus, as players get older and compete in at more selective levels, some of that selection is on the basis of sportsmanship. So there is some marginal selection for honorable players to make it to the highest levels.
- There is a strategic aspect to honor. It induces reciprocity in your opponent through the threat of shame. If you are honorable and walk, then when it comes time for your opponent to do the same, he has added pressure to follow suit or else appear less honorable than you. Even if he has no intrinsic honor, he may want to avoid that shame in the eyes of his fans.
- But to get to the raw strategic aspects, reputation can play a role. If a player is known to walk whenever he is out then by not walking he signals that he is not out. In those moments of indecision by the umpire, this can tip the balance and get him to make a favorable call. You might think that umpires would not be swayed by such a tactic but note that if the player has a solid reputation for walking then it is in the umpire’s interest to use this information.
- And anyway remember that the umpire doesn’t have the luxury to deliberate. When he’s on the fence, any little nudge can tilt him to a decision.
- Most importantly, a player’s reputation will have an effect on the crowd and their reactions influence umpires. If the fans know that he walks when he’s out and this time he didn’t walk they will let the umpire have it if he calls him out.
- There is a related tactic in baseball which is wh
ere the manager kicks dirt onto the umpire’s shoes to show his displeasure with the call. It is known that this will never influence the current decision but it is believed to have the effect of “getting into the umpire’s head” potentially influencing later decisions. - Finally, it is important to keep in mind that a player walks not because he knows he is out but because he is reasonably certain that the umpire is going to decide that he is out whether or not he walks. The player may be certain that he is not out but only because he is in a privileged position on the field where he can determine that. If the umpire didn’t have the same view, it would be pointless to try and persuade. Instead he should walk and invest in his reputation for the next time when the umpire is truly on the fence.
How does the additional length of a 5 set match help the stronger player? Commenters to my previous post point out the direct way: it lowers the chance of a fluke in which the weaker player wins with a streak of luck. But there’s another way and it can in principle be identified in data.
To illustrate the idea, take an extreme example. Suppose that the stronger player, in addition to having a greater baseline probability of winning each set, also has the ability to raise his game to a higher level. Suppose that he can do this once in the match and (here’s the extreme part) it guarantees that he will win that set. Finally, suppose that the additional effort is costly so other things equal he would like to avoid it. When will he use his freebie?
Somewhat surprisingly, he will always wait until the last set to use it. For example, in a three set match, suppose he loses the first set. He can spend his freebie in the second set but then he has to win the third set. If he waits until the third set, his odds of winning the match are exactly the same. Either way he needs to win one set at the baseline odds.
The advantage of waiting until the third set is that this allows him to avoid spending the effort in a losing cause. If he uses his freebie in the second set, he will have wasted the effort if he loses the third set. Since the odds of winning are independent of when he spends his effort, it is unambiguously better to wait as long as possible.
This strategy has the following implications which would show up in data.
- In a five set match, the score after three sets will not be the same (statistically) as the score in a three set match.
- In particular, in a five-set match the stronger player has a lower chance of winning a third set when the match is tied 1-1 than he would in a three set match.
- The odds that a higher seeded player wins a fifth set is higher than the odds that he wins, say, the second set. (This may be hard to identify because, conditional on the match going to 5 sets, it may reveal that the stronger player is not having a good day.)
- If the baseline probability is close to 50-50, then a 5 set match can actually lower the probability that the stronger player wins, compared to a 3 set match.
This “freebie” example is extreme but the general theme would always be in effect if stronger players have a greater ability to raise their level of play. That ability is an option which can be more flexibly exercised in a longer match.
- One implication of a theory I have written about before is that a best of 5 set match confers a greater advantage on the stronger player than a best of 3 set match. (The basic idea is that the 5 sets gives the stronger player more flexibility in timing his bursts of effort.) Here are some data that would shed light: compare men’s versus women’s Grand Slam matches in terms of the probability that a higher-seeded player will win. Even better: divide the data into non-Grand Slam and Grand Slam matches. Ask how much more likely a higher-seeded player wins a Grand Slam match versus a non-Grand Slam match. Do this for both women and men. Then do the difference-in-differences. This gives you a nice control because women play 3 sets whether its a Grand Slam or not. Men play 5 sets in Grand Slams and 3 sets in almost all non-Grand-Slam events.
- Four Grand Slams, only three surfaces. It’s time the US Open switched to ice. (with skates.)
I once wrote about height and speed in tennis arguing that negative correlation appears at the highest level simply because they are substitutes and the athletes are selected to be the very best. At the blog MickeyMouseModels.blogspot.com, there is a post which shows very nicely the effect using simulated data. Quoting:
Suppose that, in the general population, the distribution of height and speed looks roughly like this:
Where did I get this data? It’s entirely hypothetical. I made it up! That said, I did try to keep it semi-realistic: the heights are generated as H = 4 + U1 + U2 + U3 feet, where the U are independently uniform on (0, 1); the result is a bell curve on (4, 7) feet, which I prefer to the (-Inf, +Inf) of an actual normal distribution. (I’ve created something similar to the N=3 frame in this animation.)
The next step is to give individuals a maximum footspeed S = 10 + U4 + U5 + U6 mph, with the U independently uniform on (0, 5). By construction, speed is independent from height, and falls more or less in a bell curve from 10 to 25 mph. Fun anecdote: my population is too slow to include Usain Bolt, whose top footspeed is close to 28 mph.
Back to tennis. Let’s imagine that tennis ability increases with both height and speed — and, moreover, that those two attributes are substitutable: if you’re short (and have a weak serve), you can make up for it by being fast. With that in mind, let’s revisit the scatterplot:
There it is: height and speed are independent in the general population, but very much dependent — and negatively correlated — among tennis players. The plot really drives the point home: top athletes will be either very tall, very fast, or nearly both; and excluding everyone else creates a downward slope.
Kobe Bryant was recently fined $100,000 for making a homophobic comment to a referee. Ryan O’Hanlon writing for The Good Men Project blog puts it into perspective:
- It’s half as bad as conducting improper pre-draft workouts.
- It’s twice as bad as saying you want to leave the NBA and go home.
- It’s just as bad as talking about the collective bargaining agreement.
- It’s twice as bad as saying one of your players used to smoke too much weed.
- It’s just as bad as writing a letter in Comic Sans about a former player.
- It’s just as bad as saying you want to sign the best player in the NBA.
- It’s four times as bad as throwing a towel to distract a guy when he’s shooting free throws.
- It’s four times as bad as kicking a water bottle.
- It’s 10 times as bad as standing in front of your bench for an extended period of time.
- It’s 10 times as bad as pretending to be shot by a guy who once brought a gun into a locker room.
- It’s 13.33 times as bad as tweeting during a game.
- It’s five times as bad as throwing a ball into the stands.
- It’s four times as bad as throwing a towel into the stands.
- It’s twice as bad as lying about smelling like weed and having women in a hotel room during the rookie orientation program.
- It’s one-fifth as bad as snowboarding.
That’s based on a comparison of the fines that the various misdeeds earned. The “n times as bad” is the natural interpretation of the fines since we are used to thinking of penalties as being chosen to fit the crime. But NBA justice needn’t conform to our usual intuitions because this is an employer/employee relationship governed by actual contract, not just social contract. We could try to think of these fines as part of the solution to a moral hazard problem. Independent of how “bad” the behaviors are, there are some that the NBA wants to discourage and fines are chosen in order to get the incentives right.
But that’s a problematic interpretation too. From the moral hazard perspective the optimal fine for many of these would be infinite. Any finite fine is essentially a license to behave badly as long as the player has a strong enough desire to do so. Strong enough to outweigh the cost of the fine. You can’t throw a towel to distract a guy when he’s shooting free throws unless its so important to you that you are willing to pay $250,000 for the privilege.
You can rescue moral hazard as an explanation in some cases because if there is imperfect monitoring then the optimal fine will have to be finite. Because with imperfect monitoring the fine cannot be a perfect deterrent. For example it may not possible to detect with certainty that you were lying about smelling like weed and having women in a hotel room during the rookie orientation program. If so then the false positives will have to be penalized. And when the fine will be paid with positive probability even with players on their best behavior you are now trading off incentives vs. risk exposure.
But the imperfect monitoring story can’t explain why Comic Sans doesn’t get an infinite fine, purifying the game of that transgression once and for all. Or tweeting, or snowboarding or most of the others as well.
It could be that the NBA knows that egregious fines can be contested in court or trigger some other labor dispute. This would effectively put a cap on fines at just the level where it is not worth the player’s time and effort to dispute it. But that doesn’t explain why the fines are not all pegged at that cap. It could be that the likelihood that a fine of a given magnitude survives such a challenge depends on the public perception of the crime . That could explain some of the differences but not many. Why is the fine for saying you want to leave the NBA larger than the fine for throwing a ball into the stands?
Once we’ve dispensed with those theories it just might be that the NBA recognizes that players simply want to behave badly sometimes. Without that outlet something else is going to give. Poor performance perhaps or just an eventual Dennis Rodman. The NBA understands that a fine is a price. And with the players having so many ways of acting out to choose from, the NBA can use relative prices to steer them to the efficient frontier. Instead of kicking a water bottle, why not get your frustrations out by sending 3 1/2 tweets during the game? Instead of saying that one of your players smokes too much weed, go ahead and indulge your urge to stand out in front of the bench for an extended period of time. You can do it for 5 times as long as the last guy or even stand 5 times farther out.
Not surprisingly, all of these choices start to look like real bargains compared to snowboarding and impoper pre-draft workouts.
Nonsense?
For Shmanske, it’s all about defining what counts as 100% effort. Let’s say “100%” is the maximum amount of effort that can be consistently sustained. With this benchmark, it’s obviously possible to give less than 100%. But it’s also possible to give more. All you have to do is put forth an effort that can only be sustained inconsistently, for short periods of time. In other words, you’re overclocking.
And in fact, based on the numbers, NBA players pull greater-than-100-percent off relatively frequently, putting forth more effort in short bursts than they can keep up over a longer period. And giving greater than 100% can reduce your ability to subsequently and consistently give 100%. You overdraw your account, and don’t have anything left.
Here is the underlying paper. <Painfully repressing the theorist’s impulse to redefine the domain to paths of effort rather than flow efforts, thus restoring the spiritually correct meaning of 100%>
Cap curl: Tim Carmody guest blogging at kottke.org.
In tennis, a server should win a larger percentage of second-serve points compared to first-serve points; that much we know. Partly that’s because a server optimally serves more faults (serves that land out) on first serve than second serve. But what if we condition on the event that the first serve goes in? Here’s a flawed logic that takes a bit of thinking to see through:
Even conditional on a first serve going in, the probability that the server wins the point must be no larger than the total win probability for second serves. Because suppose it were larger. Then the server wins with a higher probability when his first serve goes in. So he should ease off just a bit on his first serve so that a larger percentage lands in, raising the total probability that he wins the point. Even though the slightly slower first serve wins with a slightly reduced probability (conditional on going in) he still has a net gain as long as he eases off just slightly so that it is still larger than the second serve percentage. Indeed the lower probability of a fault could even raise the total probability that he wins on the first serve.
Seth Godin writes:
When two sides are negotiating over something that spoils forever if it doesn’t get shipped, there’s a straightforward way to increase the value of a settlement. Think of it as the net present value of a stream of football…
Any Sunday the NFL doesn’t play, the money is gone forever. You can’t make up for it later by selling more football–that money is gone. The owners don’t get it, the players don’t get it, the networks don’t get it, no one gets it.
The solution: While the lockout/strike/dispute is going on, keep playing. And put all the profit/pay in an escrow account. Week after week, the billions and billions of dollars pile up. The owners see it, the players see it, no one gets it until there’s a deal.
There are two questions you have to ask if you are going to evaluate this idea. First, what would happen if you change the rules in this way? Second, would the parties actually agree to it?
Bargaining theory is one of the most unsettled areas of game theory, but there is one very general and very robust principle. What drives the parties to agreement is the threat of burning surplus. Any time a settlement proposal on the table it comes with the following interpretation: “if you don’t agree to this now you better expect to be able to negotiate for a significantly larger share on the next round because between now and then a big chunk of the pie is going to disappear.” Moreover it is only through the willingness to let the pie shrink that either party can prove that he is prepared to make big sacrifices in order to get that larger share.
So while the escrow idea ensures that there will be plenty of surplus once they reach agreement, it has the paradoxical effect of making agreement even more difficult to reach. In the extreme it makes the timing of the agreement completely irrelevant. What’s the point of even negotiating today when we can just wait until tomorrow?
But of course who cares when and even whether they eventually agree? All we really want is to see football right? And even if they never agree how to split the mounting surplus, this protocol keeps the players on the field. True, but that’s why we have to ask whether the parties would actually accept this bargaining game. After all if we just wanted to force the players to play we wouldn’t have to get all cute with the rules of negotiation, we could just have an act of Congress.
And now we see why proposals like this can never really help because they just push the bargaining problem one step earlier, essentially just changing the terms of the negotiation without affecting the underlying incentives. As of today each party is looking ahead expecting some eventual payoff and some total surplus wasted. Godin’s rules of negotiation would mean that no surplus is wasted so that each party could expect an even higher eventual payoff. But if it were possible to get the two parties to agree to that then for exactly the same reason under the old-fashioned bargaining process there would be a proposal for immediate agreement with the same division of the spoils on the table today and inked tomorrow.
Still it is interesting from a theoretical point of view. It would make for a great game theory problem set to consider how different rules for dividing the accumulated profits would change the bargaining strategies. The mantra would be “Ricardian Equivalence.”
Jonah Lehrer writes about how bad NFL teams are at drafting talented players, particularly at the quarterback position.
Despite this advantage, however, sports teams are impressively amateurish when it comes to the science of human capital. Time and time again, they place huge bets on the wrong players. What makes these mistakes even more surprising is that teams have a big incentive to pick the right players, since a good QB (or pitcher or point guard) is often the difference between a middling team and a contender. (Not to mention, the player contracts are worth tens of millions of dollars.) In the ESPN article, I focus on quarterbacks, since the position is a perfect example of how teams make player selection errors when they focus on the wrong metrics of performance. And the reason teams do that is because they misunderstand the human mind.
He talks about a test that is given to college quarterbacks eligible for the NFL draft to test their ability to make good decisions on the field. Evidently this test is considered important by NFL scouts and indeed scores on this test are good predictors of whether and when a QB will be selected in the draft.
However,
Consider a recent study by economists David Berri and Rob Simmons. While they found that Wonderlic scores play a large role in determining when QBs are selected in the draft — the only equally important variables are height and the 40-yard dash — the metric proved all but useless in predicting performance. The only correlation the researchers could find suggested that higher Wonderlic scores actually led to slightly worse QB performance, at least during rookie years. In other words, intelligence (or, rather, measured intelligence), which has long been viewed as a prerequisite for playing QB, would seem to be a disadvantage for some guys. Although it’s true that signal-callers must grapple with staggering amounts of complexity, they don’t make sense of questions on an intelligence test the same way they make sense of the football field. The Wonderlic measures a specific kind of thought process, but the best QBs can’t think like that in the pocket. There isn’t time.
I have not read the Berri-Simmons paper but inferences like this raise alarm bells. For comparison, consider the following observation. Among NBA basketball players, height is a poor predictor of whether a player will be an All-Star. Therefore, height does not matter for success in basketball.
The problem is that, both in the case of IQ tests for QBs and height for NBA players, we are measuring performance conditional on being good enough to compete with the very best. We don’t have the data to compare the QBs who are drafted to the QBs who are not and how their IQ factors into the difference in performance.
The observable characteristic (IQ scores, height) is just one of many important characteristics, some of which are not quantifiable in data. Given that the player is selected into the elite, if his observable score is low we can infer that his unobservable scores must be very high to compensate. But if we omit those intangibles in the analysis, it will look like people with low scores are about as good as people with high scores and we would mistakenly conclude that they don’t matter.
