Friday, January 22, 2010

What tennis players maximize

Nikolay Davydenko recently remarked that he cares less about tennis than Nadal and Federer:
"I have a good life. It's not only about tennis for me. Maybe I am not a champion like Nadal or Federer [demonstrating a pose to indicate single-mindedness]. For them, it's only about winning a trophy, winning a grand slam, maybe dreaming every day about it. I am not that guy, I am different. I don't cry like Federer at winning a grand slam. He holds it in all two weeks and then explodes. I am different."
This type reasoning is common among those who have ever put forth an effort to compete against others on some quantifiable scale and have fallen short of the number one spot (even though from our perspective it seems ridiculous that Davydenko would need to console himself for being only the fourth best tennis player on the planet). I suspect nearly everyone (including myself, almost daily) has at some point said to himself or herself "I must admit that this person [is more popular/is more wealthy/gets better grades/is a better worker/is more intelligent/is more attractive/weighs less/weighs more/has nicer things/has a cleaner house/is a better driver/plays the banjo better/is more articulate/gives more to charity/is more righteous/is more fun/has a deeper knowledge of alchemy] than me, but that’s ok because I care about things other than this one activity and this superior person lives an incomplete life for spending so much energy on this one thing."
When we say this, we are implying that the only dimension that matters is how good people are at maximizing their total well-being. Once we have done this, it is simple to assume that our definition of well-being is what everyone should be trying to maximize, and since other people appear to be pursuing something other than their own well-being (as defined by us), their lives are shallow and incomplete, despite how happy they may appear to be. As soon as we feel we are losing, we change the game into one in which we actually are the winner.
The question of what people are trying to maximize and how they go about doing so is key to field of economics at the moment. Traditional economics is driven by the assumption that people and firms rational maximize "utility," which can really be defined to be whatever you want it to be. Behavioral economics questions the assumption that people rationally maximize anything.
The recent financial crises struck a blow to economics because most economists were surprised and confused by it. On a large scale and for an extended period of time, banks appear not to have been rationally maximizing the present value of their expected profit stream. There was clearly a housing price "bubble," in which prices of houses were out of line with what would be expected in an efficient market for a long period of time. That economists have not yet developed a good model for bubbles is a serious problem if they hope to understand and explain the economy.
The reaction of traditional economists to examples of people that appear to be acting irrationally is that people are indeed rational maximizers, but sometimes people are maximizing something strange (this sentiment, ironically, seems a bit like they are trying to change the game into something in which they are still the winner). Behavioral economists suggest that people irrationally attempt to maximize their well-being.
I used to think that this distinction was unimportant. Whether people are rationally maximizing something totally crazy or irrationally maximizing something sensible seemed like two sides of the same coin to me. When I was watching the Roddick match the other night, and thinking about his strange serving habits, it occurred to me that this distinction is absolutely huge.
If you missed my previous post on the topic (The Behavioral Economics of the 2nd Serve), my basic thesis was this: When Roddick steps up to the line for a 1st serve, he wins the point 58.2% (71%*82%) of the time. If he misses his first serve, why would he bother hitting a conservative second serve if he has less than a 52% chance of winning the point with it? If he's trying to win points, he should just be hitting bombs for both his first and second serves.
A traditional economist would say that Roddick, like Davydenko, cares about more than maximizing the probability of winning the match. He is willing to lose a few matches if he loses with dignity and avoids criticism for foolishly being so aggressive and hitting so many double faults.
A behavioral economist might say that Roddick is attempting to maximize his chances of winning the match, but is for some reason irrationally avoiding double faults.
The traditional economist, therefore, is optimistic about Andy’s ability to pursue his own happiness. There is no problem if Roddick has decided he wants to be a mediocre top-ten tennis player who plays with style and is doing everything he can to achieve that.
The behavioral economist would say that someone needs to regulate Andy’s serving and prevent him front sabotaging his goal of winning tennis matches.
Even in this relatively simple example, it is a very deep and complicated problem to examine a tennis player’s motivations for playing a certain way.

Monday, August 17, 2009

Coaching by Committee and the Wisdom of Crowds

There is a trend in professional tennis toward an entourage of coaches rather than a single coach. This approach is epitomized by Andy Murray, who has become far more successful after dumping the well-respected Brad Gilbert in 2007 for a team of coaches. I believe the concept of having a single "coach" doesn't actually make much sense in tennis, but has just been passed on from other sports.

The position of coach for a professional tennis player is unusual. Unlike team sports, which require centralized authority to govern the team, tennis coaches don't "call the play" or make any decisions for the player during a match. In fact, "coaching" - defined in the ATP rulebook as "communications of any kind, audible or visible, between a player and a coach" - is prohibited during ATP play. (In reality, general words of encouragement from a coach are tolerated as long the coach does not attempt to impart any technical or tactical wisdom during the match.)

I believe the work of tennis coach primarily includes the following services:

1. Source of confidence and motivation
2. Strategic advisor - both generally and against particular opponents
3. Diagnosing and repairing technical flaws
4. Physical trainer
5. Hitting partner

These tasks are mildly related, but each can easily be outsourced to a specialist. It would be surprising if it were optimal for a single coach to handle all of these tasks.

Confidence and motivation is probably the most important and might best suited to a family member, which might explain why so many successful players have a parent, uncle, girlfriend, brother, etc. as a coach. It would also be confidence-inspiring to have a group of experts advising you.

I have often wondered how valuable a coach actually is as a strategic advisor. On the surface, it would appear to be the primary purpose of a coach and hugely important to observe how the player is actually winning and losing matches and describe the big picture to the player; Andre Agassi claims that Brad Gilbert had a significant positive influence on his game because Brad explained what made him feel uncomfortable when he played Agassi and helped Agassi feel what his opponent feels. (Indeed, a tragic aspect of tennis is that you will never know what it feels like to hit against yourself and experience how heavy your forehand feels or how difficult your serve really is to return)

On the other hand, the best tennis is played by intuition. Your mind keeps track of the points you have won and lost and it usually knows what you need to do to win. Consciously hitting a shot against your instincts in a match is often a mistake. I think conscious strategy is really only effective if it is very simple, like "keep the ball away from Federer's forehand," and a player doesn't need a brilliant tactical coach to come up with such a strategy.

It's probably more important for players to be confident that they have a winning strategy than to actually have one, so it would make sense to use a former great player or noted tactician as the "strategy" coach. Better yet, the player can employ the wisdom of crowds and receive counsel from a strategy committee, which would be more likely to produce the best strategy and inspire its own kind of confidence.

A tour player usually will not make much progress correcting technical flaws. By the time players turn professional, they have had so much court time that the marginal benefit of working on a particular stroke is usually insignificant. A notable exception is Nadal, who has obviously improved his serve and backhand in the last few years. But, I suspect that he has done this with endless hours of practice rather than any tips from Uncle Toni. Players who want to improve a particular stroke should seek out a specialist on the particular stoke (such as Mark Woodforde for volleys), or a group of specialists.

The role of physical trainer is usually already outsourced to a specialist, as it should be. As for hitting partner, there's no reason why players should be wasting their time hitting with their coaches. Players should be hitting with a fellow pro or with a player with a particular style they would like to master (Federer, for instance, has been known to pay the travel expenses of a lefty who hits with a lot of topspin for a hitting partner).

In almost every case, the services provided by a tennis coach would be more reliable if provided by a group of experts. Darren Cahill, Brad Gilbert, and Patrick Macenroe, when speaking as commentators, don't always agree on the approach that the player should take, but when they agree you can be almost certain that they are correct.

Thursday, September 11, 2008

Eli Luthier

Other than studying for the bar, I spent my summer building music gear.  It all started when I was informed that my sister in law wanted some accompaniment to sing "The way I am" at her wedding.  We had a drummer, a guitarist, and some guitar gear, but we had no bass or bass amp.  Obviously, the easiest thing to do would be to buy a broken vintage tube bass amp on eBay and restore it, and build an electric bass from scratch.  This experience led to other projects.  Predictably, I got carried away.  

This is the bass I built.  It wasn't exactly from scratch; I bought the neck, an unfinished body and some various other parts.  The hardest part was really finishing the body.  I HATE polyurethane finishes on any kind of musical instrument.  The finish is overly glossy and hard, making the guitar feel sterile and killing some tone.  Unfortunately, 99% of the guitars for sale at a place like Guitar Center are finished in poly. 

Part of the appeal of vintage guitars, perhaps unconsciously, is their lacquer finishes.  You can control the level of gloss on the lacquer by polishing it, and it usually ends up glossy, but not too glossy.  Lacquer also ages very nicely; parts that are touched more often when played will be a bit glossier, and small dents, chips, and cracks from weather checking end up giving the instrument some personality over time.  A beat up guitar from the '80's will never look as good as a beat up guitar from the '60's because hard poly finishes look awful when damaged.  

So, part of my motivation to build my own bass was that bass bodies finished in lacquer are hard to find and expensive.  I found a nice unfinished one-piece ash body on eBay and finished it in Surf Green nitrocellulose lacquer.  

Finishing guitars is hard because you can't just spray the paint on.  I spent about a week prepping the body by filling in all of the wood grain with grain filler, smoothing it with sanding sealer, and priming it, with a generous amount of sanding between every step.  It took me a while to learn how to spray the paint so that it wasn't too wet or too dry.  You have to do a lot more sanding if you miss either way.  I spent many hours listening to my bar lectures and wet sanding the body.  It was actually a good combination.  

The neck is from Warmoth.  It is made from goncalo alves with an ebony fretboard.  The nice thing about the goncalo alves is that it is naturally a nice dark color and doesn't require any finishing.  I like the feel of a raw wood neck.  

The metal hardware is all used; I went for the rustiest stuff I could find.  I like old things.  I don't know why.

The bridge pickup is a hot split coil wired in series like a Precision Bass pickup while the bridge pickup is a traditional Jazz Bass pickup.  This way, I am able to get both Precision Bass and Jazz Bass tones and it still looks like a Jazz Bass, which is the look I prefer. 

The other thing I did was restore an Ampeg B25 bass amp.  I got a chassis in pretty sad shape that had been removed from a combo.  It didn't work.  I got new tubes for it, replaced all of the electrolytic capacitors, insulated the case of the output transformer because it was arcing, cleaned up the electrolytic fluid on the board, and resoldered all of the suspicious-looking joints.  It took me months to track down all electrical issues, and I was on the verge of giving up a few times, but I finally got it sounding good.  

I built a cabinet for it out of birch plywood and covered it with Fender tweed, which I had finished with amber lacquer.  It now looks like a 50's Fender instead of a 60's Ampeg.  By the time I had finished it, I lost my taste for the 50's Fender look.  I am now selling it; I never really got attached to it because it caused be so much frustration and my bass skills are not really worthy of it now that it's going strong.

One of my easier projects that I'm really proud of is my guitar amp.  I bought a stock Epiphone Valve Junior head (a very cheap all-tube amp) on craigslist and a damaged cabinet with a broken speaker off of ebay.  I read a lot about valve junior mods, and ended up going with mods that imitated a Vox circuit.  The basic structure of the circuit remained intact, but most of the resistors and capacitors were changed to different values.  I also added a "bright" switch which puts an extra tone cap parallel with a preamp resistor.  I put a Weber Blue Dog speaker in the cabinet, which is a good but inexpensive imitation of the Celestion Blue speakers used in Vox amps.  It now really sounds like a Vox, which is by far my favorite guitar sound.  
My biggest regret of the summer is that my primary instrument became the soldering iron rather than the things that actually make the music.  

Tuesday, July 8, 2008

The One Hit Wonder Effect

    As I have spent the summer so far building and repairing bass guitar equipment while studying for the bar, I have been thinking quite a bit about my favorite bands.  My all-time favorite band is the Arctic Monkeys.  So far, their career has been typical of a modern band; their first album was their masterpiece and the second album wasn't quite as good (though in the case of the Arctic Monkeys, the second album is also a masterpiece).   
Most bands who become popular are never able to repeat the quality of the album that put them on the map.  A few examples are Pearl Jam, Nirvana, Smashing Pumpkins, Stone Temple Pilots, Weezer, Fiona Apple, Guns n' Roses, the Violent Femmes, Zero 7, Franz Ferdinand, even Britney Spears and Miles Davis.  A few of those had earlier albums, but they were pretty much unknown until their big second album.  I am willing to bet that a more scientific sample of popular music would show that subsequent albums generally don't do as well as the big first album.  
I have two explanations for why this might be the case.  First, and most obviously, the second album after becoming a star is more costly to create with fewer benefits if it's good.  When someone has become a rock star, his or her time is more costly.  The new star can spend it either by making a lot of money by touring or by enjoying the benefits of their stardom by doing whatever rockstars do, which I suppose is purchasing castles and entering celebrity golf tournaments.  Musicians also have less to gain by making another great album; they are already stars and people will buy the next album regardless of what goes on it.  Since working hard to create the next album is much more costly with fewer potential benefits, it would be a surprise to find musicians working hard to make it as good as the first album.  
The second reason for the dip in quality is that artistic output is probably somewhat random over a group's lifetime and a group is more likely to become popular when they get lucky and create something unusually appealing.  Even if stardom has no effect on artistic output, it will appear that quality has dipped after the "breakthrough" album.  Consider Nirvana, who released three major albums: Bleach, Nevermind (the breakthrough album), and In Utero.  Bleach did not make Nrivana stars, and In Utero probably wouldn't have if it had been their first album.  No matter what order the albums were released in - B-N-IU; IU-N-B; N-B-IU; N-IU-B; N-B-IU; IU-B-N; or IU-N-B - it would appear that the quality dipped after they became stars.  
I have usually attributed the one hit wonder effect to reason number one, but I suspect that most of it is the more mundane, but somewhat interesting, reason number two.  My next post will be in August hopefully after I have passed the bar exam. 

Tuesday, June 10, 2008

The Behavioral Economics of the 2nd Serve

            Throughout the 2007 US Open, Andy Roddick's first serve percentage was 71%.  When he got the first serve in, he won 82% of the points.  He won 52% of his second serve points.  He rarely double-faulted.  I couldn't find his double fault numbers, but I'm guessing his 2nd serve percentage was around 99%.

            Though these numbers are typical of Roddick, and similar for other players with big serves, they are totally bizarre.  When he steps up to the line for a 1st serve, he wins the point 58.2% (71%*82%) of the time.  If he misses his first serve, why would he bother hitting a conservative second serve if he has less than a 52% chance of winning the point with it?   If he's trying to win points, he should just be hitting bombs for both his first and second serves.  Sure, he will double fault a lot, but it's still his best chance of winning the point.  If he had hit nothing but bombs when he played Federer at the US Open last year, the numbers suggest he would have won the match. 

            If he is trying to win points, Roddick, like many other players, is not serving rationally.   It really is strange that players would continue to spin in their second serve when the numbers show this plainly that it is a bad idea.  You would think that coaches would look at stats to see if there are any obvious areas of improvement like this.  Sampras even demonstrated that you can have great success hitting huge 2nd serves, even with a healthy amount of double faults.  

             I'm sort of at a loss to explain this anomaly.  Either Roddick is irrational, or he is maximizing something other than his probability of winning points.  That's not to say that I don't empathize with Roddick; I too have an excessive fear of double-faulting.  Nothing is more infuriating in tennis.  Your opponent is just standing there waiting for you, and you lose the point before it starts because you can't even get it in the box.  For some reason, it feels much worse to lose a point this way than after a nice rally.  

         Maybe winning isn't all Roddick cares about, and how he wins or loses is important to him.  If hates double faulting a lot, he might be willing to lose some matches to avoid too many double faults.  If he were consciously making that choice, it seems like unusual behavior for a professional athlete.

        Maybe Roddick and I are overconfident in our groundstrokes and we think, "if I can just get the serve in, I will probably win the point anyway."  Other than that, I don't really have any other idea of how to explain this.  It's just so strange.

            Whatever the reason for this apparent irrationality,  I think it can be overcome.  All Roddick needs to do to win another grand slam is serve rationally.  

Rental Car "Insurance"

Welcome to my blog.  I have been researching the subject of my first post for many months, so it might be a little involved.  Since it seems no one else has done much research on it, this is probably the only thing that I'm uniquely qualified to talk about, so enjoy it.  In my future posts, I plan on turning to the traditional blog format of ranting mindlessly about things I really know nothing about. 

Contracting in the free market is remarkably efficient.  Self interest guides information to interested parties with speed and precision, constantly creating a myriad of mutually beneficial exchanges.  Those who offer an inferior product at an inflated price will soon have few customers, as word spreads of the unattractive terms.

However, someone will occasionally find a way to sell a product on unattractive terms to a large number of purchasers.  When a product depends entirely on a lack of information or irrationality to be marketable, it might be appropriate for law to intervene and prevent a misallocation of resources.             

The rental car loss damage waiver (LDW) or collision damage waiver (CDW) is such a product.  Anyone who has rented a car has felt the pressure from agent to purchase this optional "insurance" for anywhere between $10 and $40.  You might have noticed two suspicious aspects of this transaction; the rental agent seems overly eager to sell this product to you, and is careful not to refer to it as "insurance."

The rental agent is so eager to sell the product to you because rental companies absolutely depend on you buying it to make money.  In the United States, people spent about $800 million last year on rental car LDWs. They account for 4% of revenue for rental car companies.  Margins in this industry are such that if rental car companies could not sell LDWs, NONE of the major rental car companies would be profitable.  

The rental agent is careful not to refer to the product as insurance because if it were sold as insurance, it would be subject to insurance regulation requiring that it be fairly priced. The product is formally a waiver of liability.  Rental companies must provide liability insurance for you free of charge, but you remain liable for damage you cause to the rented vehicle.  For the price of the LDW, the rental car company agrees that it cannot collect from you if you mess up their car.  

Few informed consumers would purchase the LDW; the LDW is expensive relative to insurance and usually duplicative of the renter’s own auto insurance or coverage on a credit card.  The LDW is 20 times more expensive than a day worth of typical collision coverage.  If you paid $26/day you would end up spending $9490 a year just for collision insurance!  

Most credit cards and almost all collision coverage under a regular auto insurance policy cover rental cars.  It doesn't even make sense for people without collision insurance to purchase the LDW; they drive their own car without collision coverage, so why would they spend so much to drive a rental car on better terms than they drive their own car?  I admit that you might be more likely to get in an accident if you are renting a car, but the difference is certainly not they great.

Why do people remain uninformed and continue to buy such an awful product?  If Ford started selling terribly unreliable cars, their business would crash pretty quickly.  The problem here is the nature of the information.  No one can say "You should not buy the LDW."  All you can say is that "Almost no one should buy the LDW."  Until you go through all the effort of calling your credit card and insurance provider, you might actually be the one person who would like to be covered but has a strange credit card and strange car insurance policy with no coverage.  Everyone needs to find out for themselves whether they need to buy it.  This sort of information does not spread quickly because no one else can tell you that you don't need it.  

State governments have tried to keep people from wasting money on LDW's, but their attempts to do so have been misguided.  California, New York, and Illinois have set a price ceiling on LDW's.  In Illinois, rental car companies cannot charge more than $12.50 for an LDW.  Enterprise totally ignores these restrictions and charges $18 for an LDW at O'Hare.  The apparently weak enforcement of this law is to be expected since most people renting a car are from out of state; why should Illinois spend tax dollars protecting these people from wasting money in Illinois?  

A price ceiling has a more troublesome aspect.  From the perspective of rental car companies, uninformed consumers are a common resource susceptible to a tragedy-of-the-commons type problem.  Renters are more likely to become informed if the last time they rented a car they arrived at the rental counter to find out that the LDW was very expensive.  Perhaps they purchased it anyway since there was no time to find out whether they needed it, but they will remember the unpleasant experience and do some research the next time they need to rent a car.  

If there were a single rental car company, it would choose to price the LDW low enough that consumers are not driven to informing themselves in the future.  Multiple firms are would be less concerned with this because it is unlikely they will have many repeat renters anyway.

If multiple firms are approaching the pricing problem differently than a single firm would, their decisions will be incongruous with the welfare of the industry.  By setting a high price for the LDW, each firm is imposing an external cost on other firms by decreasing the stock of uninformed renters.  The rental firms would “overuse” the uninformed consumers by pricing too high, and motivating them to become informed. 

Firms might want to collude to set a price ceiling for the LDW.  This is precisely what a statutory maximum price does.  The enactment of such legislation in some states could possibly have been proposed by rental company lobbyists as a creative way to enact a binding collusive agreement.

Most states have disclosure laws that require the rental contract to mention that you "may" already be covered by a credit card or other insurance.  If anyone reading this has ever been deterred from purchasing an LDW by this message buried deep in the "terms and conditions" folder you get your rental agreement in (after you have already signed the rental agreement), I will send you $20.  

New York's other attempt to solve this problem is much better.  New York requires auto insurance policies to apply to rental cars.  This is unintrusive because most insurers do this already.  It also does a lot to solve the information problem.  If you have New York auto insurance, I can tell you for sure, "You don't need the LDW."   

Unfortunately, I don't know anyone in New York to whom I can recommend my blog and pass along this valuable information.  To the rest of my readers, after researching this issue for months, I honestly cannot tell you for sure that you should never buy the LDW.  

THAT is the problem.