Olympic Game Theory

by on August 11, 2012 at 7:30 am in Economics, Sports | Permalink

How can you win a race by going slow? Check out the following video from the World Cup 2012 Individual Sprint Track Cycling (similar scenes can be found at the Olympics). The two cyclists, some of the fastest riders in the world, start out by going as slow as possible, almost like something out of Monty Python. In some races the riders will even come to a standstill.

Loyal reader Andy Garin has the analysis:

…in an all-out sprint, drafting creates a huge advantage, as the leading cyclist wears out very quickly. So both drop their speed so low that neither can take advantage of the other–well, at least until the last lap, at which point the advantage to being in front is about the same as the advantage of drafting from behind for 2/3 of a lap or so.

But note that this sort of problem arises because there are only two cyclists in the race. In Tour De France style road racing (or even the Keirin even on track, which is apparently also an Olympic event), one cyclists’ speed decisions only very marginally change the incentives of other riders. But in the Individual Sprint, you see something more like Bertrand-style dupolistic competition–that is, in the latter, one’s strategy is entirely based on the behavior of the other player. Specifically, it’s always better  to “undersell” the other player (i.e. to be in the rear) in the first two laps. And thus, you get the odd equilibrium where both set their speed to a negligible exertion level.

Unlike in the badminton tournament where some teams tried to lose, the cyclists are trying to win so going slow isn’t considered unsporting but it does make for a peculiar race.

Cyclists in the group event, however, will sometimes deliberately crash, as just happened in the Olympics.

“I just crashed, I did it on purpose to get a restart, just to have the fastest ride. I did it. So it was all planned, really,” Hindes reportedly said immediately after the race. He modified his comments at the official news conference to say he lost control of his bike.

…”He (Hindes) should not have told the truth,” Daniel Morelon, a Frenchman who coaches the China team, told the AP. “It’s part of the game, but you should not tell others.”

Hindes and his team went on to win, so engineering a crash can earn you gold. Surprisingly, cycling turns out to be kinda like banking.

Jone August 11, 2012 at 8:16 am

“Hindes and his team went on to win, so engineering a crash can earn you gold. Surprisingly, cycling turns out to be kinda like banking.”

Well, they’re both cyclical.

david August 11, 2012 at 10:50 am

*groans, throws tomatoes*

Brian Donohue August 11, 2012 at 4:43 pm

slow clap.

dearieme August 11, 2012 at 8:43 am

At least nobody threw tacks on the track.

chuck martel August 11, 2012 at 9:01 am

Hall of fame cyclist Steve Tilford has some thoughts on the whole scene: http://stevetilford.com/?p=21103

GiT August 11, 2012 at 9:47 am

Seems like a rather lame optimal strategy to have a sport settle in to. I’m sure there’s much tactical intrigue to it, but there would be tactical intrigue in “pin the tail on the donkey” if it was an Olympic sport.

Adrian Ratnapala August 11, 2012 at 2:58 pm

I think it’s wonderful. Most race sports have tactical intruge it is true. But I think a sport gains something when the very nature of the activity changes by the moment depending on the games stratergies.

Miley Cyrax August 11, 2012 at 6:39 pm

Indeed. There’s a certain beauty in finding the best way to win.

GiT August 12, 2012 at 8:42 am

That’s a nice way of describing what does occur. I guess that is rather unique. I can’t think of many sports where that happens. Maybe part of the problem is I’m thinking of it as a race, and as a race it seems silly. As a sort of duel it makes much more sense.

DRDR August 11, 2012 at 10:09 am

There’s no fundamental difference between throwing a single badminton match to ensure a better chance of winning a larger tournament vs. biking slower in a single lap. Both strategies involve losing a meaningless battle in order to win the war.

The main difference involves the fans: badminton fans pay to see individual matches, while cycling fans don’t pay for individual laps.

prasad August 11, 2012 at 11:24 am

Exactly right. To be honest, I find thinking about the strategy and what might motivate it, and how officials might align rules to maximize popcorn consumption among viewers rather more interesting than the sporting contest itself. It’d be really cool if the commentators made the strategic points during the slow laps, instead of wittering about the “tremendous levels of respect” or whatever that was.

John Thacker August 11, 2012 at 12:15 pm

You might like NASCAR, then. The sport is also about drafting, and about the game theoretic implications of cooperating and letting someone draft (or not) and pass (or not), and how repeated plays over a race and a season affect that. Strategic decisions in the race play a large part.

The driving aspect of the sporting contest is typically mocked as just turning left, but that’s because NASCAR is more about strategy and game theory than about driving.

Yet for some reason it seems to have fewer fans among people who might otherwise claim to prefer strategy to sporting achievements than one might expect otherwise.

prasad August 11, 2012 at 1:44 pm

Is it more fun than Formula 1? Because I loved the strategic aspect there (pitting and fueling, tires, overtaking etc) but the sporting action is like watching paint dry. Just cars droning on, and they all look basically the same.

prasad August 11, 2012 at 1:45 pm

Re people disliking Nascar, that’s probably like folk versus country. What you say you like signals team membership, etc.

AD August 11, 2012 at 10:34 am

Nearly every Olympian needs to be disqualified for not going all out either in semifinal races or in part of the final. Start revoking medals now!

Ryan August 11, 2012 at 10:42 am

I think this race is an even better example, although not Olympic. http://www.youtube.com/watch?v=BkkTSVVrPYk

Matt August 12, 2012 at 1:17 am

That race is great but as I understand it the rules now require the cyclists to maintain at least a walking pace as judged by referees on the inside of the track.

Mitch Berkson August 12, 2012 at 12:48 pm

I wonder what the race would look like if they were allowed to go backwards.

Peter Twieg August 11, 2012 at 10:47 am

It’s the Mario Kart strategy!

Olaf August 11, 2012 at 11:02 am

this has been around a hundred years, similar to the subject matter of that post recently about europeans “now” and”surprisingly” being able to claw-back days they have taken off from work, but on which they have become ill (prompting the giddy prediction that surely now everyone will claim to have become ill on his holidays…yaaawn).

at least no prediction here ;)

and “drafting”, really? well no, it’s not about “drafting” on these kind of tracks. it’s about the total race time being meaningless and about the tactical element of being able to surprise the competitor with the start of one’s final sprint. that’s why the front guy has his eyes glued back over his shoulder…no you’re not gonna be worn out if you’re in front here (as is the case in “drafting” situations i.e. long races), but as in every SPRINT situation you are gonna be surprised if you’re not extremely attentive. THAT’s why you don’t want to be in front. should be obvious of course.

mkt August 11, 2012 at 6:40 pm

This is the first time that I’ve read someone say that it’s not about drafting. If drafting is irrelevant, then why doesn’t the cyclist in front simply go all out, give that he’s already got a small lead? What is the advantage in being behind? According to your explanation, the racer who’s behind can surprise his competitor — so why doesn’t the competitor simply sprint full speed from the beginning, (which would also make surprise irrelevant)? Track sprinters in distances from 100m to 400m don’t worry about being surprised by their competitors (granted they race in separate lanes unlike bicyclists), they just go out and sprint.

Olaf August 11, 2012 at 9:04 pm

- leader can go all out, it happens, but works only if he gets ahead enough (let’s call that a successfull “supersprint”). otherwise (if he can’t put a minimum distance between himself and the other guy) by accelerating the race he has actually made drafting by the guy behind possible. I think it is more likely to achieve a successfull supersprint from the behind position (the front guy must have a longer reaction time) because putting in place the initial distance is crucial.
- so it’s not that drafting is totally irrelevant (I overreached here), it can be relevant in the last round when both are fast, but during the majority of the race the advantage of being behind is not drafting as such (you can tell because the back guy usually doesn’t even line up but rather stays “uptrack”; also they sometimes even stand motionless on their bikes – that’s not drafting obviously, but rather a tactical wait, and so is their entire behaviour when they drive below maximum speed and jockey for position, which is 90 perc. of the race), but rather the tactical positioning behind to be able to (i) draft in the end-phase or (ii) to “supersprint” by surprise (i.e. preferably from behind), in which case drafting by either is out of the picture.
- so you can either try the supersprint at some point (from first or second position) or you must reverse engineer your behaviour from the assumption that you must be in a “close behind” position at the begin of the last phase of the race, so that you can then (assuming neither has successflly supersprinted) draft.
- in summary: drafting plays an indirect role, but the behaviour we’re observing here is itself not drafting, but jockeying for the best position (being behind) to start a surprise-supersprint or (as fall-back option) to draft at the very end.

Eric August 12, 2012 at 2:03 am

Olaf… you said drafting didn’t matter. Then when he said if drafting didn’t matter why wouldn’t you go balls to the wall. Then you said well, in that case drafting would matter. Make up your mind.

Olaf August 12, 2012 at 3:25 am

as I expressly conceded in my second post, drafting matters indirectly, hence these races are – among various other things not even mentioned here – about drafting. but I think its much more about surprise.

it’s not like in a long race where the guy behind is automatically drafting just by lining up behind someone else. that’s what I call drafting. here it matters mainly in an anticipatory way. you go slow to stay behind. you want to stay behind to be able to surprise your opponent and get a material lead. if that works, noone ever drafts. if the front guy tries to get away you try to stay close and draft.

mkt August 13, 2012 at 2:29 pm

Okay, that’s a good answer; if I’m understanding correctly it’s like this: the go-slow-in-order-to-be-behind strategy renders drafting largely irrelevant. But drafting, or better put the potential to draft, is what makes that a good strategy in the first place.

casey August 11, 2012 at 11:18 am

The Australian woman won the gold medal in the sprint this year, by doing a little fake speed up, then stopping into almost a track stand… the brit couldn’t stop as quick, ended up in front and led out the australian. The aussie caught the draft and easily won.

caey August 11, 2012 at 11:21 am

And no tennis player plays full out when the score is say… 6-4, 0-5 (love-40).. Every tennis player is going to save their energy for the next set.

prasad August 11, 2012 at 11:29 am

Another thing tennis players do sometimes (but only rarely) when ahead is to deliberately lose their serve then break to win the set. The benefit is that they’ll have the advantage of serving first in the next set. The problem is that breaking serve is a low probability event, and if you’re really that confident about breaking serve you shouldn’t be worried about winning the match. It’s more common in tie breaks. The guy serving up 6-2 can afford to lose that point, since he has more chances left to win a point for a set.

Brian Donohue August 11, 2012 at 5:11 pm

The curious and arbitrary division of points in tennis has always intrigued me. It reminds me of the English system of measures or currency.

That you could out point an opponent 108-62 and lose a match, in theory, I always found fascinating. All points are not created equal.

I would guess a different division of points would produce basically the same world rankings, but it might produce a different dynamic, kinda like match play in golf (although not finishing holes or rounds creates a similar ‘funny smell’ as instances of not trying discussed here.)

prasad August 11, 2012 at 5:36 pm

The points scoring is not very imaginatively arbitrary – it’s pretty much always a score of X with a minimum difference of two required. So a set is six games, but with a difference of two games – or a tie break, which is also 7 points, with a difference of two. Normal games are the same as well – it’s four points with a difference of two. For some reason the simple within-game scoring is festooned with the most baroque numbers. The points go 15, 30, 40, and then you have an “advantage” which goes back and forth via 40-all or deuce.

It is true that the winner of the match (most number of sets) need not the the one who wins most games, who further need not be the one who wins most points, but the way the scores are reported is way more crazy than the scoring system itself.

Eric August 12, 2012 at 2:07 am

“It is true that the winner of the match (most number of sets) …. need not be the one who wins most points.”

That’s exactly the part he considers crazy. You don’t award the football or basketball game to the team who wins the most quarters.

prasad August 12, 2012 at 7:54 am

I understood the point he made, and said as much. But it’s equivalent to noting that all points aren’t equally important. Every tennis commentator (even the stupidest) knows about “big” points, those on which the set or even the match hinge. Makes those points (and those surrounding them) enormously more exciting. Tennis would be a pretty dull watch if everyone played (say) first to a hundred points, since you’d lose all these mini climaxes.

It may sound ‘crazy’ to someone who’s not used to the ‘group of groups’ dynamic, but that dynamic is pretty common in sport. Just off the top of my head, table tennis, badminton and billiards all use it.

Mike in Qingdao August 11, 2012 at 11:58 am

You obviously don’t know your readers very well. Everyone knows it was the Community Reinvestment Act rather than bankers that caused the financial crisis.

Eric H August 11, 2012 at 3:03 pm

Apparently it’s just one reader that Alex doesn’t know well.

ya obviously August 11, 2012 at 7:29 pm

or maybe mike’s just quicker to spot implied idealogy than the typical libertarian literalist.

mike, you funny man!

Miley Cyrax August 11, 2012 at 9:25 pm

One needs not a staunch libertarian literalist mindset to realize that government actions such as the Community Reinvestment Act distorted incentives to pave the way for bankers and consumers/borrowers to do their thing.

Willitts August 11, 2012 at 3:09 pm

I’m skeptical of the comparison to a Bertrand competition model. What is the consumer and what are the prices?

These cycle races actually resemble firstpast the post, winner take all political races in closely matched contests with physical energy and other dynamics of physics taking the place of voters. I suppose that answers my question above.

zbicyclist August 11, 2012 at 4:42 pm

The same type of cycling strategies can play out in road races when there are a pair of cyclists on a breakaway.

I recall a stage of the Tour de France a few years ago when the two riders in a successful breakaway jockeyed so slowly for position that the peleton caught up with them and they both got nothing.

Sports is all about strategy. You have to race to the rules to get your maximum advantage / minimum disadvantage versus everyone else who’s racing to the rules.

They should not have suspended the badminton players. They should have banned whoever set up the tournament this way from planning any future tournaments. Remember the last weeks of the NBA season before they instituted the lottery?

Brian Donohue August 11, 2012 at 4:59 pm

Agreed. It’s a design problem- at some level ineradicable (we can’t level out the importance of each moment, even in something as straightforward as a 100-meter dash, until we get to the 10 seconds that is the Olympic final), but games should be designed to minimize egregious lack of effort.

zbicyclist August 11, 2012 at 7:20 pm

Even in the final it’s possible it’s in your interest not to try your hardest … Bolt seemed to ease up at the end of the 200 meters when he clearly had it won. Why? Well, there are meets where they give you extra money if you break the world record. Why not showboat a little and also try for a couple of extra paydays?

Remember Vasily Alexeev, the famed Russian weightlifter who seemed to love this strategy some decades ago? He used to show up on “Wide World of Sports” pretty often. There was a “.. series of 80 world records the weightlifter set between 1970 and 1977.He received bonus funds every time he set a world record by the Russian Federation so he made it a point to gradually increase his world records by 1.1 pounds or 1/2 kilo”

http://en.wikipedia.org/wiki/Vasily_Alekseyev

Olaf August 12, 2012 at 3:56 am

I heard that too, that it’s standard situation in track and field meets. If you can win gold, but don’t necessarily go full out but rather save the record breaking for autumn, then you’ve optimised (financially).

Reminds me about the classic problem with corporate budgets and manager’s behaviour: in good periods they try to limit their overperformance (compared to budget) to the amount that is bonus relevant and push the rest (i.e. excess revenues that will trigger no extra credit) into the next reporting period.

If the management incentives were structured like in the bike example (pairs of managers pitted against each other and NO relevance attached to their absolute results but only to the binary metric “which one wins this race”), I could imagine results could be at least somewhat similar: Each ignores absolute results, watches the competitor, defers reporting of good results as much as possible, avoids going all-in and alarming anyone, rather unleashes a suprise attack later at just the right time and (through surprise and mobilising the “deferred” results) puts enough distance between himself and the other so the latter cannot catchup by outperforming in the last part.

Vernunft August 12, 2012 at 5:38 am

The strategy of losing early in a Swiss-pairing tournament is known (tongue-in-cheek) as the “Swiss gambit” in chess.

londenio August 13, 2012 at 3:36 am

This kind of strategy matters also in road racing, but it is many orders of magnitude more complex.

Nick Croom August 13, 2012 at 10:24 am

Minor point – they aren’t allowed to stop anymore. Shame I sort of liked them at a standstill staring at each other….
Also it’s not just about drafting, it’s also about track position – if you’re behind you can sit higher up on the banking and use the downhill to build up speed.
Londenio – many order of magnitude? I guess it is more complex because you can use your own teammates for the lead out…

mkt August 13, 2012 at 2:56 pm

I think he’s right about road racing being many orders of magnitude more complex. I don’t know the details but I have friends who like to follow the Tour de France, Giro d’Italia, etc. and there’s a huge array of elements to take into account: even though an individual gets the yellow jersey, this comes about only because of a team effort. And there are diffeerent stages: flats, mountains, time trials and teams strategize about when is the best time to attack. Breaking away, bridging, and blocking are some of the tactics that teams use, and when and how to use those tactics involve taking into account additional variables (Where are the leaders? How strong are the cyclists who are close to you? Can you catch them by surprise and break away while making it harder for them to chase?) Finally, the Tour de France (I don’t know about the other races) has multiple types of winners: in addition to the yellow jersey, there’s green, a polka dotted one, I think white, and I don’t know what else. Plus there are team awards too. So even the objective function is a lot more complex than in most other competitions, where the goal is simply to beat the opponents end of story. In the Tour de France there are multiple goals one might pursue although of course one is clearly more important than the others.

Wi August 13, 2012 at 11:02 am

The issue is that the racetrack design is insane.

If they instead used two separate parallel straight (and level) tracks, then racers would have to maximize average speed.

mkt August 13, 2012 at 2:36 pm

The do do the equivalent of that, in individual pursuit. The two cyclsts start one-half lap apart from each other, so there’s no drafting or positioning.

OTOH I believe that pursuit is used only for longer distances, not for sprints.

GiT August 13, 2012 at 9:22 pm

Which is great for finding out, “who can cycle the fastest”, but really is sort of stupid as far as an interesting game goes.

I’ve developed a division in my mind between “real sports”, where one physically interferes in the performance of one’s opponent, and “mere” record-setting competitions (really, more like demonstrations), where at best one can psychologically intimidate/”psych out” an opponent.

Lanes unique to each racer, like in most track events, would certainly get rid of this component of physical interference and turn the thing in to much more of a straight up “race” than a more complex game. I mean, there really isn’t much of a game at all to a straight up race. Go as fast (or as heavy or as far or as high or as accurately) as one can, within the defined limits, conserving energy as appropriate given your overall competitive goals and the strength of the field you’re being compared against. You’re really just optimizing effort and technique given a particular set of constraints, leading up to that moment where conditions lead you perform at your own personal maximum.

It’s only when you add an opponent who can actually intervene in your performance that races become much more game like (as in Nascar, Formula 1, Tour de France, &etc)

Ann Onymous August 14, 2012 at 12:40 pm

But I thought the Obama administration has banned the unfair practice of drafting.

Nels August 14, 2012 at 6:28 pm

Finally! A topic I am qualified to comment on. Olaf has it pretty much nailed. I would only add that there is a physiological component in play here as well. The energy systems used to generate the power required to launch one’s bike to 45+ mph is only good for 10-15 seconds.

To better understand the track sprint event, picture Usain Bolt and Justin Gatlin in a 1 mile race. They would also probably fool around until the last 150 meters. Now that I mention it, that would be a fascinating race to watch! The increased significance of drafting in cycling, (due to its increased speed and the fact that drag increases as a square of speed) means that even if you put Taoufik Makhloufi (Gold in the 1500m) in the race, Usain and Justin would easily maintain his pace. Its hard to understand just how huge drafting is in cycling without experiencing it yourself.

Of course game theory applies to all cycling races, and is best expressed in the book “The Rider”. “Always attack as late as you can, but before the others do.”

Comments on this entry are closed.

Previous post:

Next post: