Thursday, 21 November 2013

Chess vs Running: prize money sharing

Green to play?
The 2013 world chess championships are underway, and although I do not much follow chess, I noticed how they shared their winnings is markedly different than running. By comparison, running is more of a winner take all. But there is a spectrum of distributions filling out the middle.

Below is the money distribution for Chess. The ratio from first to 8th is 115/21 = 5.47. Even more generous is the first and second-place ratio of  a mere 1.07.
  • 1st place – €115,000
  • 2nd place – €107,000
  • 3rd place – €91,000
  • 4th place – €67,000
  • 5th place – €48,000
  • 6th place – €34,000
  • 7th place – €27,000
  • 8th place – €21,000
By comparison, here's the prize structure for the 2013 Boston Marathon:
  • 1st place – $150,000
  • 2nd place – $75,000 
  • 3rd place –  $40,000 
  • 4th place –  $25,000 
  • 5th place –  $15,000 
  • 6th place –  $12,000 
  • 7th place –  $9,000 
  • 8th place –  $7,400 
The 1st/8th money ratio here is 150/7.4 = 20.2, and 1st/2nd ratio of 2. So in chess the runner up makes almost what the winner does, and 8th place make 18% of the winner, though not fantastic, compare to the runner-up for Boston who makes 50% while the 8th place makes only 5% of the winner. Boston is typical for running. For instance the ratios are similar to London, for which 2nd place makes 55% of the purse and 8th gets 7.3%.

But I wanted to see which, between chess and running, is more the outlier. That is, compared to other sports or competitions.
First of all, perhaps it's the tournament structure that's the cause? Let's compare chess to another tournament game. Here's the 2013 Wimbledon prize money for eight tennis rounds:
  • 1st place – $1,600,000
  • 2nd place – $800,000 
  • Semis –  $400,000 
  • Quarters –  $205,000 
  • 4th round –  $105,000 
  • 3rd round –  $63,000 
  • 2nd round –  $38,000 
  • 1st round –  $23,500 
While the first to second money ratio is 2, the winnings ratio from 1st to 8th is 68.1 . For the lower ranked players, this prize structure looks much worse than running! But notice that there are multiple 7th-rounders, 128 of them in fact (half of whom advance), so that Wimbledon pays out over $1.5 million to 64 first-round losers. Thus for a fair comparison, one then looks at the 8th-ranked player -who would sit in the quarters- netting them income ratio of 7.8 compared with respect to the winner. This value is closer to the chess partition than running.

And with the PGA Open Championships, the top 8 make the following:
  • 1st place – $945,000
  • 2nd place – $545,000 
  • 3rd place –  $350,500 
  • 4th place –  $272,500 
  • 5th place –  $220,000 
  • 6th place –  $190,000 
  • 7th place –  $162,500 
  • 8th place –  $137,500 
Here the 1st/2nd money ratio is 1.73 and the 1st/8th is 6.87. Again, this is closer to chess and tennis than running. Here's the prize structure for the main world poker tour event in Vegas
  • 1st place –$1,150,297
  • 2nd place –$650,275
  • 3rd place – $421,800
  • 4th place –$289,988
  • 5th place –  $223,203
  • 6th place$173,993
  • 7th place –$137,085
  • 8th place – $101,935
The 1st/2nd ratio is 1.77 while the 1/8 is 11.3. For a second-place player in poker you're doing as well as a golfer, runner, or tennis player. Dropping down to 8th a card player is doing half as well as a chess player but twice as well as a runner. Ok enough talk, here's the combined results for places 1-8:

Relative money going to each player
Same graph as above but with a y-axis log plot to differentiate slopes

You can see for the three running races I chose show the sharpest slopes, i.e, the fastest drop-off of income as you go down the placings. Considering this (albeit limited) dataset, when compared with other individual sports or competitions this spectrum sees running events at one end with chess at the other. Why might this distribution be as it is?

My theory is that some sports require the runner-up to be as "interesting" as the winner while others like running, aren't as heavily reliant on other people. That is, if a grandmaster plays chess against a nobody, the game itself will be less interesting to watch. By contrast if in a running race a top-rated individual competing against nobodies but setting a course record might still make for interesting television.

Tennis also needs good players to act as the foil the the world champ. But consider that lower ranked players still had to fight for to get a better payday. In 2013 Wimbledon increased its total purse by 40%, while early-round players got a 60% income boost, mostly due to strong advocacy by such players. Does running have a sufficient voice for prize sharing to be as fair?

The total purses are also interesting to compare:

Unsurprisingly the absolute value of running purses are often meagre compared with other sports and competitions.  Together in 2013 London, Dubai -one of the largest purses in the world-, and Boston handed out $865,600 USD total to the top eight runners. The combined money of all eight runners at all three races win about the same as the runner-up at men's worlds Tennis. The world cross country championships is even worse, with the winner taking home only $30,000. I already said the money in running is peanuts compared with tennis and golf. That difference is complex due to negotiations, yet simple, as the best runners are not a household name. How prize money is shared between the victors is another debate, but an equally important one. In tennis and golf players ranked much lower than 8th place make money; perhaps the top 100 will take home official prize money. Outside the top 10 in running races few make any significant cash. 

Running is comparatively amateur, unregulated form of competition. It's easy to organize a road race, and the running boom shows it's not hard to attract large numbers of fun runners. Far more challenging is the work to promote the upper echelon of competitors, and this is true in any sport. Household names require an organized effort. Such an effort does not exist by default. Running race prize money shows the winner receives proportionally more money than in other competitions. This steep slope indicates spectators are more interested in the potential winner than names of specific individuals beforehand.    

Therefore increasing the money for second, third, fourth, etc to help promote competition may in fact be confusing cause and effect. The real essence of the distribution problem is that if winning is the only way to get noticed in a race then most of money will only go to the winners. It is possible to make early impressions in golf or tennis without winning outright. The only way to do similarly in running is to sprint ahead in a distance race, which usually leads to condescending remarks.

There is work to do for finding ways of getting lower ranked runners noticed in races. This is not an original observation by any means, but I hope these plots shed some light on how prize money drops off more sharply in running compared with other tournaments. In being so sharp, we also see being the winner is comparatively more important. What to do? Perhaps we should find some ways of creating a tournament-style race for distance events. I've been interested in ways of creating a match-play model for running, which is non-existent as far as I know.

For instance, make a series of increasingly longer races until one person stands. i.e. start round 1 with a 200m race and carry forward the top X fastest runners. Then round 2 take the top 400m times, and then 800m, and finally the mile, where a small group of the best middle distance racers compete one-on-one.

Comments? Ideas? I'd be interested in hearing anyone's thoughts.



  1. Hey Graydon,

    Love the idea of a tournament style event. Do you think it would work at the pro level or would it have to be handicapped? In track now a days with the exception of Mo Farah, very few runners can jump into different distances and still compete (his 1500m time of 3:28 is my the numbers is better then his 5km-10km-half pr's. Even though he is the most dominant at the 5 and 10km) Obviously the roads are a different scenario. But on the track I think the tournament would work best if you had an all comers type of meet that didn't involve professionals. Starting at the 200 and working up to the mile would work great.

    Also, there was some talk last year of Bolt vs Farah at 600m. What do you think they would look like? Bolt has run 45 high for the 400. I would venture to say that Farah could run mid to high 1:43 based on his 3:28 1500m (And the fact he closed a slow 5000m in 50.7 last year). It would be the perfect distance in theory for them to meet.

    Enjoyed the post!

    1. Hey David. I don't know how a tournament might work at the pro level, but I think it would hold fairly well. Having a sprinter's speed would get you past the early rounds, but then fade as distances get longer. Almost all middle distance pros have sprint speed. For non-pros it still could work.
      Guys like me would be lucky to survive the early rounds, but at least it would motivate me to improve my "early" game (to borrow from chess). Imagine signing up for a mile, but knowing only the 50th percentile make it past each round.

      I think since Bolt isn't even practised on a 400 he'd be pretty rusty at 600. I doubt he'd keep the lead for more than 500m in the best of situations. But Reigel-type predictors don't work well for shorter than 400m, so who knows.


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