The Cost of Fixing a Tennis Match

Italian translation at settesei.it

In the last week, we’ve seen an enormous amount of speculation about match fixing in men’s tennis. There are plenty of signs that players are fixing matches and some alarming evidence that the sport’s governing bodies aren’t taking action.

A few numbers have popped up in interviews with insiders: A player might be offered $50,000 or $60,000 to fix a match. Back when Novak Djokovic was apparently asked (indirectly) to lose on purpose, the price is said to have been $200,000.

Those of you who know your tennis economics know that those are huge sums relative to what most players can expect to earn on tour. At most ATP 250s, only the titlist takes home a check worth more than $50,000. Even at Masters-level events, a player has to reach the quarterfinals to earn that much.

Most of the players whose names turn up in fixing allegations are rarely reaching those heights. Instead, they’re playing a first-rounder at a 250 for the chance to earn an $3,000 or $4,000. Even when giving a full effort, these players are rarely heavy favorites, so they might only have a 50% chance of winning that second-round money in matches they don’t fix.

It’s clear that the vast majority of ATP matches are worth much less to the players–in prize money terms–than they are to gamblers. If press reports are to be believed, gamblers offer payments to many more players than ever accept them, so the gamblers presumably have a reasonably good idea of what it costs to fix a match.

If we can pin down the value of a match played fairly, we can get an idea of the sort of multiple that gamblers must pay to fix a match. Of course, the multiple won’t be the same for every player, or in every situation, but it will shed some additional light on the situation.

I’ve attempted to quantify the prize-money value of every match in the 2015 ATP and ATP Challenger seasons for both players. For each match, using the same general methodology as my tournament forecasts, I generated the probability that each player would reach the next round and every round beyond that. When combined with the additional prize money a player earns for reaching each successive round, these probabilities give us an “expected value” for each match. That’s our best guess of what a player forgoes if he opts to fix a match.

As an example, consider Fernando Verdasco at last year’s ATP 250 in Metz. In the first round, my model gave him a 53% chance of defeating Alexander Zverev. Based on the entire draw, it estimated Verdasco’s chances of reaching each successive round, up to a 2.9% chance of winning the title. Run the numbers, and his expected value for that match was $3,855–incidentally, the lowest expected value of any of his matches last year.

Once Verdasco advanced to the second round and was guaranteed second-round prize money, he had a 54% chance of getting past Gilles Muller, and an expected value of $6,239 for playing that match honestly. Overall, the median expected value of a Verdasco match last year was roughly $9,500, and the highest expected value of any match–his US Open first-rounder–was just over $45,000.

As it turns out, that $9,500 median is very close to the median for all ATP tour-level matches, $9,667. Put another way, well over half of last year’s ATP matches–had an expected value under $10,000–20% of what gamblers are apparently willing to pay to fix a match.

The value of not fixing is even lower for many substantial subsets of tour matches. The median expected value of a first-round match–including the lucrative ones at the majors–is only $6,200. The median expected value of a first-round match at a 250- or 500-level event is a mere $4,200.

Consider the case of Andrey Golubev, a player who has turned up in fixing allegations in the past, and appeared among the players flagged by Buzzfeed’s recent investigation. The median expected value of his 13 tour-level matches last year was $3,450; all but three were under $5,100.

So far, we’ve only discussed tour-level matches–and for players, that’s where the real money is. Most fixing allegations these days pertain to the Challenger level and below, where the entire purse of some events is equal to what a single first-round loser will receive this fortnight in Melbourne.

Golubev played the majority of last season on the Challenger tour, so we can see what it was worth to him to play honestly at the lower level. In 21 matches, his median expected prize money was a whopping $692, and 15 of the 21 matches had expected values under $1,000.

Want another example? Take Denys Molchanov, who has also been identified as a possible fixer. In 27 Challenger matches last year, his median expected prize money was $612, 23 of the 27 matches had expected values under $1,000, and no match he played was, by this measure, worth more than $1,200.

Altogether, the median expected value of a Challenger match last year was $514, and almost 80% of matches had expected prize money values of less than $1,000. The betting volume on Challenger matches is generally lower, so the value of fixing these matches is also lower, but the prize money discrepancy is at least as great.

Without knowing more about how much players have been paid to fix matches–and adjusting for the possibility that they are sometimes injured, with correspondingly lower chances of winning, when they do so–we’ll never be able to establish a precise relationship between expected prize money values and fixing fees. That said, the available anecdotal evidence, combined with my analysis here, can give us a rough idea.

If we take $50,000 as a typical payment to fix an anonymous early-round ATP match, that’s probably about 10 times the expected value of that match to the player who fixes it. It’s less clear, though, whether that extra $45,000 should be understood as a 10x multiple of expected value, or a fee to offset the very high cost–albeit one with very low probability–of the player suffering a long-term suspension, banishment from the game, or even legal penalties.

Further, the expected value of a match is more than just its prize money. When a player wins matches, he gains more ranking points, and those points can get him entry into higher-level (and higher-paycheck) events and earn him seedings at the events he’s already playing. It’s very difficult to assign a money value to ranking points, especially since they are non-linear: The 50 points that push you past the Grand Slam direct entry threshold are enormously valuable, but the 50 points that move you from #41 to #39 are usually worthless.

For both of these reasons, we can’t explain exactly how fixing fees are established, or–more importantly–how fixing might be affected by increased prize money. After all, plenty of people have been clamoring for years for more prize money at the lower levels of the game, and when we see players apparently losing matches on purpose in order to finance their life on tour, that gives more ammunition to their cause.

However, based on the numbers we’ve seen so far, it’s far from obvious that increasing prize money–whether at the Challenger level or in early rounds of 250s–would do much to solve the problem.

Consider a radical move such as doubling prize money at all Challengers. That would cost about $8,000,000 per season, and it would make tennis a much more viable option for the many players who don’t receive substantial support from their national federations. But would it put a dent in match-fixing?

Simply doubling the numbers above, we find that almost half of all Challenger matches would still be worth $1,000 or less, with almost 80% under $2,000. If some players will fix matches for ten times the expected prize money, that means we still have thousands of matches that are “fixable” for $10,000. Perhaps an increase in overall prize money would mean that more players would refuse to fix on moral grounds. But financially, even an expensive solution like this one is very unlikely to eliminate fixing.

If recent reports are to be believed, the governing bodies of tennis are doing very little to stop match fixing. Spending that same $8,000,000 to massively increase the size of the Tennis Integrity Unit (assuming that it uses that money wisely and acts on its findings) would probably have a much greater effect than the same amount spent to increase prize money.

If enforcement is more effective, the risk that a player takes each time he fixes a match is that much greater. Increasing that risk would require that gamblers pay a higher multiple (or a higher “risk of banishment” flat fee) for every match, not just those for which prize money is higher. It wouldn’t prevent every corrupt player from entering the sport, and it wouldn’t address non-financial issues like situations in which a player’s family is threatened, but it would make fixing matches a lot more expensive.

Comparing fixing fees to the prize money expectations I’ve generated, it’s clear that the players who do fix matches–themselves already in the minority–charge a very high premium for doing so. They are very concerned about getting caught, or they would simply rather not fix matches. The problem can’t be solved by any feasible boost in prize money, but it can be mitigated by increasing the premium that gamblers have to pay.