## How Dangerous Is It To Fix a Single Service Game?

Earlier this week, I offered a rough outline of the economics of fixing tennis matches, calculating the expected prize money that players forgo at various levels when they lose on purpose. The vast gulf between prize money, especially at lower-level events, and fixing fees suggests that gamblers must pay high premiums to convince players to do something ethically repugnant and fraught with risk.

So much for match-level fixes. What about single service games? In Ben Rothenberg’s recent report, a shadowy insider offers the following data points:

Buying a service break at a Futures event cost \$300 to \$500, he said. A set was \$1,000 to \$2,000, and a match was \$2,000 to \$3,000.

In other words, a service break is valued at between 10% and 25% the cost of an entire match. The article doesn’t mention service-break prices at higher levels, so we’ll have to use the Futures numbers as our reference point.

Selling a service break might be a way to have your cake and eat it too, taking some cash from gamblers while retaining the chance to advance in the draw and earn ranking points. But it won’t always work out that way.

I ran some simulations to see how much a service break should cost, based on the simplifying assumption that prices correspond to chances of winning and, by extension, forgone prize money. It turns out that the range of 10% to 25% is exactly right.

Let’s start with the simplest scenario: Two equal men with middle-of-the-road serves, which win them 63% of service points. In an honest match, these two would each have a 50% chance of winning. If one of them guarantees a break in his second service game, he is effectively lowering his chances of winning the match to 38.5%. dropping his expected prize money for the tournament by 23%.

If our players have weaker serves, for instance each winning 55% of service points, the fixer’s chances of winning the match fall to about 42%, only a 16% haircut. With stronger serves, using the extreme case of 70% of points going the way of the server, the fixer’s chances drop to 34%, a loss of 32% in his expected prize money.

This last scenario–two equal players with big serves–is the one that confers the most value on a single service break. We can use that 32% sacrifice as an upper bound for the worth of a single fixed break.

Fixed contests have more value to gamblers when the better player is guaranteed to lose, and in those cases, a service break doesn’t have as much impact on the outcome of the match. If the fixer is considerably better than his opponent, he was probably going to break serve a few times more than his opponent would, so losing a single game is less likely to determine the outcome of the match.

Let’s take a few examples:

• If one player wins 64% of service points and other wins 62%, the favorite has a 60% chance of winning. If he fixes one service break, his chances of winning fall to just below 48%, about a 20% drop in expected prize money.
• When one player wins 65% of service points against an opponent winning 61%, his chances in an honest match are 69.3%. Giving up one fixed service break, his odds fall to 57.4%, a sacrifice of roughly 17%.
• A 67% server facing a 60% server has an 80.8% chance of winning. With one fixed service break, that drops to 70.7%, a loss of 12.5%.
• A huge favorite winning 68% of service points against his opponent’s 58% has an 89.5% chance of advancing to the next round. Guarantee a break in one of his service games, and his odds drop to 82%, a loss of 8.4%.

With the exception of very lopsided matches (for which there might not be as many betting markets), we have our lower bound, not far below 10%.

The average Futures first-rounder, if we can generalize from such a mixed bag of matches, is somewhere in the middle of those examples–not an even contest, but without a heavy favorite. So the typical value of a fixed service break is between about 12% and 20% of the value of the match, right in the middle of the range of estimates given by Rothenberg’s source.

Even in this hidden, illegal marketplace, the numbers we’ve seen so far suggest that both gamblers and players act reasonably rationally. Amid a sea of bad news, that’s a good sign for tennis’s governing bodies: It promises that players will respond in a predictable manner to changing incentives. Unfortunately, it remains to be seen whether the incentives will change.

## The Weirdest Thing About David Marrero’s Suspicious Mixed Doubles Match

You’ve probably seen the news: There was suspicious betting activity on a mixed doubles match a few days ago, hinting that some bettors knew ahead of time that David Marrero and Lara Arruabarena were going to lose to Andrea Hlavackova and Lukasz Kubot.

I don’t know whether it was a fix, or if someone leaked information, or if it was a publicity stunt by Pinnacle, who reported the suspicious activity. I don’t really care. Instead, what stuck out to me was this odd claim from Marrero, as reported by the Times:

“Normally, when I play, I play full power, in doubles or singles,” said Marrero, who won the doubles title at the 2013 ATP World Tour Finals. “But when I see the lady in front of me, I feel my hand wants to play, but my head says, ‘Be careful.’ This is not a good combination.”

As the Times also points out, Marrero’s record in mixed doubles is abysmal: 7-21 (with nine different partners), including 10 consecutive losses. He has, at times, ranked among the best doubles players in the world, yet managed to lose mixed matches alongside other greats, such as Hlavackova and Sara Errani. In six matches with Arantxa Parra-Santonja, a doubles specialist with eight tour-level titles, he’s lost the lot.

Assuming Marrero isn’t regularly fixing Grand Slam mixed doubles matches–after all, fixing a match this week would be awfully dumb–it’s clear that he’s not very good in this format. Here’s the weird thing: Before this mini-scandal, nobody was paying any attention.

Yeah, of course, it’s mixed doubles, which is little more than a glorified exhibition. Tennis isn’t great when it comes to statkeeping, and there’s virtually no one paying attention to doubles stats. The situation with mixed doubles is even worse. But if singles player had a losing streak of 10 of just about anything, fans would know about it, and people would be watching closely.

Given the nature of the mixed doubles event–specialists frequently switch partners, and the format includes a super-tiebreak in place of a third set–we wouldn’t expect too many extremes. In fact, of the 36 players who have contested at least 15 mixed matches since 2009 (28 slams plus the 2012 Olympics), only Leander Paes, with a 63-21 record, has been as good as Marrero has been bad. No one else has won more than 70% of their mixed matches.

And since mixed doubles draws are full of non-specialists (like Naomi Broady and Neal Skupski, who beat Marrero and Parra-Santonja at Wimbledon in 2014) we would expect the specialists to perform better than average. Sure enough, of those 36 regulars, 25 have winning percentages of 50% or better, and all but four have won at least 43% of matches. Only Marrero and Raquel Atawo (formerly Kops-Jones) hold winning percentages below 36%.

Let’s say we give Marrero the benefit of the doubt–as far the fixing goes, anyway–and accept his claim that he’s uncomfortable playing when there’s a woman across the net. It’s a strange state of affairs when (a) he continues playing almost every possible mixed doubles event despite his discomfort; (b) women choose to partner with him, either ignorant of his discomfort or simply happy to get into the draw; and (c) it’s possible to play 21 Grand Slams before the public gets any inkling that one of the 64 players in the mixed draw has a fundamental issue playing normally on the mixed doubles court.

Such comprehensive, long-standing ignorance isn’t out of place in tennis, especially in doubles. But given what we now know about David Marrero, the suspicious betting activity isn’t the influx of money against him–it’s the fact that anyone ever put money on him to win a mixed doubles match.

## The Cost of Fixing a Tennis Match

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.

## Westerhof, Van Der Duim, and a Strong Whiff of Match Fixing

This afternoon at the ATP Meerbusch Challenger in Germany, all eyes were definitely not on a first-round match between Dutchmen Boy Westerhof and Antal Van Der Duim. Both are ranked outside the top 250, neither has ever cracked the top 200, and both are in their late twenties.

It appears that the two players assumed no one would be watching. Before the match, the markets on Betfair were very suspicious:

For those of you not accustomed to parsing betting markets, here’s a summary of what the market thought was going to happen:

• Van Der Duim’s chances of winning the match were between 75% and 80%.
• Van Der Duim’s odds of winning the first set were roughly 35%.
• There was a better than 50/50 chance that Van Der Duim would win the match in three sets. The odds of any other specific outcome (e.g. Westerhof wins in three) were minuscule in comparison.

The match odds in themselves might have raised a few eyebrows, but could be written off as owing to Westerhof’s recent run of poor play, or perhaps some information gathered on site about a nagging injury. When combined with the other markets, however, it’s clear that something very fishy was going on.

The match went precisely according to script. After Westerhof took the first set, 6-4, the market got more and more confident about Van Der Duim winning the second set:

Van Der Duim remained the favorite even after going down an early break in the second set. Shortly thereafter, with no cameras watching, Westerhof seems to have decided not to waste any more time: