Category: Injuries

Grand Slam Prize Money Whack-a-Mole

Eagle-eyed Twitterer @juki_tennis noticed the following tweaks to the rules for the 2020 grand slams:

Let’s start with the first underlined section. I’ll get to the doubles tweak in a bit.

The ITF is learning that incentives are tricky. In the olden days, back when Adrian Mannarino still had hair, prize money was simple. If you played, you got some. If you didn’t, you got none. Players who get hurt right before one of the four biggest events of the season suffered in silence.

Except it’s never been quite that simple. The slams have spent the last decade taking turns breaking prize-money records, raising in particular the take for first-round losers. A spot in the main draw of the Australian Open is now worth $63,000 USD ($90,000 AUD). Some players in the qualifying draw barely make that much in an entire season. Whatever one’s hangups about honesty or fair play, if you have a chance to grab that check, you take it.

The same logic applies whether you’re healthy or injured. The last decade or so of grand slam tennis has been littered with first-round losers who weren’t really fit to compete. That’s bad for the tournaments, bad for the fans, and probably not that great for the players themselves, even if $63k does buy a lot of physiotherapy.

Paid withdrawals

Two years ago, the ITF took aim at the problem. Players with a place in the main draw could choose to withdraw and still collect 50% of first-round loser prize money. The ATP does something similar, giving on-site withdrawals full first-round loser prize money for up to two consecutive tournaments. The ATP’s initiative has been particularly successful, cutting first-round retirements at tour-level events from a 2015 high of 48 to only 20 in 2019. In percentage terms, that’s a decline from 4.4% of first-round matches to only 1.6%.

The results at slams are cloudier. On the men’s side, there were nine first-round retirements in 2010, and nine in 2019. The ITF’s incentives might not be sufficient: 50% of first-round prize money is still a substantial sum to forego. In fairness to the slams, retirements may not tell the whole story. A hobbled player can still complete a match, and perhaps the prize money adjustment has convinced a few more competitors to give up their places in the main draw.

None of this, however, keeps out players who consciously game the system. Both the ATP and WTA allow injured players to use their pre-injury rankings to enter a limited number of events upon their return. Savvy pros maximize those entries (“protected” in ATP parlance, and “special” in WTA lingo) by using them where the prize pots are richest and, if possible, bridging the gap with wild cards into smaller events.

Emblematic of such tactics is Dmitry Tursunov, who played (and lost) his last six matches at majors, all using protected rankings. Two of those, including his final grand slam match at the 2017 US Open against Cameron Norrie, ended in retirement. Three of the others were straight-set losses. In one sense, Tursunov “earned” those paydays. He was ranked 31st going into Wimbledon in 2014, then missed most of the following 18 months. Upon return, he followed ATP tour rules. But with the increasingly disproportionate rewards available at slams, protected rankings seem sporting only when used as part of a concerted comeback effort.

While the ITF’s late-withdrawal policy wasn’t in place for Tursunov, it’s easy to imagine a player in a similar situation taking advantage. And that’s the gap that the latest tweak aims to plug. The new rule is not limited to players on protected or special rankings, which typically require absences of six months, not just one. Yet the idea is similar. You can no longer enter, turn up on site, plead injury, and take home tens of thousands of dollars … unless you’ve competed recently. It’s a low bar, but it raises the standard a bit for players who want to take home a $30,000 check.

One of two prongs

The rule adjustment wouldn’t have affected Tursunov’s lucrative protected-ranking tour of 2016-17. However, had the Russian come back from injury a couple of years later, his income might not have gone uncontested.

In 2019, both Roland Garros and Wimbledon invoked another rarely-used clause in the rulebook. It requires that players “perform to a professional standard,” and a failure to do so can result in fines up to the amount of first-round prize money. Anna Tatishvili–using a special ranking–was docked her full paycheck at the French Open, and Bernard Tomic–a convenient whipping boy whenever this sort of thing comes up–lost his take-home from the All England Club. Both fines were appealed, and Tatishvili’s was overturned. (Tomic’s should have been, too.)

What matters for the purposes of today’s discussion isn’t the size of Tatishvili’s bank account, but the fact that the majors have dug the “professional standard” clause out of cold storage. It’s worth quoting the various factors that the rulebook spells out as possibly contributing to a violation of the standard:

  • the player did not complete the match
  • the player did not compete in the 2-3 week period preceding the Grand Slam
  • the player retired from the last tournament he/she played before the Grand Slam
  • the player was using a Protected or Special Ranking for entry
  • the player received a Code Violation for failure to use Best Efforts

Every major has a few players who are skirting the line, perhaps returning to action a bit sooner than they would have if the grand slam schedule were different. With the fines in 2019, the ITF has made clear that they expect to see credible performances from all 256 main draw players. And with the prize money adjustment for 2020, the governing body has closed the door on five-figure paydays for players who shouldn’t have been on the entry list, even if they never take the court.

I promised to talk about doubles

The second section of the rulebook quoted above is a bit problematic, because I believe it is missing a key “not” in the opening sentence. Unless the ITF has some bizarre and unprecedented goals, the intention of the doubles regulations is to discourage singles players from retiring in doubles unless they are truly injured, and to prevent singles players from even entering doubles unless they plan to take it seriously.

Doubles prize money pales next to the singles pot, but even first-round losers in men’s and women’s doubles will take home $17,500 USD per team, or $8,750 per player. That’s enough to convince most singles players to enter if their ranking makes the cut, no matter how little they care about doubles during the 44 non-slam weeks of the year.

The majors determine which teams make the doubles cut the same way that ATP and WTA tour events do. Teams are ordered by their combined singles or doubles ranking. Each player can use whichever is better. The tours allow pros to use their singles rankings to encourage superstars to play doubles, and at events like Indian Wells, many big names do take part. At the slams, the bigger effect is on the next rung of singles players, giving us oddball doubles teams such as Mackenzie McDonald/Yoshihito Nishioka and Lukas Lacko/John Millman at the 2018 US Open.

As with other details of the entry process, most fans couldn’t care less. But they should. Whenever the rules let one team in, they leave another team out. By including more singles players in the doubles draw, the standard for full-time doubles players is made almost impossibly strict. An up-and-coming men’s singles player can crack the top 100–and gain admission to grand slam main draws–with a solid season on the challenger tour, but even the best challenger-level doubles teams are often left scrambling for partners whose singles rankings are sufficient to gain entry.

This year’s rulebook edit should help matters, at least a bit. (As long as someone inserts the missing “not,” anyway.) Grand slam doubles is not an exhibition, and it shouldn’t be contested by players who treat it that way. The ATP and WTA should follow suit, penalizing players who withdraw from doubles only to prove their health by continuing to play singles.

Incentives and intentions

These rule changes, while technical, are aimed at something rather simple: to ensure that the players who enter slam main draws–both singles are doubles–are healthy and motivated to play. The latest tweaks won’t close every loophole, and we can expect more disputes over issues like the Tatishvili and Tomic fines.

The bigger issue, complicated by the on-site withdrawal adjustment, is the underlying purpose of the rise in first-round loser prize money. The slams represent a huge proportion of the season-long prize pool, especially for players between approximately 50th and 110th in the ATP and WTA rankings. These competitors miss the cut for many of the most prestigious Masters and Premier tournaments. Even in later rounds, they are usually playing for four-figure stakes–if that. Four times a year, pros with double-digit rankings get a guaranteed cash infusion, and the potential for much more.

The presence of the four majors effectively funds the rest of the season for many players. The slams have upped first-round prize money–both nominally and relative to increases in later-round awards–partly in recognition of that fact. It is expensive to be a touring pro, and without paydays from the majors, it can easily be a money-losing endeavor.

Salary, not prize money

The majors rely on the less-lucrative tours for year-round publicity and a pool of highly-skilled players to drive fans and media attention to their mega-events. Much of the first-round loser prize money is in recognition of that fact. No one really thinks that the 87th-best player in the world deserves $63k just for showing up and giving Serena Williams a mild 59-minute workout. But does the 87th-best player in the world deserve to collect annual revenue of $250k–a figure that will largely go to cover travel, training, coaching, and equipment expenses? I think so, it appears that the slams think so, and I suspect you do, too.

So, when the ITF closes loopholes like these, keep in mind that they are operating within the silly $63k-per-hour framework, not the more reasonable $250k-per-season model. It is an important goal to ensure the integrity and quality of play at slams, but it ought to be paired with an effort to support tennis’s rank-and-file, even when those journeymen are injured.

A more sensible policy would be to separate much of the first-round loser prize pool from the literal act of playing a first round match. Perhaps the slams could each contribute $7.5 million each year–that’s $30k per singles player–to a general fund that would disburse annual grants to players ranked outside the top fifty, and lower every singles award by the same amount. (The details would be devilish, starting with these few parameters.) Such an approach would come out in the wash for most players, who would simply receive the extra $30k per slam in a different guise. But it would help injured players return to top form, and it would leave plenty of money for high-stakes combat at the sport’s biggest stages. Such a solution, of course, would require a lot more than a few minor edits to the rulebook.

Handling Injuries and Absences With Tennis Elo

Italian translation at settesei.it

For the last year or so, every mention of my ATP and WTA Elo ratings has required some sort of caveat. Ratings don’t change while players are absent from the tour, so Serena Williams, Novak Djokovic, Andy Murray, Maria Sharapova, and Victoria Azarenka were all stuck at the top of their tour’s Elo rankings. When their layoffs started, they were among the best, and even a smattering of poor results (or a near season’s worth, in the case of Sharapova) isn’t enough to knock them too far down the list.

This is contrary to common sense, and it’s very different from how the official ATP and WTA rankings treat these players. Common sense says that returning players probably aren’t as good as they were before a long break. The official rankings are harsher, removing players entirely after a full year away from the tour. Serena probably isn’t the best player on tour right now (as Elo insisted during her time off), but she’s also much more of a threat than her WTA ranking of No. 454 implies. We must be able to do better.

Before we fix the Elo algorithm, let’s take a moment to consider what “better” means. Fans tend to get worked up about rankings and seedings, as if a number confers value on the player. The official rankings are, by design, backward-looking: They measure players based on their performance over the last 52 weeks, weighted by how the tour prioritizes events. (They are used in a forward-looking way, for tournament seedings, but the system is not designed to be predictive of future results.) In this way, the official rankings say, “this is how good she has played for the last year.” Whatever her ability or potential, Serena (along with Vika, Murray, and Djokovic) hasn’t posted many positive results this year, and her ranking reflects that.

Elo, on the other hand, is designed to be predictive. Out of necessity, it can only use past results, but it uses those results in a way to best estimate how well a player is competing right now–our best proxy for how someone will play tomorrow, or next week. Elo ratings–even the naive ones that said Serena and Novak are your current No. 1s–are considerably better at predicting match outcomes than are the official rankings. For my purposes, that’s the definition of “better”–ratings that offer more accurate forecasts and, by extension, the best approximation of each player’s level right now.

The time-off penalty

When players leave the tour for very long, they return–at least on average, and at least temporarily–at a lower level. I identified every layoff of eight weeks or longer in ATP history, taken by a player with an Elo rating of 1900 or above*. In their first matches back on tour, their pre-break Elo overestimated their chances of winning by about 25%. It varies a bit by the amount of time off: eight- to ten-week breaks resulted in an overestimation around 17%, while 30- to 52-week breaks meant Elo overestimated a player’s chances by nearly 50% upon return. There are exceptions to every rule, like Roger Federer at the 2017 Australian Open, and Rafael Nadal, who won 14 matches in a row after his two-month break this season, but in general, players are worse when they come back.

* I used the cutoff of 1900 because, below that level, some players are alternating between the ATP and Challenger tours. My Elo algorithm doesn’t include challenger results, so for lower-rated players, it’s not clear which timespans are breaks, and which are series of challenger events. Also, the eight-week threshold doesn’t count the offseason, so an eight-week layoff might really mean ~16 weeks between events, with the break including the offseason.

Translated into Elo terms, an eight-week break results in a drop of 100 Elo points, and a not-quite-one-year break, like Andy Murray’s current injury layoff, means a drop of 150 points. Making that adjustment results in an immediate improvement in Elo’s predictiveness for the first match after a layoff, and a small improvement in predictiveness for the first 20 matches after a break.

Incorporating uncertainty

Elo is designed to always provide a “best estimate”–when a player is new on tour, we give him a provisional rating of 1500, and then adjust the rating after each match, depending on the result, the quality of the opponent, and how many matches our player has contested. That provisional 1500 is a completely ignorant guess, so the first adjustment is a big one. Over time, the size of a player’s Elo adjustments goes down, because we learn more about him. If a player loses his first-ever match to Joao Sousa, the only information we have is that he’s probably not as good as Sousa, so we subtract a lot of points. If Alexander Zverev loses to Sousa after more than 150 career matches, including dozens of wins over superior players, we’ll still dock Zverev a few points, but not as many, because we know so much more about him.

But after a layoff, we are a bit less certain that what we knew about a player is still relevant. Djokovic a great example right now. If he lost six out of nine matches (as he did between the Australian Open fourth round and Madrid) without missing any time beforehand, we’d know it was a slump, but most of us would expect him to snap out of it. Elo would reduce his rating, but he’d remain near the top. Since he missed the second half of last season, however, we’re more skeptical–perhaps he’ll never return to his former level. Other cases are even more clear-cut, as when a player returns from injury without being fully healed.

Thus, after a layoff, it makes sense to alter how much we adjust a player’s Elo ratings. This isn’t a new idea–it’s the core concept behind Glicko, another chess rating system that expands on Elo. Over the years, I’ve tinkered with Glicko quite a bit, looking for improvements that apply to tennis, without much success. Changing the multiplier that determines rating adjustments (known as the k factor) doesn’t improve the predictiveness of tennis Elo on its own, but combined with the post-layoff penalties I described above, it helps a bit.

The nitty-gritty: After a layoff, I increase the multiplier by a factor of 1.5, and then gradually reduce it back to 1x over the next 20 matches. The flexible multiplier slightly improves the accuracy of Elo ratings for those 20 matches, though the difference is minor compared to the effect of the initial penalty.

No more caveats*

* I thought it would be funny to put an asterisk after “no more caveats.”

Post-layoff penalties and flexible multipliers end up bringing down the current Elo ratings of the players who are in the middle of long breaks or have recently come back from them, giving us ranking tables that come closer to what we expect–and should do a better job of predicting the outcome of upcoming matches. These changes to the algorithm also have minor effects on the ratings of other players, because everyone’s rating depends on the rating of all of his or her opponents. So Taro Daniel’s Elo bounce from defeating Djokovic in Indian Wells doesn’t look quite as good as it did before I implemented the penalty.

On the ATP side, the new algorithm knocks Djokovic down to 3rd in overall Elo, Murray to 6th, Jo-Wilfried Tsonga to 21st, and Stan Wawrinka to 24th. That’s still quite high for Novak considering what we’ve seen this year, but remember that the Elo algorithm only knows about his on-court performances: A six-month break followed by a half-dozen disappointing losses. The overall effect is about a 200-point drop from his pre-layoff level; the “problem” is that his Elo a year ago reflected how jaw-droppingly good he had recently been.

The WTA results match my intuition even better than I hoped. Serena falls to 7th, Sharapova to 18th, and Azarenka to 23rd. Because of the flexible multiplier, a few early wins for Williams will send her quickly back up the rankings. Like Djokovic, she rates so high in part because of her stratospheric Elo rating before her time off. For her part, Sharapova still rates higher by Elo than she does in the official rankings. Despite the penalty for her one-year drug suspension, the algorithm still treats her prior success as relevant, even if that relevance fades a bit more every week.

Elo is always an approximation, and given the wide range of causes that will sideline a player, not to mention the spectrum of strategies for returning to the tour, any rating/forecasting system is going to have a harder time with players in that situation. That said, these improvements give us Elo ratings that do a better job of representing the current level of players who have missed time, and they will allow us to make superior predictions about matches and tournaments involving those players.

Under the hood

If you’re interested in some technical details, keep reading.

Before making these adjustments, the Brier score for Elo-based predictions of all ATP matches since 1972 was about 0.20. For all matches that involved at least one player with an Elo of 1900 or better, it was 0.17. (Not only are 1900+ players better, their ratings tend to be based on more data, which at least partly explains why the predictions are better. The lower the Brier score, the better.)

For the population of about 500 “first matches” after layoffs for qualifying players, the Brier score before these changes was 0.192. After implementing the penalty, it improved to 0.173.

For the 2nd through 20th post-comeback matches, the Brier score for the original algorithm was 0.195. After adding the penalty, it was 0.191, and after making the multiplier flexible, it fell a bit more to 0.190. (Additional increases to the post-layoff multiplier had negative results, pushing the Brier score back to about 0.195 when the 2nd-match multiplier was 2x.) I realize that’s a tiny change, and it very possibly won’t hold up in the future. But in looking at various notable players over the course of their comebacks, that’s the option that generated results that looked the most intuitively accurate. Since my intuition matched the best Brier score (however miniscule the difference), it seems like the best option.

Finally, a note on players with multiple layoffs. If someone misses six months, plays a few matches, then misses another two months, it doesn’t seem right to apply the penalty twice. There aren’t a lot of instances to use for testing, but the limited sample confirms this. My solution: If the second layoff is within two years of the previous comeback, combine the length of the two layoffs (here: eight months), find the penalty for a break of that length, and then apply the difference between that penalty and the previous one. Usually, that results in second-layoff penalties of between 10 and 50 points.

Known Unknowns for Rafael Nadal

When Rafael Nadal returns to the tour–very soon, we hope–he will be entering uncharted territory.  Plenty of players miss time to injury, but it is rare for a top player to miss anywhere near this much time.

In fact, only three top 10-ranked players have ever left the tour and returned after a layoff of six months or longer.

Only one of those three–Juan Martin del Potro, in 2010–was forced to rest due to injury.  John McEnroe twice left the tour for stretches of several months, and Tommy Haas took time off in 2002 to take care of his family.  Haas’s layoff turned into something a bit more relevant, as his sabbatical was extended by a shoulder injury he suffered in preparation for a comeback.

While del Potro’s future is still unclear, the precedent for Nadal is concerning.  None of those players ever returned to their pre-layoff rankings.

Del Potro’s story, in fact, is the most encouraging.  When he suffered his shoulder injury, he had recently won the US Open and reached the final of the World Tour Finals, reaching a career-high ranking of #5.  With the exception of a brief return in October of 2010, he missed almost exactly one year.  While he didn’t return to the top 10 for another year, he won two small tournaments early on and reached the semifinals of Indian Wells barely two months into his comeback.  Two years later, his ranking is up to #7, still short of his pre-injury peak.

When Haas left the tour at the end of 2002, he had just recently fallen from his career-high ranking of #2.  When he returned more than a year later, he had early success similar to Del Potro’s, reaching the 4th round at Indian Wells and winning two events in his first six months.  Yet he didn’t return to the top 10 for nearly three years.

McEnroe is the enigma of this bunch.  Ranked #2 in the world at the beginning of 1986, he needed a break from the tour.  Seven months later, he began a comeback at Stratton Mountain, where he reached the semis and lost to Boris Becker.  After a clunker of a first-round loss at the US Open, he reeled off 18 consecutive wins, including three over top-10 players.  That put him back in the top 10, but it was two years into the comeback that he regained a position in the top 5–in part due to another six-month layoff beginning in September 1987.

Aging patterns

What the recaps of Haas’s and McEnroe’s layoffs hide is that, while they weren’t playing, they were headed into an age range where most pros start declining.  At the time of their returns, McEnroe was 26, Haas 25–a typical player’s peak age, at least before today’s new era of indestructible 30-somethings.

While McEnroe has shown astonishing longevity, his years as a contender for world #1 were probably about over when he took his sabbaticals.  And Haas missed the year in which he might have played his very best tennis.

Neither player is a clear precedent for a clay court genius with knee problems, but the age factor is tough to ignore.  Nadal turned 26 in June, putting him right in between Haas and McEnroe at the times of their departures from the tour.

Assuming Rafa is healthy, there’s little doubt he’ll maintain his position in the top 10.  I’d be surprised if he didn’t win at least a couple of clay court events this year, even if he maintains a much-reduced schedule.  But if history is any indication, he has seen the last of the top two.