Is Grand Slam Qualifying Worth Tanking For?

Earlier today in Hobart, Naomi Osaka lost her second-round match to Mona Barthel. Coming into the match, she was in a tricky position: If she won, she wouldn’t be able to play Australian Open qualifying. For a young player outside the top 100, a tour-level quarterfinal would be nice, but presumably Melbourne was intended to be the centerpiece of her trip to Australia.

Since she lost the match, she’ll be able to play qualifying. But what if she hadn’t? Is this a situation in which a player would benefit from losing a match?

Put another way: In a position like Osaka’s, what are the incentives? If she could choose between the International-level quarterfinal and the Slam qualifying berth, which should she pick? Or, put more crassly, should a player in this position tank?

Let’s review the scenarios. In scenario A, Osaka wins the Hobart second-rounder, reaches the quarterfinal, and has a chance to go even further. She can’t play the Australian Open in any form. In scenario B, she loses the second-rounder, enters Melbourne qualifying and has a chance to reach the main draw.

Before we go through the numbers, take a guess: Which scenario is likely to give Osaka more ranking points? What about prize money?

Scenario A is more straightforward. By reaching the quarterfinals, she earns 30 additional ranking points and US$2,590 beyond what a second-round loser makes. Beyond that, we need to calculate “expected” points and prize money, using the amounts on offer for each round and combining them with her odds of getting there.

Let’s estimate that Osaka would have about a 25% chance of winning her quarterfinal match and earning an additional 50 points and $5400. In expected terms, that’s 12.5 points and $1,350. If she progresses, we’ll give her a 25% chance of reaching the final, then in the final, a 15% chance of winning the title.

Adding up these various possibilities, from her guaranteed QF points to her 0.94% chance (25%*25%*15*) of winning the Hobart title, we see that her expected rewards in scenario A are roughly 48 ranking points and just under $4,800.

Scenario B starts in a very different place. Thanks to the recent increases in Grand Slam prize money, every player in the qualifying takes home at least US$3,150. That’s already close to Osaka’s expected financial reward from advancing in Hobart. The points are a different story, though: First-round qualifying losers only get 2 WTA ranking points.

I’ll spare you all the calculations for scenario B, but I’ve assumed that Osaka would have a 70% chance of winning qualifying round 1, a 60% chance of winning QR2, and a 50% chance of winning QR3 and qualifying. Those might be a little bit high, but if they are, consider it compensation for the possibility that she’ll reach the main draw as a lucky loser. (Also, if we knock her chances all the way down to 50%, 45%, and 40%, the conclusions are the same, even if the points and prize money in scenario B are quite a bit lower.)

Those estimated probabilities translate into an expectation of about 23 ranking points and US$11,100. Osaka isn’t guaranteed any money beyond the initial $3,150, but the rewards for qualifying are enormous, especially compared to the prize money in Hobart. A first-round main draw loser in Melbourne takes home more money than the losing finalist does in Hobart.

And, of course, if she does qualify, there’s a chance she’ll go further. Since 2000, female Slam qualifiers have reached the second round 41% of the time, the third round 9% of the time, the fourth round 1.8% of the time, and the quarterfinals 0.3% of the time. Those odds, combined with her 21% chance of reaching the main draw in the first place,  translate into an additional 7 expected ranking points and $2,600 in prize money.

All told, scenario B gives us 30 expected ranking points and US$13,600 in expected prize money.

The Slam option results in far more cash, while the International route is worth more ranking points. In the long term, those ranking points would have some financial value, possible earning Osaka entry into a few higher-level events than she would otherwise qualify for. But that value probably doesn’t overcome the nearly $9,000 gap in immediate prize money.

I hope that no player ever tanks a match at a tour-level event so they can make it in time for Slam qualifying. But if one does, we’ll at least understand the logic behind it.

Should Andy Murray Skip the Tour Finals to Prepare for Davis Cup?

After advancing to the Davis Cup final, Andy Murray floated the idea that he might skip the World Tour Finals to prepare. The Belgian hosts are likely to choose clay for November’s Davis Cup tie (in part to make Murray less comfortable), and if Murray reached the final round in London the week before, he would have only four days off to recover and adjust to the different surface.

A lot of factors will go into Murray’s ultimate decision: how much importance he gives each event, how much he thinks fatigue will affect him, and how likely it is that the ATP would sanction him for skipping a required event. For today, I’ll have to ignore all of those and focus on the one most amenable to analysis: The effect of switching surfaces right before a Davis Cup tie.

Shifting from one surface to another immediately before Davis Cup is common. From 2009 to the present, there have been just over 2,000 World Group, Group 1, and Group 2 Davis Cup singles rubbers, and almost 450 of those involved at least one player who had played the previous week [1] on a different surface. It’s very rare that both players switched surfaces, so we have a sample of 432 matches in which one player changed surfaces from the previous week, and the other player either played or (presumably) prepared on the same surface.

At the simplest level of analysis, the switchers have been surprisingly effective. In those 432 matches between switchers and non-switchers, the switchers won 275, or 63.6% of the time. When we narrow the sample to the 130 times the switcher reached at least the round of 16 the week before Davis Cup (and, thus, had even less time to adjust), the results are surprisingly similar: 82 wins, or 63.1% in favor of the switchers.

Of course, there are all sorts of biases that could be working in favor of the switchers. The better the player, the less likely he can change his schedule to better prepare for Davis Cup, leaving him stuck on the “wrong” surface the week before a tie. And the better the player, the more likely he was a switcher in the smaller sample, one of those who reached the round of 16 the week before.

To evaluate the effect of switching, then, we must proceed with more subtlety. If switchers are more likely to be the favorites, we need to consider each player’s skill level and estimate how often switchers should have won. To do that, we can use JRank, my player rating system with surface-specific estimates for each competitor.

Immediately, we lose about 15% of our sample due to matches involving at least one player who didn’t have a rating at the time [2]. These are almost all Group 2 matches, so its doubtful that we lose very much. In the slightly smaller pool of 361 matches, the switcher won 62.0%, and when the switcher reached the round of 16 the previous week, he won 60.0%.

JRank confirms that the sample is strongly biased toward switchers. The player changing surfaces was favored in 69.8% of these contests. To take an extreme example, Murray went from hard courts at the 2013 US Open to clay courts in the World Group playoff against Croatia. Against Borna Coric, who hadn’t played the week before, Murray was a 99.1% favorite, and of course he won the match.

Once we calculate the probability that the switcher won each of the 361 matches, it turns out that the switchers “should have” won 227, or 62.8% of the time. That’s almost indistinguishable from the historical record, when the switchers won 224 matches. In the smaller sample of 120 matches when the switcher reached the round of 16 the previous week, switchers “should have” won 72 matches. As it happened, they won exactly 72.

In other words, it doesn’t appear to be a disadvantage to play Davis Cup matches on an unfamiliar surface. JRank-based predictions are primarily based on “regular” matches, so if switchers are performing at the level that JRank forecasts for them, they’re playing as well as they would at, say, the third round of a Slam, when the surface is familiar.

This isn’t a clear answer to Murray’s dilemma, of course. If he plays, say, Roger Federer and Novak Djokovic in back-to-back three-setters on Saturday and Sunday, then travels to a different venue, handles tons of press, and practices with a different set of coaches and fellow players before a big match the following Friday, he faces more of a challenge than your typical surface-switcher in our dataset.

However, there’s little evidence that surface-switching alone is a good reason to skip the Tour Finals. If history is any guide, Murray will play very well on the Belgian clay–just as well as he would at the same venue in the middle of the clay season.

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