Wimbledon 2013: Who benefits the most from Day 1 upsets?

Day 1 at Wimbledon gave us something we almost never see: two stunning top-five upsets (Steve Darcis over Rafael Nadal and Monica Puig over Sara Errani). Upsets like those throw the most chaos into the pre-tournament storylines and predictions, which is what makes them so fun. After the dust settles, there’s always a logical question that follows -- How do the upsets affect everyone else’s chances in the draw?

It’s pretty obvious Nadal’s elimination makes Roger Federer’s path to the title a lot easier now that he can’t face Nadal in the quarters. But how far do the ripples extend? How are the chances of contenders like Novak Djokovic and Andy Murray, further away from Nadal in the draw, affected? What about John Isner and Lleyton Hewitt, semi-serious grenade throwers who were slated for a potential fourth-round matchup? And what about the guy that actually beat Nadal, Steve Darcis? Even though Darcis still probably won’t win Wimbledon, how does his overall outlook change from getting over a huge first-round hurdle?

To put some numbers to these ripple effects, I went back and looked at the Advanced Baseline forecasts for Nadal and Errani. Then I reran the tournament simulations where the only change was giving Darcis and Puig a bye to lock in their wins. The differences between the two forecasts represent the ripple effect of Nadal and Errani being removed from the draw.

It’s easiest to convey that forecast differential in terms of expected points (discussed at length here) for a couple reasons. Not only does it convey the full range of outcomes beyond just odds of winning the tournament, but expected points are also zero-sum. If you think of Nadal’s 533 expected points as his total equity in the prize pool, when he loses, he forfeits 523 of those points (you get 10 points for playing in the first round), which have to be redistributed among the rest of the field.

First, a couple quick qualifiers. Nadal’s early exit isn’t quite as earth-moving as some are making it out to be -- I only had him at 8.4 percent to win, so the size of the ripples aren’t as big as something like a Djokovic or Federer upset. And Errani’s ripples are heavily dampened by Serena Williams’ dominance over the field, basically summed up as “doesn’t matter, Serena’s still going to win.” That being said, Errani had the sixth-highest expected points total, so the ripples are still noteworthy.

Here are the top 12 players that ended up with the most of Nadal’s and Errani’s expected points (top seeds in bold):

How many points you gain from a big name getting upset depends on two things: your proximity to that name in the draw and your overall skill level. On the women’s side, 11 of the 12 top gainers are in Errani’s section of the Sharapova region. Proximity in the draw to the upset seems to be the driving variable, which is why contending names like Li Na and Victoria Azarenka don’t show up here. Monica Puig, who did the hard work of pulling off the upset, gained 36 percent of Errani’s prize pool equity.

The men’s side is a little more interesting to look at, because Nadal was in the Federer region, and Federer was the pre-tournament Advanced Baseline favorite. Eight of the top 12 gainers were in Nadal’s section of 16. Interestingly, the ripples extended all the way to Jo-Wilfried Tsonga and David Ferrer on the complete opposite sides of the draw, but not to Djokovic or Murray. The math gets a little fuzzier here, but it seems like when you get far enough away from the upset in the draw and you have a higher ranking than the upset victim, your ranking takes over as the dominant variable, and the ripples don’t affect you as much.

Federer’s expected points rose by a whopping 14 percent (and his odds of winning Wimbledon by seven percent) without lifting a finger. Compare that to Steve Darcis, who pulled off the upset but only got 18 percent of Nadal’s prize pool equity. It’s an interesting contrast to the women’s table; just because you pull off the upset, it doesn’t mean you automatically gain the most expected points. And the more your draw is unbalanced, like it was this year with a Federer/Nadal quarterfinal matchup, the more likely the ripple effects of the upset won’t spread beyond the imbalanced section. Whether that’s a bug or a feature is a really interesting question.

A lot of your success is determined by factors outside of your control. Federer got an amazing boost to his win odds without doing a thing. Yes, he was in the best position to capitalize because he’s very good at tennis, but it doesn’t change the fact that part of Steve Darcis’ efforts worked directly to Federer’s benefit. It’s a reminder that not all Slam achievements are created equal. As easy as a shortcut as it might be to cite players’ best Slam records when debating who’s better, that leaves a whole lot of information out of the story.