The Summer of Jeff

The Wild Card Effect

Posted in tennis by Jeff on January 24, 2011

I’ve written before about the types of players awarded wild cards into professional men’s tennis tournaments.  While they can be categorized in different ways, there are two characteristics that are true of almost all wild cards:

  1. Without a wild card, they would not be able to play in the tournament.
  2. Tournament organizers see them as an asset to the event.

The first isn’t quite true; many wild cards would otherwise enter the qualifying draw, and some would reach the main draw that way.  We can still conclude that WCs are, at least according to ATP entry rankings, inferior to other players who appear in the main draw.  The only possible exceptions worth mentioning are qualifiers and other wild cards.

The second doesn’t necessarily tell us anything about the skill level of a player.  Simply having James Blake in the draw probably boosts tickets sales for any event in the U.S.  Other WCs are awarded to promote a tournament in other ways, perhaps by giving one WC to the winner of a junior event, or a special qualifying tournament for local amateurs.

While these cases are common enough, a major factor in the awarding of wild cards is the tournament organizer’s belief that a WC can compete.  So the WC goes to a player returning from injury, or a veteran coming back from retirement.  Or a junior who is rocketing up the rankings, or who has recently won a major collegiate event.

All this is to say, in the aggregate, players granted wild cards are usually better than their ranking says they are.

Thus, when we look at matches with one wild card and one non-wild card and apply my algorithm to predict the winner, we should anticipate that wild cards outperform expectations.

Empirical results

In fact, they do.  The effect is substantial, and it holds at multiple levels of competition.

In testing the hypothesis, I controlled for home court advantage, an important consideration that is easily conflated with the wild card effect.  After all, a large percentage of wild cards are granted to local players, so without careful analysis, it would not be clear how much of the advantage can be attributed to the wild card selection or the benefits of playing in one’s home country.

I ran the numbers with a dataset comprising all ATP main draw, ATP qualifying draw, and Challenger main draw matches from 2008 to 2010.  The results were fairly consistent from year to year.

At the ATP main draw level, the dataset yielded over 900 matches between a wild card and a non-wild card.  The wild card won the match about 15% more often than expected.  We can approximate this effect by multiplying the WC’s ranking points by 1.3.

The other two levels showed even larger effects over about 2600 relevant matches.  In ATP qualifying and Challenger main draw matches, wild cards won more than 25% more than expected.  We can approximate this effect by multiplying the WC’s ranking points by 1.55.

Commentary

The existence of a positive “wild card effect” is not a surprise, nor is the magnitude.  Essentially, when a player is awarded a wild card, we’re given more information about him than ranking points otherwise offer.

I suspect the difference in magnitude between the higher and lower levels is fairly straightforward, as well.  While some players receive ATP wild cards straight from the amateur ranks, as can be the case with collegiate champions, most ATP wild cards go to somewhat established players on the fringes of success.  These players are often inside the top 150, meaning that they’ve played a lot of professional tournaments, so while their ranking might undervalue them slightly, it is a fairly accurate gauge of their ability level.

By contrast, qualifying and challenger-level wild cards often go to less experienced players.  They may not be full-time professionals or they may spend most of their time playing collegiate or junior tournaments.  They usually have rankings, but the point totals may only be based on a handful of events.

Example from Australia

The most successful wild card in the Australian Open was Aussie youngster Bernard Tomic, who reached the third round, beating Jeremy Chardy and Feliciano Lopez before losing to Rafael Nadal.

As he was a local and a wild card, we now know to adjust his ranking points twice before estimating his likelihood of winning a match.  Instead of estimating his talent with his pre-tourney ranking point total of 239, we adjust upward to 435.  That still puts him as an underdog against Chardy’s 960 points, but it means we would have given him a 30% chance of winning instead of an 18% chance.

Of course, the 2011 Australian Open isn’t very instructive here, since six of the other wild cards lost their first matches, while the final WC, Benoit Paire, drew qualifier Flavio Cipolla in the the first round, and was a favorite.

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