Withdrawal Effects

Yesterday, Mardy Fish withdrew from his fourth-round match against Roger Federer.  As we saw earlier today, Federer may gain some benefit from the extra rest, but with the additional rest days built into the grand slam schedule, Roger runs the risk of getting too little time on court.

What’s the true effect, then?  Will the extra rest make Federer an even bigger favorite in his quarterfinal match against Tomas Berdych?  Or will match-court rust hold him back?

As it turns out, there is virtually no effect.  Players handed a walkover win almost exactly half of their next matches, and a closer look at those matches reveals that 50% is about what we would’ve expected from them, walkover or not.

To hunt for a potential relationship, I found 139 ATP main draw walkovers since 2001 where the winner went on to play another match at the same tournament–in other words, excluding finals.  While it may seem that players tend to withdraw when they’re least likely to win a match (as with Fish this week, or like the other two players to withdraw before facing Federer this year), there’s nothing to that theory, either. The average pre-match odds of the withdrawing player are about 51%.

Thus, we can work on the assumption that there’s little bias in the pool of 139 men who received a free pass to the next round.  For every Federer, there’s a Donald Young advancing uncontested over Richard Gasquet.  Balancing the withdrawals of players without a chance may be higher-ranked players who are quicker to withdraw because their success allows them to play it safe and make longer-term decisions.

In the 139 follow-up matches, our players went 67-72, winning 48.2% of the time.  Prematch predictions (generated by Jrank) would have projected a winning percentage of 48.9%.

If we narrow the search to slams, we get a nearly-meaningless pool of only 12 matches.  The player coming off the walkover went 6-6; prematch numbers would’ve predicted 7-5.  Perhaps rust does play a small part; considerably more likely is that the walkover simply doesn’t affect the beneficiary.

For Federer fans, though, there’s little reason for concern.  This is the ninth time in his career he’s advanced via walkover, and he’s only lost the next match twice.  One of those was in 2002.  The other was in Indian Wells in 2008.  The man who beat Fed?  Mardy Fish.