Why tennis players don’t take more risks on second serve

So turns out tennis players basically have the maths right.

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Why Tennis Players Don’t Take More Risks On Second Serves
04/09/2014
Five Thirty Eight
Carl Bialik

If you’ve ever watched a tennis player dominate with the first serve but saw the second serve obliterated by the returner, you might have wondered: Why don’t more players go for it on their second serve? Wouldn’t they be better off treating their second opportunity to serve like their first one?

The answer almost always is no.

Most servers win a much higher percentage of points on their first serve than their second serve. For example, in his five-set marathon loss to Kei Nishikori as Monday night turned to Tuesday morning at the U.S. Open, Milos Raonic won 87 percent of his first-serve points but just 47 percent of his second-serve points.

During that match, Min Han, a biologist at the University of Colorado, emailed me. “I wonder whether some of the big servers in men’s tennis should serve the fast ‘first’ serve all the time,” Han wrote. “For some of these guys, the difference between the winning percentage on their first serve and that on the second serve seems huge.”

It’s a good suggestion. But the season-long numbers suggest nearly every player would be hurt, not helped, by treating the second serve like a first serve. Except in a couple of cases, the higher probability that the second serve lands in the court more than compensates for the higher effectiveness of first serves.

Let’s start with the average Top 50 men’s player. This year heading into the U.S. Open, he wins 73.6 percent of service points when the first serve lands in, compared to 57.5 percent when the second serve lands in. But his first serve lands in just 61.9 percent of the time, compared to 91.1 percent of second serves. So if he went for his first serve on both points, he’d win 73.6 percent of second-serve points when the ball lands in, but double fault on 38.1 percent of them. His second-serve winning percentage would be just 45.6 percent, compared to 52.4 percent now. Bad move.

This is just an average. It varies widely by player. Mikhail Youzhny has a relatively weak first serve without landing in the court all that often, so he’d be especially unwise to go for his first serve again given a second opportunity. His second-serve winning percentage would drop by 12.7 percentage points.

By contrast, Ivo Karlovic, who is 6 feet 10, has a relatively weak second serve and usually lands his excellent first serve in, so he’d gain 2 percentage points on his second-serve winning percentage if he went for his first serve twice. That’s a modest gain, and Karlovic is the only player in the Top 50 who’d get a high enough reward to justify the high-risk tactic. (Raonic would be nearly even, but slightly worse off — as he would have been if he’d gone for second-serve bombs against Nishikori, since he missed so often on first serves in that match.)

Read the rest of the article (including the graphs)

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