Robin Vik, a 25-year-old from the Czech Republic, double-faulted 13 times in a near upset of hometown favorite Lleyton Hewitt in the first round of the Australian Open this week. If Vik had just double-faulted 23 times, his chances of winning the match would have improved.

As much as Vik might learn about heart and grit from his 6-4, 2-6, 5-7, 7-6 (4), 6-3 loss to Hewitt in three hours and 46 minutes, the greater lesson might be in probability.

For the match, Vik attempted 165 first serves, making 104 of them for a firstserve percentage of .630. He won the point on 71 of those 104 first serves, a winning percentage of .683 (average firstserve speed was 104 mph; his fastest was 121 mph). So far, so good.

Vik’s second serve was not so good. Truth be told, it was awful. He attempted 61 second serves (average speed: 86 mph) and missed 13 of them (his 13 double faults). Of the 48 second serves he hit in the box, he won 22 points. In sum, Vik’s winning percentage on second serves was 22 of 61 (.361). Remember, missed second serves – that is, double faults – count as lost points, unlike missed first serves.

We now know the probability of Vik winning a point on his second serve: .361.To determine the probability of Vik winning a point on his first serve, one can multiply his first-serve percentage (.630) by his first-serve winning percentage (.683), or if it helps to clarify matters,divide the number of points he won on his first serve, 71, by the number of first serves he attempted, 165. Either way, the answer is .430.

Now compare. The probability of Vik winning a point on a first-serve attempt was .430, compared to .361 for a secondserve attempt. If Vik’s coach were a statistician, he might instruct Vik to uncork first serves every time, double faults be damned. Vik attempted 61 second serves. If he instead went for first serves during those attempts and made only 63% of them – his first-serve percentage – he would have ended the match with 23 double faults (23 missed second serves). But of the 38 serves he made, he would have won 26 of them (38 times .683, his first-serve winning percentage). That’s 26 points won with an aggressive second serve and 23 double faults, versus the 22 he did win with a weak second serve and 13 double faults.

It’s not certain that Vik would have prevailed had he won four more points (he won five more points than Hewitt as it is).When he served for the match in the fourth set, leading 6-5, he lost the game at love – four points to none. Before we get too excited, it must be said that Vik suffered a statistical aberration in that game. He made three of four first serves and did not win a single one. Those first serves were 114 mph, 100 mph, and 101 mph, respectively; Hewitt hit an amazingly difficult – and unlikely – return off the first one, so Vik might have been better off going for more on the next two points rather than being awed by Hewitt’s skill and easing up.

After Hewitt rallied in the fourth set, ESPN2 commentator Brad Gilbert said Hewitt should go for more on his second serve, since Vik was pounding those returns. This was a case of perception not coinciding with reality. Rather than heed Gilbert’s advice Hewitt should have taken something off his first serve and put more of them in the box.

Using the same formulas, the probability of Hewitt winning a point on his first serve was .366 compared to .418 on his second (this is a function of Hewitt’s low first-serve percentage,.575).So,if he had hit second serves the entire match, he would have won 111 points on serve rather than 101 (.418 multiplied by 265, the total number of serves – first and second – that Hewitt attempted). He would have double faulted 7 times, rather than 13. If he had gone for first serves every time, he almost certainly would have lost the match, winning 97 points compared to 101 and double faulting 34 times.

This analysis is by no means the end of the story. Hewitt fared better on firstserve returns as the match wore on, losing 93% and 86% of those points in sets two and three, but only 52% and 57% in sets four and five. Service placement and spin are of paramount importance, too. And while it is very often accurate to say that a player with a weak second serve would win more service points by cutting loose, the opposite cannot be stated with as much confidence. Increasing service percentage with slower serves might give an opponent too many softballs and too much time to find a groove. The lesson for Hewitt is that he should have varied his serves more. But under no circumstances should he have tried to hit his second ones any harder.

Fear and nerves cannot be overestimated, either. It’s easy for a columnist to say a player should just fire away and not worry about 23 double faults, but for an inexperienced player in a Grand Slam against the no. 3 seed in his home country – well, that’s another matter. Still, for someone with a second serve as unreliable as Vik’s, it merits consideration.

Two other top pros could have let up on their first serves during Wednesday’s second-round matches. Maria Sharapova, who defeated Ashley Harkleroad 6-1, 7-5, had a winning probability of .538 on her second serve versus .456 on her first serve. If she could have maintained the higher probability throughout the match – hence improving her so-so first serve percentage of .544 – she would have won four more points than she did,and double faulted once rather than four times.

Roddick’s numbers are more dramatic. He has one of the best second serves in tennis, and his second-round opponent,Wesley Moodie, had no idea how to handle it in a 7-5,6-3,6-2 loss. Roddick’s winning percentage on second serves was .667, versus .526 on first serves. Extended over the match, the higher winning percentage would have resulted in 11 more points on serve than he actually won (72 to 61).

Moodie, like Roddick, is an excellent server, but his return is horrid: In 2005, he won just 16% of receiving games, 5% worse than Roddick, also a poor returner. There’s no reason to boom serves against Moodie, unless you are winning comfortably and feel like polishing your swing for later in the tournament.

There is a trend in all of this: Great tennis players more often produce numbers like Hewitt, Roddick, and Sharapova. Champions win points on second serves. Otherwise, they would end up like Vik.