Murray should hit two first serves

Well, I'm depressingly in on this Friday night, so I conducted some tennis-related research. A thought occurred to me; although it's always been accepted that you're supposed to hit a powerful first serve and safer, more spinny second one, is that the logical thing to do? If you're getting more of your second serves in than you are your first but you're also losing more points on them, would it not be equally sensible to hit two powerful first serves on every point?

I took a look at the serving data from the men's semis and it makes quite interesting reading. Here is the overall point winning percentages on the first and second serves for Djokovic in the semi:

- 1st serve: 61% first serves x 66% points won on first serve = 40% chance of winning a point when he hit a first serve.

- 2nd serve: 91% second serves x 45% points won on second serve = 41% chance of winning a point when he hit a second serve.

The rest of the players were as follows:

- Murray: 1st serve = 40% chance of winning the point
2nd serve = 26% chance of winning the point

- Federer: 1st serve = 42% chance of winning the point
2nd serve = 50% chance of winning the point

- Nadal: 1st serve = 53% chance of winning the point
2nd serve = 61% chance of winning the point

By '% chance of winning the point' here I mean the chance of both the serve going in and then the point being won after it's gone in. Based on this, Federer and Nadal should both hit two second serves, Murray should hit two first serves, and Djokovic can pick and choose since it doesn't make much difference. I couldn't watch either of these matches so I can't vouch for how the players served, and to how valid these results are.

A few observations:

- It's amusing how Federer is renowned for his effective first serve, when his second won him a higher percentage of points (although, to be fair, Federer's second serve is also known as being strong).

- Nadal's serve was easily the most effective, although I'm willing to bet Federer's returning had a lot to do with this.

- Murray's second serve is still painfully weak.

1st serve: 61% first serves x 66% points won on first serve = 40% chance of winning a point when he hit a first serve.

Not sure I follow the logic here. It says 66% chance of winning point when 1st serve...not 40%. Did I miss something?

What it says is that 40% of points are won with a first serve....not quite the same as saying 40% chance of winning the point with a 1st serve.

For the Djokovic example...61% of his first serves went in, and of those 61% he won 66% of the points. Therefore, when he went up to the baseline to hit a first serve, he had a 0.61 x 0.66 = 0.4026 (40.26%) chance of coming away with the point.

Chazfazzer wrote:...
Here is the overall point winning percentages on the first and second serves for Djokovic in the semi:

- 1st serve: 61% first serves x 66% points won on first serve = 40% chance of winning a point when he hit a first serve.

- 2nd serve: 91% second serves x 45% points won on second serve = 41% chance of winning a point when he hit a second serve.

So Djokovic hit 61% first serves and 91% second serves?

Djokovic's first serves in went in 61% of the time and his second serves went in 91% of the time. The second serve figure can be calculated by using the fact that he hit 67 second serves into play (according to the stats) and 6 double faults - 67/(67+6) = 0.91 = 91%. The percentages for the first and second serves are mutually exclusive; it's not like I'm saying he hit 152% serves overall.

This is muddled since you don't lose a point if your first serve doesn't go in (no point has been played) whereas you do if your second doesn't go in.

The matter requires reformulating.

According to your stats Djokovic has a 55% chance of losing a point on the second serve but only a 33% chance of losing a point on the first serve.

That would be according to the stats on the website. Once he's made a first serve, he has a 33% chance of losing the point. Once he's made a second serve, he has a 66% chance of losing the point. This makes sense, does it not? It's more likely that he'll lose the point after a weaker second serve. The difference between the two is that he also has a greater chance of getting the second serve in, which evens the winning percentages out.

Yes, but in terms of winning points whether you make the first serve or not is not the same as whether you make the second since the consequences are different. So whether most of your points are won on the first or second serve overall in a match doesn't affect whether or not you should use your first serve to put yourself in a position whereby if it goes in you're more likely to win the point since if it doesn't go in you have a second. It is the logical thing to do.

That's pretty much the point I'm making. You go for the safe second serve because the consequence if you miss is that you lose the point. But, especially with Murray, even though his second serve goes in much often than his first serve he would be better served (sorry about the pun!) by hitting a hard serve twice in a row. He would hit more double faults, but he would, based on these stats, win more points overall. Of course, this is based purely on the numbers; the added pressure of it being a second serve would probably make him miss a harder serve more often on the second delivery.

Ah, you're quite right.
My god, 26% is abysmal.

What Murray needs to do is to practice hitting second serve after second serve in practice/training prior to starting a Slam Major so that come the semi-final stages onwards, it is such a potent weapon that he is gaining many cheap, easy points from this serve just as the great Pete Sampras managed to do on his second serve delivery when facing the likes of Andre Agassi, Patrick Rafter.

The thing is that a second serve has little to do with practice or even stats but nerves!...or heart as we call it.

Why? cause a second serve can turn into a double fault. That's why there is a huge gap between Murray's first serve and 2nd serve. That's the reason why Sampras has 14 slams and Goran only 1. Those 2nd serve pulled their careers apart. Pete had a great gutsy second serve while Goran, despite having a better first serve, was getting very nervous on his second serve, especially on key points.

Murray's poor second serve pace is simply teh reflexion of his passive game at rallies. Give him a weak player he can physically outlast like Llodra and he shows lots of heart, give him a tougher opponent and teh fears can be easily read in his game.

What were murray's stats for the semi-final? Perhaps serving at full pace on second serves could have swung the match his way.

Murray's second serve got crushed by Djokovic 19 of 64 points, well below 30 percent of second serve won. Murray has a very good first serve. I don't think that this strategy will pay dividends in the long run. He just needs to work on the second serve. His first serve gives him some free points and he shouldn't weaken it to protect his second serve. Lets remember he is serving to the best returner in the world on a very slow surface.

Interesting stuff Chazfazzer.

Where exactly does this leave Sharapova?

The forehand and the second serve have always been Andy's weaknesses, the former having improved to an extent while the latter continues to stagnate.

His enormous desire and physical strength keep him competitive against Djokovic and Nadal, but the feeling always is that his game is too technically inefficient to beat them in grand slam play.

Look at the semi yesterday. Deep into the 5th Djokovic’s forehand still had that liquid ‘timed’ quality; Murray’s shovelled shots were guaranteed to break down earlier.

As an aside I feel it at least in part down to the equipment he has modelled his game around. That Head frame he uses is very thin for a modern racquet and he reportedly strings the thing so tight it borders on the abusive. To rally with the top guys with a stick like that must be nigh on impossible.

For Sharapova, in her last match:

- Chance of winning the point on her 1st serve: 34%
- Chance of winning the point on her 2nd serve: 15%

Basically, when hitting a second serve, she would only win the point one out of about every 6 times. Pretty awful, although she was thrashed!

And just to be clear, I'm not about to go out and start smacking my own second serves at full speed! It's just interesting how psychology may prevent us from taking the best strategy...

Chazfazzer thanks for that!

In all seriousness most club players know the value of hitting a "percentage" first serve about half way between the first and second serve with placement.

Federer is a past master of that particular serve but most seem to go all out on the first serve and hope that their second serve isn't called upon too often.

Certainly with Murray Djokovic was all over his second serve and likewise for Sharapova against Azarenka.

Maybe you're only as good as your second serve it seems?

Chazfazzer wrote:That's pretty much the point I'm making. You go for the safe second serve because the consequence if you miss is that you lose the point. But, especially with Murray, even though his second serve goes in much often than his first serve he would be better served (sorry about the pun!) by hitting a hard serve twice in a row. He would hit more double faults, but he would, based on these stats, win more points overall. Of course, this is based purely on the numbers; the added pressure of it being a second serve would probably make him miss a harder serve more often on the second delivery.

So you're saying he should hit two harder i.e. first serves as opposed to two slower second serves for both serves?

Chazfazzer wrote:

Nore Staat wrote:

Chazfazzer wrote:...
Here is the overall point winning percentages on the first and second serves for Djokovic in the semi:

- 1st serve: 61% first serves x 66% points won on first serve = 40% chance of winning a point when he hit a first serve.

- 2nd serve: 91% second serves x 45% points won on second serve = 41% chance of winning a point when he hit a second serve.

So Djokovic hit 61% first serves and 91% second serves?

Djokovic's first serves in went in 61% of the time and his second serves went in 91% of the time. The second serve figure can be calculated by ...

So you are saying that the 9% of the second serves that went out, don't count as losing the point on the second serve?

CF there is a conundrum with any player's second serve.

The problem is how to make it as effective as possible without going for too much and double faulting too often. Obviously a high 1st serve % is key here to reduce any player's reliance on a second serve especially since there are so many good returners of the serve in today's game.

So you are saying that the 9% of the second serves that went out, don't count as losing the point on the second serve?

I factored that in with the use of the 91%. Essentially, you can think of him as having a second serve percentage of 91%, rather like you would think of the normal first serve percentage stats.

So you're saying he should hit two harder i.e. first serves as opposed to two slower second serves for both serves?

For Murray, yes. Based on his match vs Djokovic, he would have been more successful had he hit two hard serves on every point rather than one hard one and one softer one. I didn't see the match, so I'm assuming Murray did follow the normal pattern of serving (ie bigger first serve, safer second). Maybe he already was hitting hard on both serves; in that case, my analysis is pretty much irrelevant.

For Federer, he would have done better hitting two 'second' serves, although the problem with Federer is that he mixes his serves up so much that defining a 'first serve' and 'second serve' can be difficult.

How would Federer have done better hitting two slower serves? The logic only goes one way, it applies to those whose second serves aren't good enough but not the other way round.

Murray when he get's going has one of the top 10 most powerful serves on the tour, no point in not using such a weapon even although it has more chance to miss. Rolling two serves in are for WTA players.

I've just realised the title has been wrong this entire time! It should have been 'first' rather than 'second' serves...

Yeah, that was the confusing bit.

Ha, apart from that minor mistake, it was all good.

You need to provide the original stats for Murray to determine whether serving two first serves or one first serve + one second serve would have been better. It cannot be determined from what you have presented for Murray due to the way you have defined the serving stats:
Murray: 1st serve = 40% chance of winning the point
2nd serve = 26% chance of winning the point

Well Nore Staat, after reading your post, I have to concede that you're correct here. I made the mistake of treating each serve as a separate event without accounting for the fact that missing the first serve would not lead to losing the point, but instead would lead to a second serve.

Still, it's quite interesting that for Murray it wouldn't make any difference whether he hit two first serves or a first followed by a second. I'll try it with Federer (vs Nadal):

Two First Serves, 100 ball scenario again
1) 1st serve: 64% first serves x 66% won on first serve
64 balls go in, and 42 of those points are won, 22 lost

36 balls remain
2) 1st serve: 64% first serves x 66% won on first serve
23 balls go in, and 15 of those points are won, 8 lost
13 are double faults

Points won = 42 + 15 = 57
Points lost = 22 + 8 + 13 = 43
Total: 57 points won, 43 points lost

One first serve, one second serve scenario
1) 1st serve: 64% first serves x 66% won on first serve
64 balls go in, and 42 of those points are won, 22 lost

36 balls remain
2) 2nd serve: 91% second serves x 55% won on second serve
33 balls go in, and 18 of those points are won, 15 lost
3 are double faults

Points won = 42 + 18 = 60
Points lost = 22 + 15 + 3 = 40
Total: 60 points won, 40 points lost

Two second serves scenario
1) 2nd serve: 91% second serves x 55% won on second serve
91 balls go in, and 50 of those points are won, 41 lost

9 balls remain
2) 2nd serve: 91% second serves x 55% won on second serve
8 balls go in, and 5 of those points are won, 4 lost
1 is a double fault

Points won = 50 + 5 = 55
Points lost = 41 + 4 + 1 = 45
Total: 55 points won, 45 points lost

So, turns out the standard serving is the best (at least for Federer), but not by an awful lot. Although I guess those few points could make all the difference over the course of a match. Thanks Nore Staat for correcting my dodgy maths!

I deleted my comment because I realised later it pertained to the Djokovic stats, so the comment I made (now deleted) was that for Djokovic it made no difference whether he served two first serves or whether he served as per normal.

For Murray it might indeed be the case that two first serves would be best but I couldn't work it out because you hadn't provided the break down of the stats.

Anyway it is good you have picked up on it - so please work it out for Murray going back to the original stats

Interesting stats...once all sorted.

One point is that I do not believe that teh stats of serving first serve twice woudl be the same. A player will feel th etension one way or another and therefore the percentage of 1st serve kind (played as a second serve) will most likely go down resulting in either even more double faults than expected...or not quite a first serve.


I suspect Pete was going for nearly 2 first serves the day he felt well, especially if serving at 40/0 or 40/15.

Ok, last one!

Two first serves:
1) 1st Serve - 63% first serves x 64% of those won
63 balls go in, with 40 points won, 23 points lost

37 balls remain
2) 1st Serve - 63% first serves x 64% of those won
23 balls go in, with 15 points won, 8 points lost
14 are double faults

Total points won: 40 + 15 = 55
Total points lost: 23 + 8 + 14 = 45

First serve, then second serve:
1) 1st Serve - 63% first serves x 64% of those won
63 balls go in, with 40 points won, 23 points lost

37 balls remain
2) 2nd serve - 86% second serves x 30% of those won
32 balls go in, with 10 points won, 22 points lost
5 are double faults

Total points won: 40 + 10 = 50
Total points lost: 23 + 22 + 5 = 50

So, my original conclusion was correct, even though I reached it in the wrong way.