Player/Team to do X first

[JustinBieber]

I am reasonably familiar with props such as who will hit more birdies or who will throw more interceptions type props and use poisson distribution to evaluate which is them most likely event.

However I have come across a lot of props such as Which team will score first or Which tennis player will score the first ace?

Say If I had found Nadal scored 2 Aces every 6 service games and Federer scored 6 aces every 6 service games, its obvious Federer is more likely to score the first ace but how do I go about calculating this?

Many Thanks.

[Justin7]

Figure the odds of each player serving at least one ace in their first game. Do you know who is serving first? If not, assume there's a 50/50 chance for each player (this is a big deal in NFL "score first" props, since weak teams could get lucky by scoring in the first possession).

Figure the odds for each scenario, and average. In some cases, neither player will have an ace in the first service. As long as you have the ace ratio correct, you can just use ratios.

[JustinBieber]

How would you go about doing this, if federer scored 6 aces in 6 games I assume I couldnt do 6/6 as this would =1, and he is never certain to score an ace in a service game, for example I would have thought to do it like this Nadal would be 2/6 = 0.33. But this way looks incorrect to me.

For another example Federers number could be something like 0.5. If Federer had a 50% chance and Nadal had a 33% chance could these numbers be applied to getting the first ace? Would it just be as simple as that? I'm sure the numbers would have to be weighted in some way so they relate to one another and total 100%.

[buby74]

here's how I would do this
1 use poisson to convert the average aces per game to the prob of scoring at least one ace
2 if fed is 50% and nadal is 33 then if fed serves first he will serve the first ace of the match in the first game in 50% of matches and nadal will get the first ace in the second game in (1-50%)*33%=16% of matches in the remaining matches we are back at the start of the game so the ratio of w to losses is 50 to 16 or 75% you then repeat the calc with nadal first which is 33% for nadal and 67%*50%=33% for fed coincidentally. which is 50% chance of fed being first. Averaging fed chances if he serves first or second is 75+50/2=62.5%. Hope this helps
James

[buby74]

Oops forgot to point poisson might not be completely accurate as it is difficult to score more than 4 aces in a game but shoulnt distort things too much

[JustinBieber]

2 if fed is 50% and nadal is 33 then if fed serves first he will serve the first ace of the match in the first game in 50% of matches and nadal will get the first ace in the second game in (1-50%)*33%=16%

Also how do you know the wins to losses is 50 to 16?

And if Federer is 62.5% that would mean Nadal is 37.5%? and not 33?

That is the formula you gave for nadal in the said example, what is the formula for Federer being 50% to score the first ace?

[buby74]

2 if fed is 50% and nadal is 33 then if fed serves first he will serve the first ace of the match in the first game in 50% of matches and nadal will get the first ace in the second game in (1-50%)*33%=16%

Also how do you know the wins to losses is 50 to 16?

And if Federer is 62.5% that would mean Nadal is 37.5%? and not 33?

That is the formula you gave for nadal in the said example, what is the formula for Federer being 50% to score the first ace?

Justin

I was typing on my iphone yesterday so I wasnt as clear as I meant to be.

I am assuming that federer has a 50% of scoring an ace against nadal in any given game but nadal only has a 33% chance of scoring an ace against federer in any given game.

We want to find out who will score the first ace.

First we will assume federer wins the toss and serves first. In the first two games three outcomes are possible.
1. Federer scores an ace in the first game which has aprobability of 50% (nadal could then score an ace in the second game but we dont care.)
2. federer doesnt score an ace in game 1 but nadal does does in game 2 =1-50% * 33% = 16.66%
3. Neither player scores an ace in the first two games = (1-50%)*(1-33%)=33%

The thing to realise is that outcome 3 effectively means you go back to the start of the match i.e. the outcome is unresolved and therefore you run through the three possibilities from step 1 again. if you do this an infinite number of times the unresolved outcomes will eventually split into a 50:16.66 ratio which equals 75:25. (by the way what happens to the prop if no ace is scored?).

As I explained yesterday you then have to repeat for nadal serving first which equals 50% so the average is 75% + 50% /2 = 62.5% for fed so nadal is 37.5%.

This is NOT the same thing as the 33% for nadal as that was nadals chance of scoring an ace in any given game against Federer. The 37.5% is Nadals proability of scoring an ace before federer does.

The questions I have for you is how did you estimte the chance of fed and nadal scoring aces against each other in the first place and also does a tennis player's ace rate change during a game or is it constant.

hope I am bit clearer today

james

[JustinBieber]

Well it was more of a theoretical question and they're just numbers I plucked out of the air. To find out how many aces they would score against one another I would look at recent career stats of aces scored divided by games played. I would also assume an ace is at a constant but obviously hugely affected by variance, there isnt really a time in tennis where you "must" hit an ace during the match length.

I think you could look at service returns for players too but I mean this is only a prop with a $500 limit or something so it starts to get nitty and overanalysing when you do things like this for a prop bet I think.