# Probability of winning a point on serve in tennis

#### Hrant

##### New member
Hello, my question about calculating the probability in tennis
I know that to calculate Pwos (probability of point won on oun serve ) for each player the following formula is used...

# P(no Fault) -The probability a player's first serve not faulting

# P(win/no Fault) -The probability a player will win the point if the first
service does not fault

# P(win/fault) -The probability a player will win the point on his second
serve

formula...
P(win) = P(noFault)P(win/noFault) + (1 - P(noFault))P(win/fault)

For an example
P(noFault) = 0,70
P(win/noFault) = 0,64
P(win/fault) = 0,55

P(win) = (0,70 * 0,64) + (1 - 0,70) *0,55 = 0,613

This is a global method for calculating Pwos for a particular player on a particular surface.
I know that to calculate the most correct (Pwos) for two players, in a particular match, on a particular surface,it is necessary that these players used to have personal meetings on the same surface.
please tell me how to use this fact that they used to play each other on this surface?
Sorry for my English

#### Jameson

Staff member
Hello, my question about calculating the probability in tennis
I know that to calculate Pwos (probability of point won on oun serve ) for each player the following formula is used...

# P(no Fault) -The probability a player's first serve not faulting

# P(win/no Fault) -The probability a player will win the point if the first
service does not fault

# P(win/fault) -The probability a player will win the point on his second
serve

formula...
P(win) = P(noFault)P(win/noFault) + (1 - P(noFault))P(win/fault)

For an example
P(noFault) = 0,70
P(win/noFault) = 0,64
P(win/fault) = 0,55

P(win) = (0,70 * 0,64) + (1 - 0,70) *0,55 = 0,613

This is a global method for calculating Pwos for a particular player on a particular surface.
I know that to calculate the most correct (Pwos) for two players, in a particular match, on a particular surface,it is necessary that these players used to have personal meetings on the same surface.
please tell me how to use this fact that they used to play each other on this surface?
Sorry for my English
Hi Hrant,

Welcome to MHB!

This sounds like a real life problem, rather than a problem from a textbook or course. Am I right? If it's from a textbook, are we missing any additional information?

#### Hrant

##### New member
hello, I read the book "Prediction of In-Play Tennis" by Michelle Anne Viney. I have a question. this is about "UPDATING THE PWOS USING POINT IMPORTANCE" . the author says that when a player wins his game losing 0 points. his PWOS grows from 600 to 612. this means that the author uses twice the formula " PAwos(n)= PAwos(n-1)+(1-Ip(a,b))×Ɵ" in one game. initial Pwos=600, optimal(Ɵ)=0.005.
but i calculate with betfair and I see that it uses the formula
" PAwos(n)= PAwos(n-1)+(1-Ip(a,b))×Ɵ" just one time in a game , the rest of the time it uses this formula
" PAwos(n)= PAwos(n-1)±Ip(a,b)×Ɵ"
please tell me how to properly update Pwos with betfair?
I know that very few people can answer to this question...
Sorry for my English

#### Hrant

##### New member
FORMULAS>>>

" PAwos(n)= PAwos(n-1)+(1-Ip(a,b))×Ɵ"

" PAwos(n)= PAwos(n-1)±Ip(a,b)×Ɵ"