Hi,
I have my GSCE in maths but since then have not been that involved with it. Recently I've got very interested in probabilities, statistics with particular reference to modelling tennis match outcomes. I'm struggling to break down and understand the below and what I'd like to do is understand it so that I can place it in excel.
I’m looking at a model where we have two player’s, A and B, and player A has a constant probability p of winning a point. With some following instructions from the paper I'm referring to.
"We set up a Markov chain model of a game where the state of the game is the current game score in points (thus 40-30 is 3-2). With probability p the state changes from a, b to a + 1, b and with probability 1 − p it changes from a, b to a, b + 1. Thus if P(a, b) is the probability that player A wins when the score is (a,b), we have:
P(a, b) = pP(a + 1, b) + (1 − p)P(a, b + 1)"
(In this example let’s assume the score is 0-0, I.e. 0,0 and p = 0.74 (74%))
Also it satiates the following - the boundary values are P(a, b) = 1 if a = 4, b ≤ 2, P(a, b) = 0 if b = 4, a ≤ 2 – and not too sure what that means.
Going to create a table that looks like the following with the above formula in each cell to with the above formula (relating to the various score lines)
In large part the reason I’m struggling to understand how the formula breaks down as I’m not clear on what the commas mean etc. Any help or pointers would be greatly appreciated and I hope I've posted in the right section.
Thanks,
Alex
I have my GSCE in maths but since then have not been that involved with it. Recently I've got very interested in probabilities, statistics with particular reference to modelling tennis match outcomes. I'm struggling to break down and understand the below and what I'd like to do is understand it so that I can place it in excel.
I’m looking at a model where we have two player’s, A and B, and player A has a constant probability p of winning a point. With some following instructions from the paper I'm referring to.
"We set up a Markov chain model of a game where the state of the game is the current game score in points (thus 40-30 is 3-2). With probability p the state changes from a, b to a + 1, b and with probability 1 − p it changes from a, b to a, b + 1. Thus if P(a, b) is the probability that player A wins when the score is (a,b), we have:
P(a, b) = pP(a + 1, b) + (1 − p)P(a, b + 1)"
(In this example let’s assume the score is 0-0, I.e. 0,0 and p = 0.74 (74%))
Also it satiates the following - the boundary values are P(a, b) = 1 if a = 4, b ≤ 2, P(a, b) = 0 if b = 4, a ≤ 2 – and not too sure what that means.
Going to create a table that looks like the following with the above formula in each cell to with the above formula (relating to the various score lines)
| 15 | 30 | 40 | Game | ||
| 15 | |||||
| 30 | |||||
| 40 | |||||
| Game |
In large part the reason I’m struggling to understand how the formula breaks down as I’m not clear on what the commas mean etc. Any help or pointers would be greatly appreciated and I hope I've posted in the right section.
Thanks,
Alex