Formula Help

Not really sure which section this should go in but has anyone got any ideas of how to solve this formula (I basically don't know what the commas mean).

M(0.6+A,(1-06))+M(0.6,1-(0.6-A)
2
Say for example M is 0.5 and A is 0.1.

It is my understanding that the solution should be > M where A is > 0 and < M where A is < 0 but I can't seem to get this to work.

Cheers

What do you mean by "solving" the "formula"? What, exactly, are you needing to do? Also, is there text that goes along with this approximation?

Thank you!

I just meant calculate the formula through (if possible) to come up with a value if you use the stated values for M and A. The thumbnail attached has the full formula from the original document. My problem is I do not know what the commas mean and to be honest don't if this formula can even be used to calculate a value or I need additional info.

To add some detail the formula is used to calculate the probability of winning a tennis match.

The M is the probability of a player winning based on normal conditions which has been previously calculated. The A as I understand it then increases or decreases the probability (therefore the output of the formula) based on how the records of the two players compare against common opponents.

The A basically tips the advantange further in one direction. So if the A is positive then the solution to the formula must be > than M.

The way it is written it appears that \(\displaystyle M_3\) (which is what I guess you mean by "M") is NOT a a number at all but some function of two variables.

Hi,

Sorry I'm not entirely sure what the above means so I will try to explain exactly what it is I'm trying to do.

Here is an extract from the document which I am looking at:

"The difference in service points won can be used as an indicative measure of the probability of a player winning a match against an opponent. In order to model how A and B would play against each other through their common opponents C1 we first need to calculate the difference in service points won against those opponents. Then we additively combine those differences to come up with an indication of how well A would play against B.

For each common opponent C1 we compute AB which represents a measure of the advantage (or if negative disadvantage) player A has against player B."

This is calculated by a formula which involves the % of points won on serve and % of points won on the opponents serve to give a figure AB. I can calculate this no problem. The document then states:

"This value (AB) can be used to additively influence an arbitrary probability of winning a point on serve for Player A against Player B in any hierarchical model. The following equation shows how to estimate the probability of A beating B given the results of their matches against C1. M3 is a function (which was previously covered in the document) to calculate an estimate of the probability of winning the match.

Equation: This is the one noted in the first posting of this thread (and in the original thumbnail)

M(0.6+A,(1-06))+M(0.6,1-(0.6-A)
2

Now I believe I have already calculated M3 (M in the above simplified notation) and can apply this value and I already have a figure for AB so should be able to solve this equation. However from what has been said in the above posts I'm not really too sure as to how M3 and AB interact as it does not appear as simple as simply calculating through an equation.

Apologies for the long winded query but any further help would be appreciated.

Thanks[FONT=MathJax_Main]
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Quoting what you copied: "M3 is a function (which was previously covered in the document) to calculate an estimate of the probability of winning the match."

M3 is a FUNCTION, not a single number.

I sort of understand that but I don't know how to apply this formula/function to ultimately generate a number which is what I need. The function for M3 (which represents the probability of winning a 3 set match) is:

M3(p,q) = S(p,q)²[1+2(1-S(p,q))]

So how do I adjust that to reflect the formula in the first post?

I don't know if M3 changes as a direct result of AB or if I can first calculate M3 and then plug this number into the second formula.

I have set up tables in excel to calculate M3 based on backward recurssion (I'm not great at maths as you can probably tell so I think I got lucky with that one). However I don't know if I now need to adjust those table to reflect the formula from the first post.

I'm just totally baffled to be honest about what I need to do to ultimately get from the initial input (% chance of winning a point on serve against all opponentes) to the final output (adjusted % chance of winning a 3 set match based on serving record against common opponents.

Perhaps if I attach the entire document I am going through that would help but it is quite a long document so I wouldn't really expect someone to go through it in detail.

Hi,

Attached are the formulas and functions that I am working on:

The first formula shows how to calculate M3 (probability of winning a 3 set tie break match) based on serve % of player A and player B.

I have caclulated this probability by using a backward recurssion table (attached) which shows a probability of 0.601 for player A to win (based on serve win % of 62% for player A and 60% for player B). I can change these percentages to anything and update the table.

Note: This is not a perfect way of calculating the true chances of player A beating player B as the %'s applied for both players represent their performance against a wide range of opponents, so for example if player A has played a significantly worse set of opponents then his figures will be inflated.

The other formulas attached (15) and (16) show how to calculate the advantage of A over B given their performance against common opponents.

I can calculate formula (15) to give me a value for AB with no problem based on statistics I have.

However the final step is proving difficult as I do not know how to use the figure to adust the probability of winning the match. The text describing formula (16) states:

"Equation 16 shows how to estimate the probability of A beating B ....."

This is the figure I need but is proving to be elusive based on my clearly poor understanding of the formula/function and what I need to do with it to produce a final output.