Calculating probabilities

Hey,

So I made soccer team power ratings in excel, these are team ratings in the range of 0,000 till 1,000. Now I want to calculate the probability of a win when these teams play each other, although I have no clue how to do this so I hope someone can help and explain it to me.

Lets say Team A with a rating of 0,690 plays versus Team B with a rating of 0,482. How can I calculate how much % change team A has to win this game?
I hope someone can explain this to me because I cant find it anywhere.

I found this but I don't understand how to do this.

Despite these difficulties, we can calculate a TSR from previous matches for each of the two teams in a Premier League contest. We can further use historical TSR match ups from previous seasons to establish the relationship between each team’s pre game TSR and the actual outcome of the game.

Logistic regression, where an outcome, such as a home victory, either happens or it doesn’t, is one route to determining match probabilities from game day TSRs for each team.

When Sunderland travelled to Tottenham on April 7th 2014, their TSR over the last 30 games was 0.43, over the last 10 it was slightly better, at 0.44. That of their hosts was 0.56 and 0.51, respectively.

Using historical, out of sample results from five previous seasons from soccer-data.co.uk and a logistic regression, the chance of a Spurs win at home to Sunderland based on 30 game averages was 68%.

The calculation involves two steps, where the respective home and away constants are obtained by running a logistic regression on matches played during the five most recent seasons of Premiership games, excluding 2013/14. The predictor variables were each team’s TSR from their previous 30 league games and the output was whether or not the result was a home win.

Firstly, calculate F= (8.19*HTSR)-(6.44*ATSR)-1.08;

Where HTSR is the TSR of the home side over the previous 30 matches and ATSR is that of the away team.

To convert this to a probability of the home team winning the game, finally take;

Home Win Probability = (exp^F)/(1+exp^F) = 0.68

The 30 game HTSR for Spurs was 0.56 and Sunderland’s ATSR was 0.43, giving Tottenham a likely winning probability of 0.68 when these numbers are put into the equations above.

This compares to a much lower home win probability of 0.53, when judged on TSR over just the previous 10 games. The home and away constants used to determine the value of F using TSR from the previous 10 matches are 7.11 and 5.12 respectively and the lone constant is 1.23. These slightly different constants are again derived from five seasons of Premiership data, but using each team’s TSR over the previous 10 games.

Originally Posted by popipipo

Maybe this:
Rating teamA divided by sum rating team A and team B

Winning chance Team A: 0.690/(0.690+0.482)=0.589
Winning chance Team B: 0.482/(0.690+0.482)=0.411

Sounds legit but isn't right as 0,56 vs. 0,43 =68%.

It are no percentages, it are just power ratings for a team based on statistics. Those can vary between 0,000 and 1,000.

Originally Posted by popipipo

If one team has 59% of winning the other team has 41 %
What is wrong with that??

I don't understand the 68 %??
68% * 0,56 =0,38

And that 68% I get from the quoted example I posted.

Originally Posted by MrShorty

Your reference is helpful. It says that the first step is the logistic regression, then assumes that you already know how to set up and perform the logistic regression. I would suggest that we start with some basic tutorials on logistic regression.

Wikipedia can be a bit detailed, but it is also usually pretty thorough: http://en.wikipedia.org/wiki/Logistic_regression
This one is interesting because he specifically explains the statistical concepts using Excel: http://www.real-statistics.com/logistic-regression/
This one looks like an interesting introduction to logisitc regression: http://logisticregressionanalysis.com/

Once we figure out the exact logistics equation that should go into this regression and the independent variables that go into it, then we can perform the regression and get the desired parameters (TSR, HTSR, and/or ATSR). Your example suggests that they are using y=(exp(F)/(1+exp(F)) where F=(8.19*HTSR)-(6.44*ATSR)-1.08. I would guess that our goal would be to use your historical data to perform the logistic regression to come up with HTSR and ATSR.

How much of that makes sense, and what are you having trouble understanding?

Thanks Shorty this helps a lot! I will look at those links first now to understand the logistic regression.
What I have trouble with understanding is how to do this in Excel but second, in the example he/she uses the numbers 8,19, 6,44 and 1,08 that I have no idea where they are coming from.

The parameters HTSR and ATSR we already have as:

HTSR = home team rating.
ATSR = away team rating.