Couple of ELO-related question

[London_Calling]

I have an ELO value for each team, one for Home, another for Away – taking the Premiership as an example, that’s effectively 40 distinct identities.

Using those ratings - together with the match final score - I want to develop a couple of indicators, one indicator might be ‘Goal Penetration’, another ‘Defencer’.

In other words, I want a value that takes into account the ability to score, but do so within the context of the relative quality of the opposition (relative to the teams in that particular league) - the ELO thing.

Example: as a home side, Middlesboro might be rated at 29.5 this week, as an away side Blackburn are rated at 21.3. Boro win 2-1. Maths:


Boro’s Penetration score = 2 x 21.3 = 42.6
Blackburn’s Penetration score: 1 x 29.5 = 29.5


Simple, probably too simple – fwiw, I won’t trouble you with the corners, shots on and shots off, etc as all that’s incidental here. Two questions:

One: What other way could I treat those raw ELO numbers in order to derive a credible value for ‘Goal Penetration’?, and

Two: Can you think of a way to use the ELO ratings to determine an ‘Defencer’ value i.e. not conceding?

[AndyR]

You need to consider the difference in the rating between the two sides, not the absolute values for an ELO system to work. You could equate the difference to an estimated goal difference, and then add/take it away from the values of your teams in the ELO rankings.

[London_Calling]

Okay, so in the above scenario:

Boro = ELO Rating of 29.5 at home
Blackburn = ELO Rating of 21.3 away

Difference = 8.2

Can you take it from there?

[AndyR]

Sure, lets say that you estimate that 10 points is a one goal advantage for Boro, so you have a 0.82 goal advantage for the home side. It is just a starting point for this estimate, known as the 'adjuster' and we will revise this in a moment. This goal difference could come about because Boro are more likely to score than Blackburn, less likely to conceed than Blackburn or a combination of the two.

So Boro win 2-1, beating the predicted goal difference by 0.18 goals, or 1.8 points. The usual thing to do is to add 1.8 points to Boro's rating and remove 1.8 points from Blackburn's rating, meaning they now stand at 31.3 and 19.5 respectively.

The important thing is that the total number of points summed over all the teams is constant, so that the adjuster doesn't need to change over time. As it seems a rather large goal difference, it is worth trying 20 or 40 points and so on per goal until you are happy with the adjuster.

For a 'Penetration' rating, you essentially do the same. You could come up with another system including corners won, shots on target etc and equate that to a number of 'theoretical' goals - eg you could sum the number of shots on target and divide by 5, giving a 'goal' difference for each five attempts for both teams. You could then use the same method above to adjust your ELO ratings.

Example: As above, the difference in Boro and Blackburn is 8.2 points, or 0.82 theoretical goals in Boro's favour. Boro get 10 shots on target and Blackburn 5, so our values are 10/5=2 and 5/5=1 giving Boro +0.18 more goals than predicted. We add this to Boro's rating and take it away from Blackburn, remembering to multiply by the adjuster.

For defensive ratings, do the opposite - take the number of shots on target conceeded, corners given away etc and award these as goal advantages to the opposition.

GL

[London_Calling]

Thanks for taking the time – it’s definitely interesting.

Can I ask, if 10.0 is a reasonable value for a one-goal advantage, what might be appropriate for 2 and 3 goal winning margins?

It's just that, in the back of my mind, I'm wondering if the method you describe returns something I might - in my own subjective terminology - consider to be a 'superiority' value?

For example, in the 2-1 match we're using as an example, I'm not sure Blackburn's Penetration rating deserves to suffer too much for scoring a goal at Boro, maybe a little . . .

btw, thanks for the interest.

[AndyR]

Yes, ELO is a 'superiority' system. And Blackburn's rating won't suffer too much - think of the opposite scoreline with Blackburn winning, they beat the goal difference by 1.18 goals and would boost Blackburn's rating by 11.8 points. As I said earlier, you have to come up with an adjuster that suits the league.

If we set 10 points as equal to one goal advantage, after the games we will see large fluctuations in the ratings of the team and they will reflect recent form quite strongly. I assume the maximum rating here is 100, so this is 10% of the rating. Paul Steele, in his book on systems, suggests using an adjuster of 2.5% and has each team starting on a rating 10 points per team.

As you might guess, the changes are more gradual and so it reflects seasonal form (or strength) more accurately than with a 10% adjuster. It is poor at assessing recent form, however, and this is something to bear in mind.

[London_Calling]

Okay, I see you’re referring to Steele’s System Eleven (Power Ratings). Steele creates a starting point of 10.0 but you’re suggesting I use my ELO Ratings instead – def interesting. Previously I just glanced through those, but thanks to your comments I reread them and saw his Adjustor in his examples. Cheers!


If I can re-state the problem: A few weeks ago Chelsea beat Birmingham 3-2 at home. Now, from a ‘Penetration’ pov, the story of that match was (a) that Brum got 2 away goals and (b) they scored two goals at Chelsea, the second best home team (according to my ELO Ratings).

If I were to use the method you describe, Birmingham’s Rating would register a negative (because they lost by one goal), when the real achievement, imo, is that they scored two goals at Chelsea – at least from the pov of the ‘Penetration’ value I’m trying to extract; scoring two goals at the second raked team is big news, I think.

I’m sure this isn’t supposed to be this tricky . . .

[AndyR]

It wouldn't be negative, because your previous rating for the game would have given Chelsea at least a goal head start, and on a penetration ranking Birmingham might not have scored any at all. By doing at least as well as predicted, the rating for Birmingham would have gone UP.

You have to first generate an expected goal difference, then the actual result minus this predicted value is used to modify the rating. If a team does better than expected - eg instead of losing by two goals, Birmingham lose by only one, the above method would credit Birmingham with the equivalent of a one goal win, assuming the rankings reflect the strength of the team.

There is a spreadsheet on the forum somewhere which can be modified to give a penetration ELO table, I have done it myself before. I will stick it up in a bit.

[AndyR]

An auto-correcting rankings simulator, based on ELO theory:

A football rating system, discussions, ideas

Go to post number 191 and download the spreadsheet. You can change the names of the teams and get recent data from www.football-data.co.uk. Try cutting and pasting the shots on target instead of results for each match, and see what happens.

You may also change the adjuster on one of the later sheets but don't touch any of the matrix transformations as Excel will probably crash.

GL

[London_Calling]

Thanks for your help Andy. I think I'm going to take a step back from this particular point for a couple of weeks and look at other issues. That was an interesting thread though, and the worksheets offer some nice ideas.

Appreciate the interest, and all the best. Cheers.