Combining rating systems

[PAW]

Couldnt find this in a search, but if it has been covered previously then I'd appreciate the link I've got this football ratings system which appears to model the results pretty accurately, ie I plot a graph in Excel of, say, percentage home win vs rating and the result is a linear slope with trendline R^2 (LINEST) figure of 0.98+ I then use the linear equation to determine the 'value' price for a home win. Basic stuff I guess to most people here Just recently I've devised another ratings system that produces a similar quality graph, and hence another set of value equations. Now, I could just run the systems in tandem, but today for instance, one said Livorno was a back, the other said back Bologna So my question is how to combine the two? This is where my limited knowledge of statistics runs out. I have two sets of ratings, each with it's own set of value equations, what's the maths?

[relf]

Re: Combining rating systems Hmm, there are a few ways you could go about doing it. If Team A vs Team B, here are the possible scenarios: 1) If both systems back the same team, it's straightforward then. 2) If only one system back a team, then it all depends how reliable you think this system is. If you believe it will produce a positive yield in the long run, then you should back the team. 3) If both systems are against each other, it would be a tricky issue. You could either back both if you think both system will produce a positive yield in the long run, or you could find out which system is the more accurate and back the team which the more accurate system suggest, or you can avoid this match altogether. After all, there are many matches in the market. As for combining, I'm not quite sure how to go about doing it. But one word of caution when combining systems though - Simpson's Paradox (http://en.wikipedia.org/wiki/Simpson%27s_paradox). In short, 2 positive trends while combined could produce a negative trend, which is something you probably not want. Not sure if I'm of much help though.:unsure

[Grex]

Re: Combining rating systems Hi, Pip...... I have the same problem.... but even worse, having 4 systems running in parallel (see "4 Systems better than 1?" thread). If you read through it, you will see that the more systems that select a particular result, then the higher the stakes. To be honest, I could never find a "formula" for predicting value away results, so all the systems predict only value home wins.... so I never have the conflict you refer to. BTW, looks like your system which predicted a Bologna win came up trumps today :ok

[PAW]

Re: Combining rating systems Excellent responses chaps I do keep an eye on your thread Grex, but you don't tackle the problem in the way I thought I wanted to solve it, hence my post, though since reading what Relf says about Simpson's I'm having second thoughts now anyway. I think I may go with what you both suggest, backing only when both systems agree. My staking system is a slightly modified Kelly, which is why I wanted to come up with a new value formula, but maybe I'll just have to stick with one of the existing ones Thanks again :ok