Price discovery is a powerful mechanism through which markets produce very accurate predictions of events and asset prices B/c markets represent the collective beliefs of all models, even the best individual model can stand to gain by incorporating the market as a signal

A simple weighted average between a model's prediction and the market's prediction yields predictions that are more accurate than either in isolation

Going a step further, adjusting this weight situationally based on how accurate the model and market have been in the recent past for specific teams generates further improvements

Put it all together and you get a model that reliably outperforms the market at predicting final margins

@greerreNFL are you using closing lines for this analysis? how does it change if you use like a wednesday line?

@canzhiye Closing, which will benefit the regressed model I can rerun it with opening lines to see how big the difference is

@greerreNFL This is interesting, we have been talking about this on the MySportsAI email forum. I presume you are manually calculating the weights so to speak unless you know of a Python library function that will do it. Ordinary regression will get swamped by the line

@SmarterSig I manually calculated because I wanted to see the gradient as the weights changed, but you could use an optimization package in python to find it more programmatically

@greerreNFL You forgot to tell me who to bet on.

@greerreNFL Does this apply to opening lines and lines early in the week (maybe less weighting?) or only to closing values of lines?

@greerreNFL The big boost will come from early lines coupled with some market move predictor, in other words a weighted regression that takes predicted final line and model line where of course predicted line is efficient