Ross Rutledge

# R2 Sports Metrics Philosophy

Updated: Jan 24

R2 Sports Metrics builds models that are intended to be used as a tool in informing decisions in betting markets. As an economist, I have tremendous appreciation of the power of betting markets to aggregate information about an event and predict the probability of that event occurring. Indeed, the Vegas line has been the best predictor of college football outcomes by mean absolute error in each of the last five years according to __thepredictiontracker.com__. So one might ask: "why would an economist with full appreciation of the predictive power of markets set out to build models intended to beat them - isn't that a fool's errand?" To some extent, the answer to that question is "yes." For instance, it is hard to imagine that any statistical projection system alone will match the Vegas line in mean absolute error. However, at R2 we believe it is possible to be more *accurate* in predicting outcomes, even if we are less precise. To explain what we mean here, we need to examine betting markets in more detail.

**How Betting Markets Produce Efficient Predictions**

The origin story of betting markets' success begins with the demand for betting markets in the first place -- simply put, there exists a demand for gambling markets because people like to gamble. Sportsbooks then step in to supply this demand for gambling services. Sportsbooks are "market-makers" that connect bettors on opposite side of a bet and make their money by taking a percentage of the action. But rarely is there a competition between two exactly equal opponents. In almost all cases, one team or contender is going to be preferred to the other(s) and if the sportsbook gave each contender 1:1 odds, the favored contender would receive the majority of the bets. If the favored contender wins, the book will incur losses. This potential to lose a significant sum of money incentivizes the book to handicap each contest such that it will attract equal amounts of bets for each contender. In other words, the prospect of losses creates demand by the book for a *statistical projection* of the outcome of the contest. ...And a star is born. A rockstar, even.

The efficiency of sports betting market projections are often touted by economists as examples of the "wisdom of crowds" and used to assert the power of other prediction markets in other arenas like futures markets and election markets. Some even suggest that these prediction markets are superior to statistical projections. But in the case of sports betting markets, its worth reflecting on the fact that ** gambling creates demand for statistical projections.** And these statistical projections are

__sharp__. **Mean Absolute Error 2014 - 2021**

As you can see, the opening betting line beats all other statistical predictions in four of the last seven years - which is an incredible run of success. No other statistical prediction system can match it consistently. Obviously, it is true that the wisdom of the crowd and the power of the market in aggregating information that is broadly dispersed throughout the betting population makes the closing line even sharper - but the opening statistical projection does a significant share of the work in making betting markets so sharp.

So how does the book produce such efficient predictions to set the opening line? We don't know exactly, but any statistical modeling system must grapple with what is called the ** bias-variance inflation tradeoff. **You can think of the total error in your predictions as the sum of two sources of error: bias and variance. Bias is error in your model resulting from omitting a variable that has a causal relationship with the outcome you are trying to predict. Variance is just some random error with mean zero.

Well, it turns out that these two sources of error are inversely correlated with each other for reasons that may seem mysterious, but I think can be explained rather simply. (If you're interested in seeing the math behind this relationship, there are dozens of data science blogs offering explainers with a quick google search, but since this is a sports blog, I'll keep it high-level.) Imagine you're building predictive college football model and you want predict the number of points a team will score. It would make sense to start out by including variables in your model that you believe provide the most "signal" and least "noise." These may be variables such as a simple rating system (opponent-adjusted points), expected points added, points per opportunity, and success rates. As you add variables, your model's predictions will be progressively less biased because it is accounting for more information. However, eventually you will come to variables that have more "noise" and less "signal" (even if there is still some signal there!) like for instance punt return fumbles lost. Adding this variable to your model may reduce bias slightly, but will also make your predictions less efficient. Furthermore, as you continue to add variables there is a tendency to introduce more variables that are highly correlated with each other, which can create a problem known as "multicollinearity." The bias-variance inflation relationship is captured nicely in the graphic below.

So what Vegas has done better than anyone else is to minimize the total error of its predictions. In the graphic above, Vegas is essentially the dotted vertical line. So is it possible to beat the opening line statistical projections? Yes -- as we saw above it has been done in the past -- but it is unlikely. However, at R2 we believe that it is possible to create modeling system that is *less biased* than Vegas. * If we tolerate some reduction in the efficiency of our predictions, we believe we can ultimately make more accurate predictions on average. *This means that our modeling will tend to be complex and feature many more variables than other prediction systems. While we believe our models will be competitive in measurements such as mean square error or mean absolute error, our models should perform better against the spread and in over/under picks than competing models.

To illustrate R2's philosophy further, consider the following graphic showing two stylized prediction distributions. The orange distribution is slightly biased, but very efficient. The blue distribution is less efficient, but also less biased. If the orange distribution is the predictive system to set the opening line, the blue distribution will pick winners ATS more often than not. So you may ask: "Why wouldn't Vegas select the less-biased blue system to establish the spread?" The answer is pretty simple - because if the blue system were used to set the opening line - the orange system would absolutely demolish the blue system. The orange system could eliminate every prediction to the left and right of its extreme values. Betters possessing the orange system could pick and choose their spots and go "all in," effectively bankrupting the book.

R2 Sports Metrics believes that Vegas establishes the opening through the use of a highly efficient statistical system (for the most part). In order to achieve that level of efficiency, it must be excluding some variables that increase the variance but reduce bias. By tolerating a bit more noise to capture a bit more signal, R2 believes it will accurately pick outcomes against-the-spread. In essence, R2 looks for the blue distribution, assuming the book has the orange distribution.

Note, however, that R2 products are built for making ATS and O/U picks - not for making moneyline ("straight-up") picks. The sportsbook's edge in efficiency gives it an advantage over the less-efficient/less-biased R2 products.

**Methodology**

For the most part, R2 Sports Metrics builds predictive sports models using machine learning methods that allow us to test hundreds of different model specifications and select the best amongst them by comparing how they perform on certain diagnostic statistics.

**To Index or Not to Index**

With one major exception, R2 generally does not create indexes - or "power rankings." This is because R2 models include matchup-specific information, and index-based systems like SP+ or ESPN FPI assess performance against an abstract "average opponent." R2 appreciates those index systems a great deal and believes that they are the best metrics outside the Vegas line or the R2 projection to assess how a team is likely to perform in a given game. That said, R2 believes that its system of using matchup-specific information to project outcomes is a significant step forward.