We have been talking about developing predictive models for tasks like evaluating draft prospects. Last time we focused on the question of what to predict. For drafting college prospects, this amounts to predicting things like rookie year performance measures. In statistical parlance, this is the dependent or the Y variables. We did this in the context of basketball and talked broadly about linear models that deliver point estimates and probability models that give the likelihood of various categories of outcomes.

Before we move to the other side of the equation and talk about the “what” and the “how” of working with the explanatory or X variables, we wanted to take a quick diversion and discuss predicting draft *outliers*. What we mean by outliers is the identification of players that significantly over or under perform relative to their draft position. **In the NFL, we can think of this as the how to avoid Ryan Leaf with the second overall pick and grab Tom Brady before the sixth round problem.**

In our last installment, we focused on predicting performance regardless of when a player is picked. In some ways, this is a major omission. All the teams in a draft are trying to make the right choices. This means that what we are really trying to do is to exploit the biases of our competitors to get more value with our picks.

There are a variety of ways to address this problem, but for today we will focus on a relatively simple two-step approach. The key to this approach is to create a dependent variable that indicates that a player over-performs relative to their draft position. And then try and understand if there is data that is systematically related to these over and under performing picks.

For illustrative purposes, let us assume that our key performance metric is rookie year player efficiency (*PER(R)*). If teams draft rationally and efficiently (*and PER is the right metric*), then there should be a strong linkage between rookie year *PER* and draft position in the historical record. Perhaps we estimate the following equation:

*PER(R) = B _{0} + B_{DP}DraftPosition + …*

where *PER(R)* is rookie year efficiency and draft position is the order the player is selected. In this “model” we expect that when we estimate the model that *B _{DP}* will be negative since as draft position increases we would expect lower rookie year performance. As always in these simple illustrations, the proposed model is too simple. Maybe we need a quadratic term or some other nonlinear transformation of the explanatory variable (draft position). But we are keeping it simple to focus on the ideas.

The second step would then be to calculate how specific players deviate from their predicted performance based on draft position. A measure of over or under performance could then be computed by taking the difference between the players actual* PER(R)* and the predicted *PER(R)* based on draft position.

*DraftPremium = PER(R) – PER(R)*

Draft Premium (or deficit) would then be the dependent variable in an additional analysis. For example, we might theorize that teams overweight the value of the most recent season. In this case the analysts might specify the following equation.

*DraftPremium = B _{0} + B_{P}PER(4) + B_{DIFF}(PER(4) – PER(3)) + …*

This expression explains the over (or under) performance *(DraftPremium*) based on *PER* in the player’s senior season (*PER(4)*) and the change in *PER* between the 3^{rd} and 4^{th} seasons. If the statistical model yielded a negative value for *B _{DIFF}* it would suggest that players with dramatic improvements tended to be a bit of a fluke. We might also include physical traits or level of play (Europe versus the ACC?). Again, we will call these empirical questions that must be answer by spending (a lot of) time with the data.

We could also define “booms” or “busts” based on the degree of deviation from the predicted *PER*. For example, we might label players in the top 15% of over performers to be “booms” and players in the bottom 15% to be “busts”. **We could then use a probability model like a binary probit to predict the likelihood of boom or bust.**

Boom / Bust methodologies can be an important and specialized tool. For instance, a team drafting in the top five might want to statistically assess the risk of taking a player with a minimal track record (1 year wonders, high school preps, European players, etc…). Alternatively, when drafting in late rounds maybe it’s worth it to pick high risk players with high upsides. * The key point about using statistical models is that words like risk and upside can now be quantified.*

For those following the entire series it is worth noting that we are doing something very different in this “outlier” analysis compared to the previous “predictive” analyses. Before, we wanted to “predict” the future based on currently available data. Today we have shifted to trying to find ‘value” by identifying the biases of other decision makers.

*Mike Lewis & Manish Tripathi, Emory University 2015.*