The Golden State Warriors beat the Cleveland Cavaliers to win the NBA championship despite the best efforts of LeBron James. With the Cavaliers depleted by injuries (particularly to Kevin Love and Kyrie Irving), James was faced with carrying his team against a very talented and well-rounded Warriors team. And he was most certainly up for the challenge, LeBron had an amazing series, shouldering even more responsibility than usual and making it competitive against the Warriors.

**LeBron’s performance in the finals got me wondering:** Can we pinpoint exactly when he started to increase his output? Did he step up his game for the finals in particular, or had he been ramping it up throughout the playoffs? Or maybe his performance in the finals was nothing unusual, although I seriously doubted that.

First things first. We should plot his data for the entire season. There are many ways to evaluate a basketball player’s impact on the court. But for our purposes, let’s just look at his points scored, rebounds and assists.

The data seem a little too noisy to say confidently where LeBron started to increase his output. It’s probably safe to say that his rebounds started to increase around game number 75 (which happens to be the beginning of the playoffs), but it is hard to say. So let’s see if we can use a statistical model to help us find the changepoints.

**Finding the changepoints**

One approach to finding changepoints in our response is to fit a model like

E(points in game 1) = $$\beta_0$$

E(points in game 2) = $$\beta_0 + \beta_1$$

E(points in game 3) = $$\beta_0 + \beta_1 + \beta_2$$

and so on. This model generalizes to:

E(points in game $$j$$) = E(points in game $$j-1$$) + $$\beta_j$$.

So anytime one of our $$\beta_j$$ is nonzero, we know that our mean has shifted up or down at game $$j$$. We can use a variable selection technique to tell us exactly which of those parameters should be nonzero. If we use the Lasso for estimation and selection (available in the Generalized Regression platform in JMP Pro), this model is a special case of a model called the fused lasso.

**And the model says...**

Let’s take a look at the results of our fused lasso model for LeBron’s points, rebounds and assists. The prediction functions for these models give us a much clearer picture than when we looked at the raw data. LeBron’s points remained constant throughout the regular season, started to increase throughout the playoffs and peaked during the finals. His rebounds steadily increased over the regular season, but increased more dramatically throughout the playoffs. Likewise, his assists jumped up during the playoffs as well.

You want your superstars to respond on the biggest stage, and I feel like LeBron truly did that. Things looked bleak when both Kevin Love and Kyrie Irving got injured in the playoffs, but the remaining Cavaliers were up for the challenge. The Warriors were expected to run them off the court, but the Cavaliers were able to make it a competitive and entertaining series, thanks in large part to LeBron’s historic performance. And this is high praise considering that the Cavaliers took out my beloved Atlanta Hawks in the Eastern Conference Finals!

**Reference**

Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., & Knight, K. (2005). Sparsity and smoothness via the fused lasso. *Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, *67*(1), 91-108.

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