Expected Points Gained, A Framework For Evaluating Actions On A Basketball Court

What is more valuable, an offensive rebound or a defensive rebound? Consult Expected Points Gained.

The currency of a basketball game is points.  This is obvious.  After all, this is the one thing we add up to determine who won and who lost.

This really simple insight actually has a lot of value as a framework for evaluating everything that happens on the court.  Each action that a player takes, be it good or bad, has to have its effect traced back to the scoreboard to be properly measured.  Of course, some actions, like made jumpers and rebounds, are neatly recorded in the box-score and others, like contesting a shot or moving the ball quickly to keep an offensive action going, are not.  But, at the end of the day, we really need to tie everything back to points.

I should point out that this framework for thinking about an NBA game was, of course, not invented by me.  Lots of really smart people have thought about the game in this flavor, including Dean Oliver in his seminal Basketball on Paper.  What I am trying to do here is present the idea in a way that I personally find appealing and intuitive.

Defining Expected Points Gained (EPG)

When I discuss relating the actions on the basketball court back to the basic currency of points, I am talking about much more than simply counting the points scored by each player at the end of the game.  What I am really getting at is something I am calling Expected Points Gained.

Expected Points Gained (EPG) = Expected Margin of Victory After an Action – Expected Margin of Victory Before an Action

An action in the above definition is just what you might expect: something that takes place on the basketball court.  Let me give you an example:

Say a player makes a 10-foot jumper.  What is the EPG from this action?  Well, currently in the 2018-19 regular season, the average team offensive rating (points per 100 possessions) is 109.7.  This means that the offense is expected to score about 1.10 points from 1 possession.  The made jumper was worth 2 points so, from the perspective of the team which made the jumper, the expected margin of victory has increased by 2.00-1.10 = 0.90 points.  Their EPG from the made field goal is 0.90 points and their opponents have a commensurate -0.90 EPG.

Simple, right?

It Gets Complicated Fast

The thoughtful reader might look at my previous example and feel like I’m leaving a bunch of stuff out.  I started with the assumption that an offensive possession was worth an expected 1.10 points.  But what if the possession was in the half-court? Half-court possessions score less points than fastbreak possessions, on average. And what if the possession belonged to the Golden State Warriors rather than, say, the Chicago Bulls?

Also, that made 2-point jumper effects more than just that one offensive possession, right?  I mean, the opponent is taking the ball out of their own basket and not sprinting down the court for a juicy transition look.  That’s got to be worth some expected points as well.

And we can go deeper and deeper.  Why use the expected margin of victory at the beginning of the possession as our baseline?  Why not consider the fact that there were 5 seconds left on the shot clock?  Perhaps the offense was only expected to make 0.90 points on average that late in the shot clock, making the EPG higher than we initially calculated.

So what’s the right level to calculate EPG at?

This is a tricky question, but in the end it really depends on context.  Evaluating an offensive (or defensive) possession for a team, we would probably want to compare the expected margin of victory after the possession has ended with the expected margin of victory when the possession began.  It makes sense to view things at the zoomed out possession level because we are evaluating the entire team’s performance, rather than that of a single player.

However, in the context of evaluating an individual player’s action, we might instead be interested in the baseline expected margin of victory immediately before their action, rather than at the beginning of the possession.  To see this, let’s think about an offensive rebound.

The Value of a Rebound

Say that our hypothetical 10-foot jumper is missed instead of made, but the center then secures the offensive rebound.  How does this fit into our EPG framework?  Well, the offensive rebound rate (the proportion of missed shots which are rebounded by the offense) this year is about 0.23, per basketball-reference.  Let’s assume for a moment that the offense will score an expected 1.10 points (the same as an average possession) if they do in fact secure the offensive rebound.

Now we can compute the expected value of the possession before the offensive rebound but after the missed shot as

Expected Points Scored Before Offensive Rebound = (Expected Points Score Given a Defensive Rebound) * Probability of Def. Reb. + (Expected Points Score Given an Offensive Rebound) * Probability of Off. Reb. = 0 * 0.77 + 1.10 * 0.23 = 0.25

After the offensive rebound, our expected points scored are 1.10, so the EPG of the offensive rebound is 1.10 – 0.25 = 0.85.  On the flip side, if the defense had instead secured the defensive rebound, their EPG would have been 0.25 because the value of the opponent’s possession would have fallen from an expected 0.25 points to 0.

A cool consequence of this calculation is that we have determined, from an EPG perspective, that an offensive rebound is more valuable than a defensive rebound.  This is really a direct consequence of the fact that a missed shot is more likely to be rebounded by the defense than the offense.

The Approximate EPG of Some Common Actions

Having already computed the EPG of a made 2-point jumper and an offensive and defensive rebound, let me display a handy table of the EPG of some of the other common, box-score recorded actions on a basketball court.

I will say from the outset that I am computing these under a few simplifying assumptions.  I am assuming that each offensive possession begins with at 1.10 expected points scored, as I did in the made 2-point field goal example.  I am also ignoring the value an action has on possessions after the current one, i.e. the value a forced live-ball turnover has from the fastbreak which proceeds it.  I am making these assumptions mainly to the make the calculations simpler.



My main goal in writing this was to encourage you, the reader, to evaluate actions on the basketball court in terms of points.  Specifically, Expected Points Gained (EPG).  Using EPG, we can assign a value to things like offensive rebounds and made 2-pointers.  Unfortunately, actually calculating EPG can get a bit messy and is inherently tied to the context we want to consider the action in.  I plan on using the concept of EPG in future posts to make some points about the value of certain things happening on the NBA court.

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