Expected Points (xP) & Points Over Expectation (POE)

In other sports, the concept of expected points, goals, etc. has been around for a while. Volleyball seemingly lacks this concept on a familiar level and so I figured I’d take a shot.

In basketball, expected points (xP) is a common metric. Oh, the Warriors on a corner 3? That’s worth 1.3 points per shot. Lakers on a pull-up midrange shot, that’s worth 0.7 points per shot. Based on specific inputs (location on the floor, type of play, distance from nearest defender, etc), we expect certain results. Basketball is easier in some respects, it’s a little more binary. The shot went in, the shot did not go in. There’s no, you missed the shot into the antenna and scored for your opponent. But the concept is the same. There is an input followed by a result.

In volleyball, because of non-terminal touches, we must account for these non-binary results. Yes, the attack wasn’t a kill, but was it a tip to the libero or a hard swing at the setter and now the defense is out of system? These outcomes have different values to the team who just attacked. For example, the attacking team is working with a perfect pass, they set the middle, and the middle tips to the libero who digs it perfectly. In this example, let’s say a perfect pass usually leads to an efficiency of .400. Pretty good. That’s like being on a fast break in basketball and all you need to do is go up for the dunk and handle your business. But oh no! Your middle gets nervous and tips the ball to the libero and it’s a perfect dig. We know from historical data that when your team is facing an opponent who just made a perfect dig, your team typically loses on the resulting attack at a rate of -.300 meaning you are now more likely to lose the rally than to win. Makes sense, as you’re trying to defend an in-system attack.

But here’s situation two. Middle gets up and tees off on the quick set and tags the libero in the face as the ball sails into the stands. A kill carries a perfect 1.000 efficiency with it. In both situations, the expectation is that the middle will hit for a .400 clip. This is the expected points (xP). But what we really care about is how well she does, relative, to what we already expect. It’s a perfect pass, we certainly expect her to do better than if she was hitting a crazy out of system set from 45 feet away. This is what we call, Points Over Expectation (POE). In the first situation, the middle’s input is .400 because it’s a perfect pass. The middle’s output is -.300 because she put the opponent in a great situation. In this case, her POE is outcome – input. This is -.300 – .400 which is -.700. That’s tough. She’s basically cost us a point here because she took a great situation and made it terrible for us.

This is the overarching concept I’d like to introduce in the coming posts. The idea that before every contact of the volleyball, there is an expectation. After every contact, there is a result. Because not every touch will be terminal, these expectations and results will be continuous variables ranging from -1 to 1. Oh, you’re about to serve, well before you even know the quality of the pass, the serving team in the Pac 12 typically loses the rally at a rate of -.220. But this makes sense, teams siding out obviously have the advantage. Now the pass happens and it’s a perfect pass. The serving team’s win rate just dropped to -.300. So they’re still likely to lose, but really, only -.300 – (-.220) or -.080 is because of the server himself. So he receives a POE of -.080.

The reason we like acknowledging expectations is because it better allows us to rank players. If Joey is a middle and only hits off a perfect pass, he’s likely to score at a great rate. But if Mateo is my opposite and he’s just in there to bat cleanup and crush high balls when we’re out of system, well, he’s likely to do worse than Joey in the aggregate – and we should account for this.

With xP and specifically POE, we can identify players/teams/conferences that handle specific skills and specific phases of the game with true excellence – those who deserve more credit for their brilliance or less credit for a statistically dull performance. But my favorite, beyond simply ranking players, is to use these metrics to see what wins games. To see the top players with better vision of when they falter – to steal their ideas when they don’t and create novel solutions when they do.