Step 11.5: Probability to Win the Point, Expected Value, and Other Metrics. A Quick Pitstop.

You may be seeing terms like Expected Value (eV), Win Probabilities, or other terms floating around this blog. I’d just like to take a quick second to help translate what’s being talked about.

Expected Value (eV) – its notation appears similar to a standard hitting efficiency. It’s shown as a rate, meaning we divide by the total number of attempts – but it’s also an efficiency in that we look at (Won Rallies – Lost Rallies) before dividing by Total Rallies. We see values ranging from -1.000 to +1.000 on a continuous spectrum, much the same as attack efficiency. Where this blog is a little unique, we’re looking at the Expected Value of any situation, much like in the NBA where every shot has an expected value based on the number of points it’s worth, multiplied by the likelihood of making the basket, given the defensive conditions (3-point shot, 40% accuracy = 1.2 expected points per shot). In our case, since all points are worth one, but I can score for either my own team…or for my opponent, we use a range of -1 to +1 to encapsulate these possibilities – and then we use (won rallies – lost rallies) / total rallies to determine the likelihood of scoring. Anything positive, is of course good for me. Anything negative, benefits my opponent. It’s like a turnover in basketball, while I may not have made a basket for my opponent, I have created an advantageous situation for them by giving them the ball. In the NBA, a turnover might be worth 0.7 (?) of a point or something along those lines. We can describe volleyball in a similar fashion: if I tip an easy ball to their libero for a perfect dig (a turnover), I’ve put my opponent in a better position – for the Pepperdine Men, this is worth exactly -0.175 points. Every time a Pepperdine attacker hits into a perfect dig by their opponent, we can think about it like giving our opponent 0.175 points. If we hit the ball out of bounds, we give our opponent a full 1.000 point. In the aggregate, we use Expected Value to better account for player actions, especially on touches or skills that do not terminate the rally (think: reception, dig, set, in-play attacks, etc).

Point Win Probability (PWP) – think of this as simply a scaled version, a normalized version of Expected Value. It’s very similar to how people think of Sideout% or Point Score%. Points won when receiving divided by total receptions or points won when serving divided by total serves (respectively). Rather than a range of -1 to 1, Win Probability ranges from 0 to 1. But of course, in a rally scoring era, if you didn’t win the point, you lost it. Personally, I think some of this notation and the way we think about these stats is leftover from the Sideout Scoring era where needed to serve in order to score. Sideout and Point Scoring were cleanly distinct from one another. But today, in Rally Scoring, who cares if I serve or receive? I want to win the point. That’s what matters. We use this simple formula to normalize the data:

All this really translates to is: Win Prob = (Expected Value + 1) / 2

Here is the exact same graph, converted to Point Win Probability (PWP).

It’s no different than Expected Value other than the values have been scaled. Some quick math tells us that a .200 difference in Expected Value is worth a 10% boost in Point Win Probability…maybe that helps you think about this? Or confuses you even more.

But this style of notation might be easier to digest in context with other sports. If you were to chart out the whole rally, based on who had the advantage as the ball changed possession mid-rally, it might be easier to say your team has a 65% chance to win given the perfect dig, you set your outside who gets a great 1-on-1 and the Win Probability jumps to 72% given this situation. And then the kid waffles the ball clean out of bounds. 0%. Dammit.

You could describe play by play in either fashion, you could do summary statistics in either fashion, Expected Value and Point Win Probability are the same numerically, just on different scales. When we say we want to have a Sideout% of 70% – all that translates to is that we want to have an Expected Value of 0.400 (remember, (0.400+1) / 2). They’re interchangeable, useful in different circumstances, and equally confusing to some of you I’m sure 🙂

But for now, I’ll leave you with the chart above. The overlay of Expected Value and Point Win Probability for the Pepperdine Men in the shortened 2020 season and let you digest these two metrics a little.