Number Theory - eV with Chad Gordon (part 2)
Number Theory - eV with Chad Gordon (part 2)
Expected Value
This is the second part of eV. Please read part one to better understand what’s being discussed here.
In part one, I explained how Expected Value (eV) can be more intuitive and beneficial than traditional skill performance metrics. This part will show examples of eV being used to compare expected outcomes to actual outcomes.
What is Number Theory? - Read here
Through his work with eV, Chad has come to see volleyball very differently than most because he has trained his intuition to better gauge the value of situations. Because he better understands the probabilities around those situations, he coaches accordingly in practice and competition. For reasons I’ll explain below, Chad puts more energy into coaching teams to not get aced than to pass perfectly. Also, he talks to attackers about “green light” and “red light” attacking situations, helping them recognize moments in which they can be more or less aggressive based on what he knows about eV. It’s important to point out that they don’t need to know exactly how good or bad a situation is in terms of eV, just a rough idea of “how far from 50%” it may be (see part 1). Calling a situation “green light” or “red light” is Chad’s way of communicating to players how far from 50%, in either direction, a situation may be. This is one way that Chad categorizes situations to help players see the contrasts between them.
When Chad and I were discussing eV, he commented that humans, by nature, notice contrast. When what you see matches your sense of what you should see, there’s no contrast. What stands out is when there is a large difference between what you see and what you expected. Expected Value is great at quantifying the difference between what a situation should yield and what it actually yields. Quantifying the difference is important, particularly when the difference is large enough to matter but evades our attention none the less. This is the principle behind Moneyball tactics for finding overlooked value. Setting better expectations and educating your intuition about situations gives you a different lens to interpret the game through. As a result, some things that may have previously escaped attention become more surprising.
One volleyball skill that looks very different through an eV lens is serve receive, for which Chad has written an excellent example. The linear nature of traditional reception grading leads coaches to value improving good passing to perfect more than the situations are actually worth. For instance, my team historically wins the rally about 62% of the time after we pass the ball perfectly, about 60% of the time after a near-perfect pass, and about 57% of the time after a medium pass (the eVs for passing a 4, a 3, or a 2 respectively). There’s not much for us to gain by improving our receptions from 3s to 4s and surprisingly little value added by improving from 2s to 3s. However, we win the rally only about 50% of the time after a poor pass (1-option). There’s much more value in improving poor passes to medium passes than there is in improving medium passes to perfect. (There’s a larger difference in eV between 2s and 1s than there is between 4s and 2s.) There’s even more value in just keeping the serve in play versus allowing an ace. My team historically wins 29% of rallies in which we couldn’t take a first swing but nobody in the history of volleyball has won a rally in which they were aced. So even though not getting a first swing is hard to overcome, there’s still a decent chance (3 in 10) of getting a point. The eV differences between in system receptions, out of system receptions, shanks, and aces are great examples of Chad’s comment that humans notice contrast. That contrast is not nearly as clear when only considering reception averages but becomes obvious when considering eV.
Another way to use eV is to quantify the concept of “bettering the ball”, where a team wants to, at best, improve the situation they are in from one contact to the next or, at worst, maintain the same level under difficult situations. Chad stated during our conversation, “all coaches are asking for is a positive change of state from one touch to the next.” Expected Value is a way to determine if a team improves the state of play from one contact to the next. As I’ve dug into eV data for my team, I’ve learned that there’s not much room to improve a team’s eV after the first contact. But, there’s an easy way to lose a lot of value with the second contact, and that’s by bump setting. Even if a team bump sets well, my data shows, their eV is 53%, regardless of first contact quality. The least successful hand set locations are all at least as valuable as a well-located bump set. Even a poor pass with a good hand set is a better situation (58% eV) than a good bump set following any first contact. So if you want to better the ball, perhaps the easiest situation to look for is one in which your setter can hand set to an attacker but isn’t, maybe because they think they’re playing it safer. This is just one example of situations you can look for to increase your team’s eV.
To measure “bettering the ball”, Chad uses Expected Value Added, or eV+. While it sounds fancy, all it does is compare the expected value of a contact to the actual outcome of the contact. Ultimately, the actual outcome is determined by if your team wins the rally or not. So, in reception, when my team gets both a perfect pass and a good set, the first ball attack has an eV of 68%, which suggests that we should win about 2/3 of those rallies. If the attacker kills the ball, the actual value is now 100% so the attacker’s eV+ is 32% because they added 32% value (100% - 68%). The attacker added value, but they also didn’t add as much value as they could have in a different situation. If that same attacker kills a ball following a poor pass, the eV+ is 56% because they have added 56%, which is more noteworthy (100% - 54% because my team’s eV on a poor reception is 54%). These two situations show how the attacker bettered the ball, but to different degrees. The kill after a poor pass is more valuable because it added more value. Consider a case where the setter betters the ball, a poor pass followed by a good set: the attack has an eV of 58%, which is a little better than the 54% eV when my team passes poorly. The setter’s good set has an eV+ of 4%. There isn’t much else the setter can do to add value, it’s up to the hitter at that point to do their best. But the setter did what they could by locating the ball well, which made the attacker’s job slightly easier.
How did I construct the eVs I’ve been using in this series? Or, more importantly, how do you build your own eVs? It can be incredibly simple or incredibly complex so you can choose how deep you want to go. Chad wrote an introduction to calculating eVs for different skills in which he provides his eVs and encourages people to “steal my numbers if you want”, which is a solid recommendation if you don’t have the time, data, or comfort to do it yourself. If you opt for using his eVs, you should do so with an awareness that they may not translate well to your world. (Joe Trinsey explain some broad differences between worlds in terms of “flippenings”.) If outcomes of rallies are significantly different or if situations happen with much different frequencies where you coach than where Chad’s data came from, then his eVs will be less useful because they will be less predictive. As Chad and I discussed, standards, like his eVs or those you might get from sources like Gold Medal Squared or Art of Coaching are helpful if you can’t build your own but those might not apply in more nuanced settings where the differences matter far more. The best way to figure out how applicable someone else’s standards are is to create your own for the sake of comparison.
But fair warning, even on the simple end of the spectrum, it does take time and data. If you’re in the college or professional games, your data comes from Volley Station (VS) and Data Volley (DV) scout files. If you’re not working with a college or professional team, you can still build your own eVs if the data you have is properly structured. At its simplest, eV needs two different pieces of information, some description of contacts within a rally and which team won the rally. The contact descriptions don’t have to be intricate, but they must be enough to allow different situations to be separated when looking at the data. That means you don’t have to measure reception on a four-point or three-point scale, you can use any criteria you want. For instance, Jim Stone explains a basic method that looks at if the ball went to target or not, which is effectively a two-point scale. As long as you can tie the description of the skill to winning rallies, you can construct eVs for that skill.
Once you have data that can be evaluated relative to winning rallies, you’ll simply calculate how often you win rallies when a skill is performed in a certain way. In part one, I told you that you already knew enough about probability to use it in the context of eV. Side Out Percentage (SO%), for instance, is fundamentally an expected value (and, therefore, a probability) because it tells you how often you can expect to win a rally when you are receiving. In fancy probability terms, here’s what SO% is saying.
This is a conditional probability, and it reads as “the probability of winning the rally given that you are receiving serve”. The numerator of the fraction is the intersection of winning points and receiving serves, so it counts every time both events occur together. The denominator of the fraction counts only times that you received serve. That can be written in a much simpler, plain-math way.
If you were thinking that all eVs and probabilities were complex and hard to calculate, SO% is the simplest example of an expected value. In part three, I’ll dig into why SO% is actually an eV and use that to begin an exploration of creating your own eVs.
Number Theory - eV with Chad Gordon (part 3)
Have questions for Chad? You can ask me here or you can email him directly.