Aggressive serving is something that is talked about a fair bit in volleyball – especially at the higher levels. Offenses are so powerful that a side out can be nearly automatic when teams pass well. Thus there’s the desire to force teams to pass less than well, which requires good serving.

There’s an obvious trade-off involved in aggressive serving, though. If a serve is missed it’s an automatic point for the other team. We can think of this in a mathematical way. The expected point value of a serve is a function of the probabilities of the various outcomes involved. Those outcomes include service errors, service aces, winning the rally and losing the rally. You can create a formula for the expected value of a serve (EVS) that looks like this:

EVS = PA – PE + (1-PA-PE) x (PRW – PRL)

Where…

PA = % chance of an ace (in decimal form – e.g. 10% = 0.10)
PE = % chance of an error
PRW = % chance of a rally win
PRL = % chance of a rally loss

Let’s put that in an example form. Say a given server gets and ace in 1 out of 20 serves (5%) and misses 2 out of 20 (10%). When the serve is in, the team wins the rally 60% of the time. The above formula would look like this:

EVS=0.05-0.10 + (1-0.05-0.10) x (0.60-0.40)
= 0.05 – 0.10 + 0.85 x 0.20
= -0.05 + 0.17
= 0.12

Thus, each time this particular player serves the team expects to score 0.12 points. If you play around with the numbers in different ways you can see how being more or less aggressive impacts that EVS value through the impact it has on ace and error percentages and the chances of winning the service rally.

We can translate the desire of coaches to get the opposition out of system into a desire to increase service rally win % – PRW from the formula above. If the team is going to get more aggressive serving it should increase the PRW (and reduce the PRL) and/or increase aces (PA) to improve the EVS, but it will also likely mean rising PE, which hurts the EVS. The question a coach needs to answer is whether the positive move in PRW and/or PA more than offsets the rise in PE. If so, then it’s a good idea. If not, then there’s a problem.

In other words, serving tougher only makes sense if the increase in service rally wins at least offsets the rise in service errors. Here’s more on the subject.

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