Stats for Spike-Let ‘er rip. Or not.

This topic comes up every quadrennial, or in this case, five years, when we are treated to the spectacle of volleyball in the Olympics, the showcase event for our sport. Why are these top-level athletes missing so many serves? They are the best of the best, why can’t they serve a ball over?

The philosophy is this: at the highest level of our game, a controlled serve does not put enough pressure on the passer to make them pass into an Out-of-System play; in order to put pressure on the passer, the serve must be as difficult to handle as possible, the intent is not necessarily to ace out the passer, but to get an Out-of-System pass.

 

As the coach, you have to give the passers the green light to rip it because human nature is such that the players respond intrinsically to the rewards/consequence cues that the coaches feed back to their play, i.e. if you want them to rip it at full speed, you have to be willing to take off all the constraints and learn to live with service errors. Coach Speraw's philosophy is that if the team does not make a certain number of service errors every set, the team is not serving aggressively which automatically translates to points for the opponent. 

 

There have been a number of responses to this idea on Volleyball Coaches and Trainers. Some sampling:

·       It is aesthetically unpleasing to see all the missed serves at this level, especially those serves into the middle of the net. Or it is shameful how our best players can’t serve a ball over the net.  I don’t think the players, or the coaches care about the aesthetics. They want to win, and to win, they must score points, to score points, they must serve tough, all the time. The aesthetically pleasing mindset also reveals a latent vein of thought: failure is undesirable and must be avoided. Even as coaches are beginning to come around to the mindset that errors are the natural way of testing the player’s skills in the competitive environment, the best way to learn,  and the only feedback mode that matters; we, in our weakest decision-making moments reach back to the safest and most certain decision-making bias because we are afraid of the unknown and we will inevitably reach for the known and safe.                The other part of this reaction is that many responders are assuming that the level of volleyball as we teach it to our players are played at the same speed, force and intensity as the volleyball that is played in the highest level of the game; that is definitely not the case. Most of us understand that the speed and athleticism displayed in every level of play is tightly coupled to the athletic and cognitive abilities of the players. As the players and games evolve, the strategies and tactics must also evolve to resolve the challenges presented at each level. We also forget that the  speed, force, and intensity at each level rises exponentially as the level of the game being played progresses.

·       Situational: when the score is close or you are approaching that end of set mark, you should just make sure that the serve is in. Or, we need to know when to throw in a changeup in our service to catch the other team unaware.  This statement will be addressed after I introduce some probabilistic definitions.

Probability and Volleyball Statistics

From Wikipedia: https://en.wikipedia.org/wiki/Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

How do we come up with the probabilities? In most cases, we use descriptive statistics, i.e. game statistics that are taken regularly in volleyball. This definition comes from (Spiegelhalter 2019).

To be clear, probability is usually associated with being a measure of uncertainty, whereas statistics are presented without including any measure of uncertainty.

There are numerous kinds of probability, the ones we usually employed are as follows, this is not a complete list:

·       Classical probability: The ratio of the number of outcomes favoring the event divided by the total number of possible outcomes, assuming the outcomes are all equally likely.  

It is easy to see that we can readily use this when we are doing counting statistics in volleyball. Hitting percentage, kill percentage, Service efficiency etc.

·       Long run frequency probability: based on the proportion of times an event occurs in an infinite sequence of identical experiments.

This kind of probability is the kind that we tend to lock into as the THE objective probability, i.e. this is the foundation of our beliefs when it comes to making our decisions. There are problems with this kind of probability, they are hard to compile because their robustness depends on the law of large number: big numbers in the denominator means that the probability is more likely to be true universally, but the statistics we take in sports have infinite numbers of correlation and factors which affects the statistics. If we chose to ignore the different factors, we are also choosing to include the effects of those factors without recognizing their effects while we are accumulating that large denominator.

·       Propensity or chance: idea that there is some objective tendency of the situation to produce an event.

This is what we choose to believe, this is the basis of our faith in the numbers.

·       Subjective or personal probability: specific persons judgment about a specific occasion, based on their current knowledge, and it's roughly interpreted in terms of the betting odds.

This is the probability that we employ when we go by gut feel or by our intuition. This has generally been dismissed as a decision-making tool because of the amount of bias that can be subconsciously included in the internal calculation of the personal probability. Yet we ignore this kind of probability at our own peril because experienced coaches and scouts have their personal probabilities which are not only valid, calibrated, but also rich in insights, which are not measurable nor consciously identifiable.

 

While professional sports have embraced the Moneyball religion, many professional teams are working with the greybeards in the sport to create a way to integrate the statistics driven approach with the personal probabilities of the experienced coaches because they are finding that just Moneyball is not enough to help them make decisions, that those intangible and unexplained gut feels might be valuable and they need to take advantage of both, in close coordination.

The most common way to generate probabilities is to take the game statistics and turn them into classical probability. The next step is to take as many of the same type of statistics and then combining them to create a long run frequency probability. The belief is that this is the Propensity or chance or the underlying objective probability of  process. For example, if I took my teams hitting percentage over the course of a season, then I have the probability by which I could use as the reference by which I can compare to each match. The problem is that the playing parameters of each match is different: easy serving team versus tough serving team, big blocking team versus a smaller team, teams that runs fast versus teams that sets high and slow, ad infinitum.

Now for the interpretation of the probability. Most people look at a probability to mean that given the same conditions, the results would mirror the probability, but the optimistic bias that we all have subconsciously makes us think that a 99% probability of success means that the action being performed successfully is a foregone conclusion, that is, we can predict that we are going to be successful 99% of the time, but we always neglect that 1% where we are not going to be successful. We would usually take that gamble because the odds are pretty good, but we also blame bad luck when we are not successful. Luck had nothing to do with it, the probability told us it was going to happen. The other part of the consideration is the assumption that the long run frequency probability is not as representative as we think it is because we are ignoring all the other factors.

Let ‘er rip

Back to the original discussion.

There are essentially two probabilities that comes into play in this decision.

The first probability is the success rate of a particular server. The second probability is the success rate of the opposing offense in siding out based on the kind of serves that they are served.

The probability of success of a particular server can be rewritten, if there were enough data into a probability distribution function: the classic bell curve, we are assuming a bell curve, normal or Gaussian distribution, because it is mostly true, and the bell curve allows us to use the classical probability data to extrapolate the results, to allow us to draw inference. Of course, as any good coach knows, the human factors play a large role in affecting the server success probability.  A ten-year-old serving in a game for the first time or  a player serving when their team is behind in the Olympics apply different psychological pressures to the server, even though the results may be the same, blow the serve and you suffer immense embarrassment. There are factors that play into the calculations as well: serving in a large gym that has bad background contrast for server depth perception; strange air flow patterns in an unknown gym, amongst many other things.

In the case of our national team, the coaches have been effusive in their praise of the statistical team, so I am sure that the coaches have good data on each server and their probabilities of success under many different conditions. I am also sure that the coaches make their own adjustments to those probabilities based on what they know of the psychological makeup of their players. I know that both teams employ sports psychologists. But that is just the side of equation that everyone seems to focus on directly.

The criticism is that they err too often. Many will bring up the fact that if they require their players to get the ball in no matter what, why can’t the national team do the same? The difference is that the jump topspin is a high risk, high reward serves, it is a chance that the national team coaches see as an acceptable risk, even if the high risk of the serve translates to higher error rates. The national team coaches understand this fact and are willing to take this chance because when compared with the probabilities from other side of the equation — the sideout rate of the other team when faced with different serves— the payoff outweighs the risks.

It is curious to me why this part of the decision-making equation is so often ignored. If there is a serve there needs to be a pass, they are continuous actions. They are, in essence, one event. We tend to split it into serve and pass components so that we can understand the action in terms of the skills, which sometimes leads us to erroneously view them as being independent actions. Serving statistics should always be spoken of as a conditional probability: we have  this kind probability of success given that we are serving this specific serve against a team that passes that specific serve with a given  probability of success. Passing should also always be spoken of as a conditional probability: we have this probability of success given that we are passing this specific serve against a team that serves the specific serve with a given probability of success.  It is at the confluence of the two conditional probabilities that we can make good decisions.

In this instance, the sideout rate of almost all the teams when served a less than full speed jump topspin has been assigned to be 100%; that is, anything that is less than full aggression will essentially give the opponent a free ball. Indeed, as we watch the Olympic teams, the sideout rate for serves delivered with full aggression are still high, but not 100%.

The question is: how realistic is this assumption? Are the coaches being intellectually lazy by just assuming that the opponents are that proficient at siding out under these circumstances? I don’t have access to the data. I would assume that all the national teams in the Olympic tournament would have extensive statistics about the top teams, at the minimum. What does the real sideout rate have to be in order for the national team coaches to back off of the Let ‘er Rip standard?  I am not sure, but seeing the serving game in Tokyo, I am going to go with the coaches.

Which brings us back to the serving abilities of all the servers. First, given the steadfast belief that the coaches have on the sideout proficiencies of the opponents and the high-risk nature of the jump topspin, no player with a horrible probability of success with a jump topspin would be allowed on the court, or they have been trained to improve their probability of success for a  jump topspin. The determining factor  has to do with the execution of the serve, how the players react to each situation, whether they hurry their serving ritual, whether they get distracted by the situation, or whether they are able to adjust to the environmental conditions. This then makes the decision not of strategy and tactic but of execution.

Someone suggested that perhaps the team can employ a surgical approach: go full out until the score gets close or when the score is close to being 25, then just get the ball in, whether by serving short or go to a jump float.  One problem is that if the teams show this kind of tendency, the opponents will undoubtedly know it, and it is difficult to trick your opponents at this level. The other problem is that since the players are human, and mostly risk averse by human nature, it is a mental struggle to actually go 100% on a swing because they will subconsciously pull back a little bit when executing, just to be safe, if they were told to pull back consciously, the edict would contradict the team philosophy of being actively aggressive, chances are that the serve that would result might be not effective, or that the opponent handles the obfuscation easily. This is not to say that it is a bad strategy, but making that decision requires that the player and coach know and understand how well the opponent knows the team and whether the opponents can be caught by surprise. More variables which contribute to the decision and complicates the calculation.

As I had said in the beginning, this discussion pops up all the time, mostly during the men’s college season and during the Olympics. It is a healthy discussion to have and I doubt this essay will change too many minds one way or the other, although I hope that this essay does introduce some probabilistic concepts as well as provide some other points of view to the coaches who have so passionately debated this particular topic.

Works Cited

Spiegelhalter, David. The Art of Statistics: Learning from Data. London: Pelican Books, 2019.

 

 

Stats for Spikes-Markov Chains

People have used the Markov chain to model volleyball for a while now. The presentation by Albert (Albert 2018) shows that Markov chains were used to:

·       Determine how long a game will last under each scheme, rally scoring or sideout scoring.

·       Determine the probability that a team wins in each scheme, rally scoring or sideout scoring.

·       Determine the value of serving first in sideout  scoring.

The Albert presentation conceptually shows how the volleyball probability tree is built using Markov chains. She demonstrates that Markov chains is useful in simulating the flow of the volleyball match so that the length of matches can be accurately determined, as it uses probability distribution functions to model the uncertainties in a match. If I recall correctly, Markov chains were used to help FIVB model the differences between sideout and rally scoring when they were thinking about changing the scoring.

This presentation piqued my interest in the Markov chain. I became curious about using the Markov chains to model the number of decision points in a match, and how these decisions are dependent and based on the probabilities that describes each action, how many different probabilities are necessary to improve the accuracy of the simulations.  

What I have done as an exercise is to model just the sequence of action in a serve receive situation. There are separate probability trees and flow charts that can be generated for different situations: my team serving, and continuous rallies. The flowchart for my team serving would be identical to the one I created for my team receiving, but with the roles and point winner reversed. There would also be a separate flowchart needed for when the team on defense reverts to offense for a counterattack, the probabilities used in this flowchart might be slightly different because of the counterattack may come from a more chaotic set of conditions, thereby changing the probabilities used. This is just a partial deep dive into the flow of the game and possible implications of the uncertainties coming from twelve individuals playing with a net. I had never intended to build a simulation based on the Markov chain; I leave that to others.

I used the flowcharting diagrams to map out the Markov chains and any errors in the assumptions and the flowcharting is entirely mine as I created this flowchart for my own edification. This is not a traditional way of representing Markov chains, but it made sense to me when I started looking into the Markov chains. It also demonstrates the complexities from the geometric concatenation of each succeeding action as the actions accumulate.

Purpose

There are two purposes:

·       Examine the number of decision points and all the probabilities that feeds into that decision.

·       Counting the number of probabilities that is necessary for just one rally.

Probability

A simple definition of a probability can be: the number of instances that an event A happens in a total of N attempts or opportunities where A could have happened. Pr(A)=Occurrences of A in total occurrences/Total Occurrences of the Event.

The reason that I set the number N to infinity is to show that the law of large numbers is at work and it is best to get as many samples as possible so that the probability calculated is as representative of the event A happening as possible.

Note that the probability is NOT a prediction, it is just a way to give the user a sense of what are the chances that A can happen. This also means that Not(A) can happen as well, the probability of that is Pr(Not A)=1-Pr(A). It can be either one, this is a critical concept to absorb.

Conditional Probabilities

I have used conditional probabilities to gain some granularity to show the dependence that the outcome of each action has on the immediately previous action. Markov chains model a specific event which is composed of many complex interactions of many previous events. Whether we like it or not, even as the play moves further away from the initial point of contact —the serve — each action level in the continued play is still historically dependent on that first contact, although the effect decrease dramatically as the play evolves away from the first contact. The conditional probability is the memory that is hardwired into the computations as it flows away from each of the past actions, because the effect of each previous action is already contained in the conditional probabilities, it is therefore not explicitly reiterated with every step.

The equation:  Pr(A|B) is read as the Probability of event A being true if we know that event B is true. In other words, the probability of A being true is dependent on the probability of B being true. This is how each level of action is linked to the previous level of action.

The probability of each result becoming true, whether it is a point for the serving team or for the receiving team can be calculated by following each action through the flowchart and multiplying the conditional probabilities for each level of action together until an end point is reached. It will become obvious as the process is explained.

Starting

The bubbles on the right notates the actions. The red oval indicates a point for the opponent. The blue oval indicates a point for us. The purple diamond indicates a decision point. The black parallelogram indicates an action and the kind of conditional probabilities that are associated with the action. The green parallelogram indicates a transition to another phase of the game which will follow another flowchart.

The first decision is which serve to execute, that decision is made by either the server or the coach of the serving team. What is left unmodelled is the decision process that goes into the server and the coach’s mind: which passers to target, which zones to attack with the serve etc., those decisions are left out for simplicity and brevity, mainly because this is not a rigorous exposition on every single consideration that goes into a decision. The probability of the success of the  serve chosen is based on the successes each  individual server has with each kind of serve, depending on whether there are enough data collected on the individual server to get a good probability distribution function. For this initial action, the five probabilities listed must sum up to 1: Pr(ST)+Pr(SF)+Pr(JT)+Pr(JF)+PR(S)=1

The next level of action involves the passing team response. I listed five possibilities: Shank, passes ranging from 1-3, and a service error. The action ends with an opponent/serving team point if the pass is shanked or if the passer is Aced and a receiving team point if the server commits a service error, whereas the action continues with a numbered passing value. Note that there are five conditional probability associated with each serve receiving outcome. There are 25 conditional probabilities that need to be collected. 

The action now shifts to a decision by the setter. Out of system plays and non-setters setting have been left out for the sake of brevity. Even with that simplification,  adequate amount of data needed to calculate those probabilities are difficult to accumulate. The setter and/or the coach will decide on the target of the set, conditional on the quality of the pass that the setter must work with. Buried in these conditional probabilities is the training and implicit bias that the setter has, such rules as: only set middles on a 3 pass, or only set outsides on a 2 pass, or only set back row attackers on a 1 pass. Whatever the prescribed solutions to the passing action, they are embedded in the conditional probabilities just as it is ingrained in the setter’s decision-making system. There are 15 conditional probabilities concatenated upon the 15 conditional probabilities based on the numbered passes which are a result of the receiving team’s reaction to the original five serving choices.

Once the setter has made their decision, the next level of results and associated conditional probabilities are given above. There are five results, one of them: the setter error, results in an opponent point; setter error can be mishandled ball, an attack error if the setter decides to attack, or an errant set. Which leaves us with four possible results: good set, attackable set, hitter need to adjust to the set, or the hitter must hit a down ball or free ball over. There are now 16 conditional probabilities based on who the setter decides to set. 

The next level of action comes from the hitter decision. There are seven results. I modelled this level while avoiding individualizing each of the hitters by creating  an “average” hitter by smearing all the statistics of all the hitter on the roster, which I had warned can lead to errant decisions (Wung 2021).

One of the results is the hitter error, which results in an opponent point. Six  conditional probabilities are left to carry on to the other side of the net.

 

The next action is the cumulative effect of the opponent’s defense, combining the reactions of the blockers and backrow defenders. There are three results: a stuff block which results in the opponents getting a point; a kill, where the attacking team gains a point; and the dug ball, where all the non-termination possibilities are combined: ricochets off the block which turns into a dug ball, or any combination of actions resulting in the opponent mounting a counter attack. This third option reverses the flow of the gameplay and the opponent team now becomes the offense and a new Markov chain flowchart needs to be created. There are 12 possible conditional probabilities.

The Point

There are 71 conditional probabilities that needs to be accumulated just for this Markov chain simulation of the serve receive game action. There are four decision points in the model, even though there could be many more if more granularities were to be pursued.

The point of this exercise is:

·       If we desired to predict the outcome of a set or even something as basic as a point, there needs to be massive amount of statistics that needs to be built up to create the conditional probability database, especially since we know that the law of large numbers tell us that we need to have many individual data points if we wish to have accurate conditional probabilities. To simulate the length of matches, these probabilities do not have to be extremely accurate, after all, the application of the Markov chain is not to accurately predict results, the idea is to predict the amount of time it takes to play a set or a match, accuracy and precision does not matter there.

·       More interesting is seeing just how many pieces of conditional probabilities affects the decision making at each decision point. Reflecting back on this thought, the immediate reaction is: of course, the swing depends on the quality of the set, which depends on the quality of the pass, which depends on the quality of the passer and the serve, etc. But it is sobering to realize the number of probabilities is needed to feed into one decision, and that calculation is done by the decision maker instantaneously.

·       Many of the conditional probabilities can be eliminated from consideration because of human bias and the strategic implications of the action, which does pare down the probabilities that have been listed, but even with a pared down list, the number of probabilities, conditional or otherwise, are very large.

As I look at my very rudimentary model, I think of all the uncertainties that are not modelled as I was trying to simplify the model and I think about how much each of them could have affect the outcome of the play. This is the problem of the unmodelled dynamics in control systems, which does affect the predictive ability of the model. But then I am reminded of one of the seven deadly management diseases cited by Dr. W. Edward Deming:  Management by using only of visible figures. (Deming 1982) Dr. Deming’s point is that there are many unknowns and many uncertainties that exists in any endeavor that involves many humans making many very human decisions. His admonition is that  it is foolhardy for decision makers to expect absolute accuracy from any system because there are many things that are unmeasurable and there are many things that are unknowable. Once we realize this, we understand that even as uncertainties and randomness affect what we do in our daily decision making, our need to absolutely eliminate uncertainties and randomness from our daily lives, and from our daily sports, is misguided. In addition, to not recognize this fact and to willingly pour more time and resource into eliminating or minimizing uncertainties and randomness in statistics is a fool’s errand. This is not to say that working on statistics will not give us more insight, we must always seek to learn more from the descriptive statistics that we have, creating statistical categories which will help us understand WHAT our team is doing, but we must never get into the mindset that our final goal is to eliminate uncertainties and randomness in our statistical ponderings; we need to understand our limitations.

Works Cited

Albert, Laura. "Volleyball analytics: Modeling volleyball using Markov chains." Slideshare.net. October 26, 2018. https://www.slideshare.net/lamclay/volleyball-analytics-modeling-volleyball-using-markov-chains (accessed March 19, 2021).

Deming, W. Edward. Out of the Crisis. Cambridge, MA: The MIT Press, 1982.

Wung, Peter. "Stats For Spikes-Use of Statistics as Goals." Musings and Ruminations. March 6, 2021. https://polymathtobe.blogspot.com/2021/03/stats-for-spikes-use-of-statistics-as.html (accessed March 6, 2021).