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.

 

 

Book Review-Leaders: Myth and Reality by General Stanley McChrystal

I don’t usually read business books unless I am convinced that the book is extraordinary. I especially don’t indulge in this kind of reading unless I am convinced that the author speaks from a point of authority. In this case I was convinced of the veracity of General McChrystal’s bona fides to speak on the topic by what I had observed of his actions as a commander. This book was a group project, which also included Jeff Eggers and Jason Mangone as co-authors, but the voice of the writing centers around General McChrystal.

I am also very skeptical of any book that speaks of leadership. I am of the opinion that leadership is something that is hard earned and amorphous rather than something that can be attained by following scripts or checking off check boxes. Most business books, even other books written by military commanders have been disappointing because they fall into the trap of churning out books that are best sellers initially but end up in the discount bins because the wisdom, or lack thereof, are pedantic, formulaic, and promises too much while delivering too little.

This book however, is honest to the point of declaring that the authors’ intent was to dispel the mythology that accompanies our cultural worship of the leader. They immediately disabuse the reader of their romantic notions, taking on one of the biggest mythological leaders in American history: General Robert E. Lee. The deconstruction of the Lee mythology took courage, especially from a West Point graduate as General McChrystal. In addition, the book delineates the three myths that has obfuscated the characteristics of a leader and the qualities of leadership. In the first chapter, General McChrystal admits that the term “Leadership” is almost impossible to define forthrightly and correctly. The authors also drolly points out that a leadership expert found 221 definitions of leadership in 587 examined publications.

The foundation of the three myths is that those who study leaders and leadership, all focus narrowly on the leader — the person — at the exclusion of anything else. The three myths which results from our hero worship, or more accurately, worshipping in a cult of personality are:

The Formulaic Myth: We think leadership is achieved through rote procedures: being formulaic and following a recipe. This myth ignores the fact that leadership is tightly coupled to environment,  situation, and context.

The Attribution Myth: We attribute all the leadership to the leader, the sole chosen focus of our studies. This myth ignores the contributions of the many in order to simplify the vast and complicated reality so that we can create bullet points.

The Results Myth: We attribute the success and failure of the leader upon whether the narrow desired outcome is achieved. The myth ignores the fact that sometimes the symbolic worth of leadership is far more valuable in the final assessment of a successful leader than just the results.

We analyze leadership in the way that we do because we are ever the optimist, and we wish to indulge in our own confirmation bias by ascribing nobility to our leaders and promote the myths and ignore reality.

 The author’s stated purpose is to dispel our very comfortable biases and  conduct the very difficult exercise of reconfiguring the idea of leadership into a different structure, to show leadership in a very different light. They do this by employing the method first used by Plutarch in his Lives. Plutarch wrote biographies of 48 worthy subjects seeking to answer the question: “What sort of man was he”? He paired his subjects and set about identifying the salient factors which would answer his question.

While the authors used the same structure, they also made significant changes to the analysis as they sought to answer the question: “What sort of leader were they?” While Plutarch only wrote of men, the authors included three women, because we should be beyond that particular bias and the three women are worthy subjects. They grouped them into pairs as well, but in different categories: Founders, Geniuses, Zealots, Heroes, Power Brokers, and Reformers.  Some are notable in their fame, others are obscure. The authors gave a succinct and clear history of each leader, highlighting both their qualities as well as their weaknesses, which served to balance out their claims to leadership and made their place in history all the more real.  

Indeed, the histories of each of the twelve personages, fourteen if you included Lee and Winston Churchill—who’s history was also documented— were well written and honest. The judgements made were fair and informative.

It is the last two chapters that sucked me in. They analyzed the three myths, spoke of how their views of the myths changed over the course of writing the book, and finally gave a different, more useful structure for assessing leadership, and avidly avoided the same mythmaking that they were trying to dispel. As I sat on my chair trying to digest their conclusions, and I must admit, I am still chewing over the structure and idea, I was struck by the possibilities that the last chapter engenders.

Being cynical to the tricks of the business book genre, but especially skeptical of the leadership specialty, I want to consume and accept the concepts laid out in the final chapter, but I will think critically about the chapter, as the authors made a significant case. I must give them the respect of indulging in the granularities of their hypothesis.