Metacognitive decision-making regarding throwing ability

The only successful tactic is…

We know that some skills, such as throwing and dodging, are highly predictive of success on the court. However, there is no tactic that is always successful. Should one play fast or slow? Defend or counter? Throw single balls or sync several in attack? Which tactic is the most successful will depend on the skill of your team, the skill of the opponents, the relative difference between the teams, as well as the playing styles of all the players on court.

The only globally successful tactic is being adaptable. The team that most readily identifies the opponent’s strengths and weaknesses, and changes its own playing style accordingly, will have the advantage. I have already outlined, on the team-level, how playing speed can give an inexperienced but technically skilled team the advantage over a much more experienced team. In this post I will explain how one can estimate the degree to which players are adaptable with regard to their throwing.

I think, therefore I throw

For each game, there are a set number of opportunities to throw at the opponent. The decision to throw will depend on the situation – distance, if defender has blocking ball, threat from other players – as well as on the players – your throwing skill, the defensive skill of the opponent, the “worth” of eliminating that opponent rather than saving the ball for another opponent.

In situations where a player decides there is a high enough probability of success, a throw will be made. Each player has a personal probability threshold, under which they will decide not to throw, which I refer to as shot-taking sensitivity. If this threshold is low, they will throw at anything that moves; if it is high, then they will keep the ball no matter what. Obviously, there is a sweet-spot, since the first will result in a lot of misses that give the opponents the chance to counter-attack, and the second will result in fewer eliminations than expected.

The location of a player’s sweet spot is highly dependent on their throwing skill. Highly skilled players will more often find themselves in situations where they know they are able to make a hit, and thus feel that they are above their personal probability threshold. Less skilled players will more often be below it, and thus keep the ball or give it to a better thrower.

The role of metacognition

Being able to determine the location of your sweet spot is crucial and at the same time very difficult, mostly because the information guiding that decision is opaque and indirect. It is only following a couple of throws that you begin to gather enough information to update your internal probabilities of success against a given opponent.

Dodgeball may not seem like an intellectual activity. However, it is highly dependent on intellectual functions such as pattern recognition and working memory. The higher these functions are, the faster and more accurately a pattern can be identified, and the better one can extrapolate from incomplete data, while at the same time keeping track of what is currently happening on court. A self-aware player (making active use of metacognition during the game) will be able to determine whether or not their relative throwing ability is above the defensive ability of the opponent, and whether the probability of success if higher than the personal probability threshold, after only a couple of throws. Instead, those who do not make use of metacognition or do not have the working memory to keep track of both the past and the present, will take longer and make incorrect inferences. The speed with which a player updates its probabilities, and acts upon them, determines the degree of adaptation. Being quick to realise the relative probability of success between you and the opponent will determine whether you make the right choice when deciding to throw or not.

Is it worth taking this shot?

When attacking, one wants to score as many points as possible. If you are more skilled than the opponent, and you find yourself in a position to throw with a high probability of a hit, it is in your interest to take the shot. To find out whether an individual is able to determine their relative skill and probability of success, one can use data regarding throwing frequency and hit percentages.

In theory, the more one throws, the lower the hit percentage. Each match has a given number of opportunities with different probabilities of making a hit. By only taking the best chances, one will end the match with only a few throws, which are likely hits. By taking additional chances, which will have inferior probabilities, one throws, and misses, more. So, if one would plot the hit percentage against the throwing frequency (number of throws per minute), one would get a slightly negative slope, all else equal. However, since players are adaptable, they can choose to influence their throwing frequency based on their perceived hit percentage.

Self-awareness

When playing against a better opponent with better dodging skills, the hit percentage is lower, than when playing against inferior opponents. The ability to quickly determine the relative skill difference, how it affects your attacking success, and then change the shot-taking sensitivity, can be quantified. Since players judge their own success rate based on their own skill (“it is easier for me to hit my opponents in this match than what I am used to”), one first needs to normalise the hit percentage for each player. What that means is that everyone is on the same scale. Two players that have had hit percentages in the ranges of 20-50% and 30-60% will both have hit percentages of, as in this example example 0-100%, where 0% is the game where they had their own worst hit percentage and 100% where they had their best, and the rest of the games are distributed in between based on their previous distribution. By making this normalisation, one puts the players on the same scale, allowing for comparisons to be made. It is also necessary due to the fact that players use their own judgment about their own skill to make changes to their playing style, so one needs to know whether each game was a good game compared with their usual performance.

By plotting the normalised hit percentage against the throwing frequency, we can identify which players are able to determine when they are successful in the attack, and change their playing style accordingly. The plot below shows this.

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It includes a lot of players because the data is recorded from games from the Euros 2018, CEC 2019 and the Swedish Nationals 2019. The legend presents the regression slope for each player (more on this below), the number of matches recorded (the more matches the more stable the result is), and the actual (not normalised) hit percentage (see comment in the end).

As I said before, the expected slope would be slightly negative if one did not possess any metacognition at all. The dotted red line represents the average for all the players. The fact that it is slightly positive means that Dodgeballers are not mechanistic pre-programmed robots, but can adapt to the game. It also gives a normative value that one can compare individual players to. I would preferably like to have data on at least 5 matches to consider a player’s slope true.

The higher the slope is, the better and faster the player adapts their playing style to the relative skill differences of different opponents. A player that is extremely slow to recognise patterns and update their beliefs will change their throwing frequency after the game has ended, resulting in a slightly negative slope. A player that wrongly judges their ability, draws wrong conclusions about success rate, or panics when facing stronger opposition, will have a negative slope. Players with positive slopes are able to correctly judge their skill in relation to the current opponents and change their playing style accordingly. The more one increases the throwing frequency when facing easier opponents, the higher the point scoring will be, as more and more situations are acted upon that eventually result in a hit. Facing a definitely stronger opponent, it is in your interest to slow the play down as much as possible to decrease their point scoring, and lower the score difference at the end of the game.

Since this measure is normalised for each individual, one can use it to compare players across teams and oppositions. I would expect this to be one of the factors counting toward each player’s tactical skill score.

Example

I’ve mentioned previously that I will write a case study about a player that has a low shot-taking sensitivity; a player that does not take all the chances it is presented with, resulting in lower attacking efficiency. This analysis further corroborates that hypothesis. The player in question is the green star, which has a relatively strong positive slope, but an extremely high hit percentage (ranging between 50% and 66%). One could expect a higher hit percentage to give a higher score for points/min, as predicted by the plots in the posts about technical skills (1 & 2). However, his hit percentages are falsely high because of a reluctance to take shots even with a high probability of success, causing a diminished attacking efficiency and lower points/min.

By increasing his shot-taking sensitivity, he will throw at opponents in situations with lower and lower probability of a hit. That will increase the Y-intercept for his slope (higher throwing frequency), which will decrease his hit percentage, but lead to more hits and points. It is not evident from this graph, but there exists an inverted U-curve when attacking, with the peak being associated with a play style that optimises point scoring. Players to the right of the peak will throw less, eliminate fewer players, and have falsely high hit percentages (consider a player that only throws once each game, when there is a 100% expected hit rate). Players to the left will miss a lot, and give the opponents the chance to attack and eliminate players from their own team, resulting in a net negative score. I will describe this in a future post, but first I need to gather more data to definitely show the inverted U-curve since there are a lot of fluctuations obscuring the pattern and this type of statistic is fairly high level (layer 4).