Point scoring and game outcome
Take home messages
- Points and points scored per minute almost perfectly predict game outcome
- Points per minute allows comparisons to be made between players and teams
To win a game of Dodgeball one must eliminate as many opponents as possible without getting eliminated yourself. Since a set (at competitions sanctioned by the European Dodgeball Federation) is at most three minutes long, one has a time limit on how long one can take to eliminate the opponents. If both teams have players left on court at the end of the set, then the team with the most players wins; an equal number of players results in a draw.
The relative proportion of eliminations thus entirely determines the outcome of a set. One can quantify eliminations by introducing points for each player that enters/exits the game:
+1 Eliminating an opponent
-1 Getting eliminated
+2 Catching an opponent’s ball
-2 Throwing a catch
-1 Other elimination (line infringement, invalid throw)
To show that this method of quantification is practically useful, I’ve plotted the outcomes of all the sets played by the Swedish Mixed Team at the CEC 2019, together with their net number of points scored in each set.
Clearly, one cannot win a set as long as the opponents eliminate more opponents than your team does. Note that the draws do not occur at 0 net points, maximal points go up to 1 more than players on court (6) and that one can still win with 0 net points. There is a slight wiggle room given this method of quantification, since one can throw a catch when there are 6 players on court, which will be scored as -2, despite the relative number of players only changing by one. I’ve made the conscious decision to always score catches this way because its effect on game outcome is minuscule (as evident in this plot), while having a big impact on assessing player skill (it is more difficult to make a catch than to hit and eliminate an opponent).
One method of determining which players are most valuable for a team is by calculating their net points scored; eliminating more opponents than getting eliminated means that player has contributed toward a win. A positive score will always be predictive of wins. However, an issue with this is that some players and teams play more than others, both by playing more sets (not being on the bench) and by getting eliminated later in the set. This does not allow us to compare the raw number of points between players and teams.
One way to allow comparison, and actually identify what the player does on court at all times, is to calculate the points scored each minute on court. Consider two players that never get eliminated but always eliminate one opponent per set, for a raw score of +1. They can be considered to have identical skill. However, if one player played all sets, and the other only one set, then the total scores will be +10 and +1. By dividing with the time spent on court, they will have identical scores. This statistic is highly stable, since any attempt to improve points/min will lead to more hits but also more eliminations, in a pattern determined by the technical skill profile of the player. However, some players and teams fare better, and others worse, when increasing activity on court, which you can read about in my post about Playing Speed.
I’ve been told that points scored per minute of playtime is an irrelevant statistic. Hopefully this argumentation and the plots I show will convince even the most fervent opponents. The plot below shows the points scored per minute for each set and their outcomes.
As I’ve shown previously, hit and defence percentages are highly predictive of points scored per minute on the individual level (player statistics). Not surprisingly, they also correlate on the team level. As you can see below, both the team’s hit and defence percentages show highly significant correlations, and by calculating the technical skill (according to the equation outlined previously) for the lineup for each set, one gets identical correlations as for the player-level analysis, corroborating the previous findings.
With these results, one can begin to identify factors that positively or negatively influenced set outcomes on the team level. For example, we won one set despite having a hit percentage of only 18% (far left green dot), and we lost one set despite a hit percentage of 42% (far right red dot). Clearly something else led to the different outcomes…
What that is can be identified using regression analysis. Similarly to how one can calculate player tactical skill using this method, this can be done for teams. By calculating the residuals from a best fit line, one can compare them to other stats, such as which players were in the lineup, whether we threw more individual balls or synchronised several balls, whether we eliminated the opponent’s males or females first, if we were more successful when countering or doing planned attacks, etc… In the end, one can identify which tactics were successful and which were not.
Update
I received a comment that it may be too simplistic to consider points scored and points/min as a measure of what a player contributes to the team, and I agree. As with any statistical analysis, there are simplifications that must be made, and one must be aware of any limitations that may affect the conclusions that can be drawn. The text above shows how point scoring for the entire team relates to outcome, and it is obviously crucial and completely predictive. How it relates to individual players is more complex.
A player that has a positive points/min will obviously have contributed toward a win, and if all players have positive scores, then victory is inevitable. However, it is not as simple as just increasing your points/min, since every throw you make could have been made by someone else. Logically, the one with the highest probability of making a hit in every situation should be the one making the throw. This will increase one player’s point scoring while decreasing that of the other players. As I showed before, it is when the average score for the entire team is positive that games are won. Being selfish, and looking to throw and score ad nauseam, may not increase the chances of winning.
I have developed a method for gauging the effect players have on their teammates because balls are a finite resource. I’ve planned to write a post about these results in a future post, but to pre-emptively respond to similar criticism as above, I’ll hint at already having considered this limitation, and briefly explain one method for parsing this effect.
When a player throws a ball, it is a throw not taken by another player. Since the team wants to score as many points as possible, it is often in their interest to give the best thrower the ball. This will decrease the points/min for the giver of the ball, and increase them for the receiver. The average points/min for the team will go up if the better thrower throws more, increasing the chances of winning. However, since different players get eliminated at different times, the team composition changes. One can calculate each player’s points/min, and that of the rest of the players that were on court each time that player threw the ball to find out how many points/min each player takes from, or gives to their teammates. By comparing the teammates’ scores with and without that player on court, one can identify the effect that the activities of one player has on the rest.
If this stealing of points from current teammates on court is lower than the total points/min that the player scores for the entire match, then the net outcome is positive, and the “selfish” player will have actually been altruistic relative to their skill difference, and contributed toward a win. One must also keep in mind that attacking balls are not the only variable. A good player may be threatening to the opponents and attract throws, in that way protecting nearby teammates ultimately increasing their teammate’s points/min. So even if a player is very active and selfish, the effect on stealing points/min from teammates will be lower than expected. But, I will explain more about the intricacies in that post.