Blitz-player and effect on game
This is a follow-up to the post about Blitz-Dodgeball.
Using regression analysis one can identify how strong the association between two variables is, and remove the effect that one variable has on another. One way this can be used is to identify ways that individual players affect a certain outcome, such as the number of points scored by the team. One way that I do that was hinted at in the previous post.
This figure shows all the sets that the Swedish Mixed Team played in the Central European Championships 2019. The marker size shows the time I spent on court; the smaller it is, the earlier I got eliminated. One can see that the larger dots cluster in the higher play speeds, and that game play slows down if I get eliminated (smaller dots).
To find out whether this observation holds water, I plotted the time I spent playing in each set against the speed of play. This showed a significant relationship in which I determine a sizeable 21% of the variability in speed of play on court.
Given this strong relationship, and the fact that our speed of play correlates with points scored per minute, one can calculate the expected points scored by removing the effect that I have on playing speed.
The first step is to calculate the expected speed of play that my team had with and without me on court. If this was football, that would be easy, since most players play either the whole game or not at all. For Dodgeball it’s a bit trickier, since one has to consider partially played games. Taking the average speed of play for all the sets that I played in would be biased because one has to factor in the proportion of time spent on court. One can do that by calculating the weighted average, which is the average speed of play for each set, but the sets where I played more count more toward the average and vice versa. First, consider the time I spent on court, with bigger dots indicating more play time. The weighted average for the team, with me on court, was 13.85 events/min for a score of 2.3 points/min.
If one instead reverses the proportions for playtime (100% - playtime in %) so that the sets in which I played the most have the largest dots, one gets the following figure. The weighted average, when I was on the bench or eliminated, was 12.65 events/min for a score of 1.1 points/min.
By excluding me from the team, and replacing me with a player that has the same speed of play (and the effect it has on point scoring) as the average of the rest of the team, we would’ve scored 1.2 points/min (2.3 - 1.1) less throughout the tournament. This makes sense given that I scored 1.9 points/min across the tournament, meaning that my addition to the team is a positive net elimination of 0.7 (1.9 – 1.2) opponents per minute. Removing me from the team obviously wouldn’t decrease team scoring by the whole 1.9 points/min, since my void, and that of my throws, would be replaced by another player and the rest of the team for 1.2 points/min.
Expected point scoring effect on team by player =
Player avg points/min – (Team avg points/min player on court – Team avg points/min player off court)
This is but one, pretty basic, way of estimating the effect that one player has on the outcome. I’ve made additional analyses, where I have used linear algebra to remove the effect I have on each individual set, and I might explain and show those findings in a future post.