Leo Fried

Quadball Under Extreme Scrutiny Today is an attempt to deeply and more thoroughly analyze player and team performance in a quadball series. For each QUEST, I will go play-by-play, analyzing and grading what and how each player did on each play, and then I will compile those into grades for the series as a whole.

This project is inspired by a similar column on mgoblog.com about University of Michigan football.

In order to properly put every play of a quadball game under extreme scrutiny, we need to have a sense of how good it is to have possession of the various balls in the sport. That is, how many points would you pay to steal the quaffle? To take control? To win the brooms up race? For 10 seconds at the snitch? Warning: some math is upcoming.

Let’s first focus on the quaffle game — we will expand to beaters in a moment. How many points is the quaffle worth? Well if teams scored on every possession, then it would be 5 points, as it means you alternate between being up by 10 and tied as the quaffle changes hands on a goal. Stealing the quaffle, then, would be worth 10 points (5 for you, -5 for your opponents), which makes sense because teams are scoring on every possession, but our opponents had the quaffle and didn’t score, so they left 10 points on the table.

This generalizes, and if teams are scoring with probability p, then the quaffle is worth 5p, and stealing the quaffle is worth 10p. In the two games that I have charted so far, teams scored on about 40% of possessions, so the quaffle is worth 2, and stealing it is worth 4. (Somewhat counterintuitively, this means scoring is really only worth 6 — you got 10 points, but gave up the quaffle, which is worth 4.)

The math for beating is a little more complex: Let’s say an offense with control scores p of the time and keeps bludger control b of the time, and an offense without control scores q of the time and steals bludger control c of the time. Then, if we let x be the value of having two bludgers on offense, and y be the value of having one bludger on offense, we get the following two equations:

x = 10p – (by + (1-b)x)

y = 10q – (cy + (1-c)x)

We can plug in p, q, b, and c to solve for x and y, and then the value of having bludger control is equal to (x – y)/2, so stealing bludger control is worth x – y (which is the difference between having two bludgers and one bludger). Inputting the values from these two games finds that x = 6 and y = -2, so bludger control is worth 4 points, and winning back bludger control is worth 8 points.

Tyler Beckman previously went through every game in the 2021 MLQ Championship Weekend and found that there, seekers were engaged for a total of 1789 seconds, while 20 snitch catches were recorded. This implies that, on average, a snitch is caught once per 1789/20 = 89.45 seconds of engaged seeker time. So 3 seconds engaged with the snitch is worth 1 point. Thank you Tyler for those stats.

Finally, during snitch-on-pitch, teams scored on 60% of their possessions, so the quaffle is worth 3 points and stealing the quaffle is worth 6 points. (Both the 40% and 60% statistics are just from the 2022 MLQ Championship series, which is a relatively small sample size. I would like to refine this number as I do more of these and gather more data.)

Thus, QUESTing a series involves going through each play and assigning the relevant players grades (positive or negative) based on their performance. Per our calculations before, each play swung the game some number of points. For example, if Team A scores but gives up bludger control during a play, then that play was worth 8 (bludgers) + 4 (quaffle) – 10 (goal) = +2 for Team B. Each player is then graded during that play based on what they contributed to that 2-point swing. If the entire play was because of one player, then that player would get a (+2) (or a (-2) if they were on Team A). In reality, plays are a result of actions by many players at a time, and so grades are given out based on how each player performed on that play.

Lastly, this is admittedly a somewhat subjective process — I am assigning grades based on my read as to who was responsible for each play going right and wrong. It is also very much a work in progress and I am very open to feedback — there is a comments section at the bottom of the page. Individual players’ grades are just based on these two particular games and are not an indication of players’ general ability or talent level. This is not meant to put down players who didn’t play as well. The purpose of this endeavor is to learn about and better understand our sport and the games and series that I QUEST.