Quidditch is the most popular sport in the wizarding world of Harry Potter. The first recorded game of quidditch was played in 1050 when a witch named Gertie Keddle witnessed the first organized game in the marsh near her house. It was a crude and rudimentary version of the modern game, with two sides of wizards on broomsticks trying to throw a leather ball through some trees at each end of the marsh. As the game grew in popularity, the game we know today began to take form, with the addition of “bewitched flying rocks” aka bludgers and, most importantly, the golden snitch.
The first appearance of the snitch occurred during a game played in Kent in 1269. A wizard named Barberus Bragge, then Chief of the Wizards Council (precursor to the Ministry of Magic), offered 150 galleons to the player who caught and killed a snidget (a small, golden bird that is very small and very fast) he had released during the game. The players involved completely abandoned the game and instead went off in pursuit of the snidget. Soon, a snidget was released during every game of quidditch and each team dedicated a specific player, the seeker, to catch it. Teams would be awarded 150 points in honor of the first ransom offered by Bragge. Sadly, snidgets were declared an endangered magical species in the middle 14th century, outlawing it from use in quidditch matches. However a skilled metal charmer named Bowman Wright was able to create a fake snidget, dubbed the golden snitch, saving the species from extinction and allowing the tradition to continue.
Capturing the snitch signifies the end of the game and is undeniably the most important objective of the match. Although it’s possible for a team to lose even after capturing the snitch, such as the legendary 1994 quidditch World Cup between Ireland and Bulgaria, capturing the snitch virtually guarantees victory. Peculiarly, it seems that there has been little innovation in regards to quidditch tactics since the rules of the modern game were codified in 1883. Each side still uses three chasers, two bludgers, one seeker, and one keeper, just like they did in early versions of the game dating as far back as the 12th century.
Yet if capturing the snitch is so important, why does each team only assign one player to the job? There is nothing in the rules that specifically states the seeker must be the one to capture the snitch. In theory, the quicker you can find the snitch, the less opportunity the other team has to score with the quaffle. As long as you can capture the snitch before the other team scores 140 points, you are guaranteed victory. Therefore teams’ primary concern should be capturing the snitch as quickly as possible. But each side is only allowed six players, not including the indispensable keeper. So what is the optimal ratio of seekers to chasers to bludgers? Let’s turn to the math.
There isn’t an existing database of quidditch scores available yet, so we must use the data at hand; scores recorded as part of the Harry Potter saga. Data aggregated by the Harry Potter Lexicon shows that the average winning team scores around 215 points per match (non-snitch adjusted) and the average losing team scores around 81 points per march. However, when adjusted for catching the golden snitch, winning teams are only scoring about 65 points per match, around 2 goals less than losing teams. Therefore it can be inferred that only in rare circumstances does scoring with the quaffle have an actual effect on the outcome of the match. What are these teams doing differently? It can only be assumed they have an elite seeker.
Having a more talented seeker on your side is the most obvious way to find the snitch first. However, by definition, every team cannot have an elite seeker. So how can teams make up the difference? What if teams instead used multiple seekers in place of other positions? Aren’t two seekers better than one? Aren’t three seekers better than one? We have seen that scoring has almost no effect on the final outcome of matches. It’s as though there are two parallel games going on at once; the “scoring match” itself and the hunt for the snitch. And we have see that one of the games, the scoring match, is virtually inconsequential as it relates to achieving victory. Therefore teams should be allocating as many resources as they can to finding the snitch (without totally abdicating the scoring match) and preventing the other side from catching the snitch first.
Bludgers are in effect a teams defense and are primarily responsible for making it difficult for the other team to score and, importantly, to capture the snitch. Teams are only allowed two bludgers by rule, so two bludgers must always be deployed. Tactically, the bludgers should always be shadowing the opposing seeker. They must do everything they can to prevent them from finding the snitch. Since the amount of bludgers must be fixed at two, the only logical reallocation must be with chasers.
Chasers are primarily responsible for scoring the quaffle. Each side traditionally deploys three chasers. However, as we have seen, scoring is effectively irrelevant to achieving victory. Therefore teams should instead deploy only one chaser, and use the other two as auxiliary seekers. Keeping one chaser in the mix will offer the minimum amount of resistance to the other team scoring, and when in possession should try to hold the quaffle as long as possible. This stalling tactic will grant their three seekers more time to finding the snitch without worrying about the other team accumulating more that 140 points.
This means a team will optimally deploy three seekers. Each seeker you deploy will decrease the amount of space each must patrol, thus increasing the efficiency by which each seeker can find the snitch. In other words, having two seekers mean each one has to cover half the territory one seeker otherwise would, and three seekers one third of the territory, and so on and so forth. Obviously diminishing marginal utility would suggest that each seeker you deploy gives you less and less of and edge, suggesting that there is an optimal ratio of seekers a team should use. And, taking tactical and practical considerations into account, the optimal positional deployment is two bludgers, one chaser, and three seekers.