Much has been said about how the game of Quidditch is ruined by the scoring system - specifically how it makes no sense that the snitch is worth 150 points and that catching it ends the game [1, 2, 3]. Most of these arguments seem to revolve around the claim that it is nearly impossible to win a match of Quidditch without catching the snitch. Is this true? Let's try and answer this question formally using statistics and R simulations:What is the probability of winning a Quidditch match without catching the snitch?
Victor Krum caught the snitch for Bulgaria, but Ireland still won (1994 World cup)
 The Game, the RulesQuidditch is a fictional team sport played on broomsticks, devised by author J. K. Rowling, that is played by wizards in the fantasy world of Harry Potter. Like any sport, the game of Quidditch has many rules, but I will summarize here only the ones pertinent to our discussion:
10 points are gained by throwing the Quaffle through one of the opponent team's three hoops.
150 points are gained by catching the Golden Snitch, which can only be caught by the Seeker.
The game ends when the Golden Snitch is caught.
The winning team is the one has the most points at the end of the game.
Given these rules and game objectives, in order to estimate the probability of winning a match we must first estimate (1) how long does it take a seeker to catch the Snitch on average, which determines how long a game lasts and thus how much time is allotted for the teams to score goals,  and (2) what is the rate of goal scoring.
Estimating the Average Game Length
Unfortunately, not many pro-Quidditch matches are described in the books, so this is quite hard to estimate. On the one hand, the only game that is described in its entirety is the 1994 Quidditch World Cup final, and it was extremely short: only 15 minutes or so [4]; On the other hand, the longest game ever lasted 6 months [5]. So the average is somewhere between 15 minutes, and 260,000 minutes. .. great.
For the sake of our simulations, then, I will assume the average game lasts 90 minutes (assuming Rowling has soccer or rugby in mind). I will also assume that the length of a Quidditch game is exponentially distributed, since the probability of catching the Snitch remains constant (as opposed to it getting easier as the game progresses) - the Snitch's ability to escape capture does not change (magic) and players are substituted throughout the game, so let's assume an unchanging level of vigilance.
Together, the distribution of game lengths looks something like this:
This makes the 6 month long game very unlikely ( $Pr(time__260,000)