**Mattan S. Ben-Shachar**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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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

probabilityof 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 Rules

Quidditch 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.

### Estimating the Average Game Length

*very*unlikely ( $Pr(time>260,000)<10^{-10,000,000}$ ), but the 15 minute game rather probable ( $Pr(time<15)=0.15$ ).

### Estimating the Rate of Goals Scored

## Simulating the Games

*that*into reading raw code, you can just skip to the conclusions at the end.)

### R Setup

### Equal Teams

Under these conditions, the probability of winning a game without catching the snitch is:

3.75%! Hmm, that does seem quite unfair… Though it does put Fred and George’s gambling odds at around 1:20!

How many games were determined by the snitch – i.e., had the snitch been caught at the same time by the other team, they would have won?

94.9%! Not the best of odds…

### Unequal (but matched) Teams

So, what is the chance of winning *without catching the snitch*?

## Conclusion

- If you’ve caught the snitch, you’ve probably won.
- If you’ve won, you probably caught the snitch.
- If you’ve lost, catching the snitch would have probably changed that.

**leave a comment**for the author, please follow the link and comment on their blog:

**Mattan S. Ben-Shachar**.

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