Last night Arsenal lost in the Premier League for the first time, after going on a 49 matches unbeaten run. The last record was 42 games by Nottingham Forest many years ago. It is said that this run will never be repeated again.
So how (un)likely is it?
To quantify things, suppose the chance of them losing a game is 5%. (and no team is _that good) The chance of winning or draw is thus 95% or 0.95. The probability of 49 consecutive wins or draws is 0.95 x 0.95 x 0.95 x … 49 times, which comes out to be about 0.08 or 8%. This is close to the chance of getting 4 heads in a row in coin flipping.
Of course 5% losing chance is an underestimate, and even with their superhuman flowing football (which I adore), a more realistic number would be about 15–20%. If we take 15%, the chance of 49 games unbeaten run is 0.035%, or about the same as getting 12–13 heads in a row.