Wayne Chang
Finance PHD Student At USC
It’s a matter of probability.
Suppose two teams are equally matched such that each team has a 50% chance of winning any particular game. Coming back from a 3–0 deficit requires winning 4 consecutive games, with a probability of only 6.3% (=.5^4).
This estimate is too high though. We should account for the fact that the other team has already won 3 consecutive games and is thus likely to be a better team. To have a majority chance of winning three in a row requires the other team to have won each game with at least a 80% probability (.8^3=51%). So the losing team only has a 20% chance of winning each game going forward. This means coming back to win 4 in row occurs with a probability of only 0.2% (=.2^4).
I’m clearly simplifying (ignoring the technicalities associated with playing basketball) and the setup isn’t entirely correct (e.g. there’s also the chance that the better team happens to fall behind and thus has a higher likelihood of catching up). But hopefully, this shows the gist of how unlikely it is.
Finance PHD Student At USC
It’s a matter of probability.
Suppose two teams are equally matched such that each team has a 50% chance of winning any particular game. Coming back from a 3–0 deficit requires winning 4 consecutive games, with a probability of only 6.3% (=.5^4).
This estimate is too high though. We should account for the fact that the other team has already won 3 consecutive games and is thus likely to be a better team. To have a majority chance of winning three in a row requires the other team to have won each game with at least a 80% probability (.8^3=51%). So the losing team only has a 20% chance of winning each game going forward. This means coming back to win 4 in row occurs with a probability of only 0.2% (=.2^4).
I’m clearly simplifying (ignoring the technicalities associated with playing basketball) and the setup isn’t entirely correct (e.g. there’s also the chance that the better team happens to fall behind and thus has a higher likelihood of catching up). But hopefully, this shows the gist of how unlikely it is.