My favorite basketball team the Golden State Warriors is on an historic run. After winning the NBA championship last year, the Warriors have rattled off 19 consecutive wins to open the season. This is the first time that a team has won that many games to open a season, and some might be starting to wonder whether the Warriors can complete an undefeated regular season. The cruel realities of probability will step in to show us why that won’t happen.
First, I’ll admit that that this analysis will omit several complicating considerations, most notably injuries. Chances are that several of the key players for the Warriors will get hurt this year, which will reduce their chances to win the games where those players are out. There are a number of other variables that cannot be accounted for, but as you’ll see the math is pretty overwhelming and is unlikely to be overcome by anything else.
Sports bettors are very interested in how likely a team is to win each game, and as a result there is quite a bit of analysis put into this idea. As a result we can say that in their toughest games the Warriors have about a 52% chance to win (on the road in Cleveland or San Antonio). In their easiest games (at home against the Lakers or the 76ers) the Warriors have about a 95% chance to win.
So what are the chances that the Warriors win the next 63 games? Well, let’s establish the range. What if the Warriors were 52% favorites in all of their remaining games? We’d have 68 independent events all of which we’d need to happen. To calculate independent probabilities, multiply them out and the product is your total probability. So, in this case we get: 0.52*0.52*0.52*… 0.52 sixty-three times! In other words, we’d get 0.52^63 = 0.000000000000000001.28295271. So that’s the low end of our range. Not very optimistic is it?
Let’s look at the high end. Let’s assume that every opponent is just as bad as the Lakers or 76ers at home. We calculate that probability the same way, only this time it’s 0.95^68. This number should be a lot bigger, right? I mean, the Warriors are huge favorites in every single game. Right?
Right around a 4% chance. That seems downright possible! But, of course all the teams the Warriors will play aren’t that bad. So how do we best estimate the rest of their schedule? We could go game-by-gam0e and look at estimates for each one to develop a number, but instead let me give you a choice that will test your estimating skills. If you were the Warriors would you rather play 32 opponents that you had a 95% chance to beat and 31 you have a 52% chance to win or all your games in the middle where you have a 75% chance to win?
The Warriors are much better off facing a lot of pretty good teams, because of the big impact that the games against the equally matched teams have.
But as you can see in either case… don’t hold your breath for an undefeated season.