Warriors 3-1 Comeback

I happened to be in the bay area this weekend. The bay area the home of the Golden State Warriors. A few days ago it wasn't looking good for them. Oklahoma City was ahead three games to one in their best of seven series. So to win, Golden State would have to win three games in a row.

There were a million sports radio shows that had their predictions of the likelihood of Golden State winning three in a row. Most all of them decided that it was not likely. But somehow they did. I like to think my presence in the bay area had a little to do with those wins. What were the chances anyway? Virtually all of the radio experts were making basketball predictions. However, it is also a good math application as well.

Theoretically I would think that 0.5 x 0.5 x 0.5 = 0.125 might be it. So the team with the lead has a 87.5% chance of winning the series. Historically, counting Golden State's win, the team that was ahead has now closed it out 95.7% of the time. It's close, but quite a bit ahead of our theoretical figure. But that does make some sense. We were assuming the chance of a single win is 50%. But if your team is ahead three games to one, you probably (but not necessarily) have the better team. Maybe that team against the same opponent would win 60% of the time. Then 0.4 x 0.4 x 0.4 = 0.064. That means the leading team would have a 93.6% chance of winning the entire series. Now we're getting there.

In fact, what winning percentage would correspond with the 95.7% figure? If the chance of winning three straight is .043 (1 - .957), then the chance of winning one game is the cube root of .043 or .350. That would mean that the team ahead in the series would normally beat the other team in a single game 65% of the time. That seems fairly reasonable.

I found a bunch of cool historical stats like this on the following website: http://www.whowins.com/tables/up31.html

I'm sure there are others like this with different scenarios. This one states the chances of winning if a team is up 3-1 in the playoffs in various settings.

• In the NBA it is now 95.7%. 
• In major league baseball it is only 85.2% (slightly less than the theoretical percent).
• In the NHL it is 90.1%
• In all three sports combined it is 91.7%

This might be of a bit more interest to students before the series is over, but regardless, I think its a pretty cool application.