Your team is up by 15 with 10 minutes left in the game. Is it time to relax? Is the win secured? What are the chances of winning?
I looked at the last 10 seasons in the NBA and checked the chances of winning as a function of the lead and time left in the game. This can all be plotted in one image where the y axis is the lead, the x axis is time and the pixel color reflects the chances of winning.
Here are the results:
Let's look at key times during the games (i.e. vertical lines through the image):
My biggest surprise looking at the data is that even a 1 point lead in the 4th quarter increases your chances of winning by a noticeable amount.
We can look at winning percentage when a team has a certain lead (i.e. horizontal lines):
So when a team is up by 15 at any point during a game they have a very good chance of winning (above 80% even if that lead is in the first quarter).
The Golden State Warriors had a 46-0 record last year when leading by 15 at some point in the game. I checked the time in each of those game when the Warriors got up by at least 15 and calculated the probability of the Warriors winning that game. The probability of the Warriors winning all 46 of those games was 1.5%. Not bad! Just for comparison Philadelphia had a 15 point lead 8 times last season and they lost 3 of those games.
As a fan when can you really relax? Let's separate the 100% chance of winning from the rest.
Statistically speaking you should never give up on a game before the 4th quarter because there is some chance for a comeback. Unless you are watching the Warriors and they are leading by 15 or more.
Conclusions:
Being a Warriors fan can reduce stress.
Acknowledgement: the idea for this post was inspired by Arie Melamed-Katz. Thank you!
Technical information:
Game scores were extracted from the play by play from the NBA website. Some (small number of) games did not have a play by play and were not included.
Fig 1 and 4 - I only included cases were there was enough statistics (N > 100).