Posted by Neil Paine on January 20, 2011
I finally got around to calculating the standard errors for our team Simple Ratings today:
Then I set up a little Monte Carlo sim to estimate what is the probability of each team being the NBA's best (aka the team with the greatest "true" SRS skill). After 10,000 simulations using the estimates and standard errors above, here were the results:
According to this, we can be about 94% sure that the best team is either San Antonio, Miami, Boston, the Lakers, Chicago, or Orlando.
One interesting idea for a playoff system would be to eliminate all teams we were 95% sure weren't the best team and set the odds of winning the playoff to mirror the uncertainty we had regarding who was the best -- i.e., rig it so San Antonio had a substantially larger chance of winning the tournament than Chicago, etc. The NBA already does this to a degree via seedings and home-court, but you could even go as far as giving teams automatic 1-0 leads in a series to get the probabilities right.
For a great article that goes further with that idea, check out this Sky Andrecheck piece on the MLB playoffs, and the philosophy of why playoffs are necessary at all: