Speaking of Nerd

So the NBA playoffs are starting so I've been reading up on some playoff predictions when I found this. It's probably too long for anyone else to want to read so let me highlight the worst part:

In fact, while much has been made of Utah's home/road splits in a negative light, I don't think enough has been made of the positive implications that has for their chances. Think about it. They were 37-4 at home, which is a winning percentage of over 90%. On the road they were 17-24, for a winning percentage of just over 41%. Not to state the obvious, but 90 is a lot closer to 100 than 41 is to zero. In other words, isn't it far more likely that Utah will win all of its home games in a given series than it is that they will lose all of their road games? Which scenario would you rather bank on?

- A team with a 41% chance of winning road games going 0-4 on the road
- A team with a 90% chance of winning home games going 2-1 at home
- A team with a 90% chance of winning home games going 3-0 at home and with a 41% chance of winning road games going at least 1-3 on the road

I know I'm a stats nerd, but does this guy really think any of this makes sense? According to his logic, the Utah Jazz have a 90% chance of winning in Utah and a 41% chance of winning in Houston, so if we treat those as independent Bernoulli random variables with p=0.9 for home games and p=0.41 for road games, that means Utah has a 78.5% chance of winning the series against Houston. Which by deduction would mean that Houston has a 21.5% chance of winning the series. So Houston, which has a better overall record and home court advantage are now somehow heavy underdogs in this series.

The problem with this logic is that we're assuming that Houston's odds of winning a game in Houston is 59% and winning a game in Utah is 10%. But if we reversed the logic and naively looked at just Houston's home and road records, they would have a 75.6% chance of winning in Houston and a 58.5% chance of winning in Utah. Which by the same statistics I used above, the Rockets have an 85.5% chance of winning the series. And last time I checked Utah can't have a 78.5% chance of beating Houston in the series at the same time that Houston has an 85.5% chance of beating Utah.