Wednesday, April 20, 2011

Picking Playoff Series Length

People who are good with numbers may have noticed that I picked an unreasonably large number of first round series' to be 5 games long. In fact, people who aren't good with numbers probably noticed it also because I picked 7 out of 8 to be the same length. It turns out however, that for a series with a clear favorite, that's the most likely out come. In fact, there are easy rules to follow.
*This all assumes that home teams win 60% of the time with equal skill. This also does not apply to the finals which have a different format (2-3-2).

When to...
Pick the home team in four
As I noted last year, sweeps are surprisingly unlikely. It's even more unlikely that a sweep is the most likely outcome, in fact there is no case where that could happen in this year's playoffs. Pick a sweep only when the home team is 3.67 or more times better than the away team, or has at least a 96.2% chance of winning.
Pick the home team in five
This is a much more common choice, especially with a lopsided first round series. Pick this when the home team is between 1.27 and 3.67 times better, or has between a 64.5% and 96.2% chance of winning.
Pick the home team in six
Never! The sixth game is on the road, so any team likely to win it probably would've already won in 5.
Pick the home team in seven
While rarer, when two teams are especially close the most likely outcome is often the home team in 7 games. Pick it when the home team is between .97 and 1.27 times better, or has between 51.2% and 64.5% odds of winning.

What?!? 51.2%? What if it's 51.0%, do you pick the home team in eight or something??
Turns out, that when the home team is slightly favored the most likely outcome is that the away team wins in 6 games, even though it's smarter to pick the other team to win. How do you compensate for this? It depends on what value is assigned to each. Using TrueHoop's 5 points for series winner and 2 points for correct number of games the boundary is set at .944 times better, or when the home team has a 50.1% chance of winning.

Pick the away team in seven
Don't do it! If they can win in seven, they're more likely to win in game 6 when they're at home.
Pick the away team in six
If you're going to pick the away team to win, unless for some super weird reason the away team is waaaaaaay better. Accordingly, pick the away team in six when it's 1.04 to 2.38 times better, or has between a 48.8% and 85.8% chance of winning.
Pick the away team in five
There's only a brief range where this is the right choice, but it still exists. If the away team is 2.38 to 2.83 times better, implying between 85.8% and 90.3% chance of winning, then pick the away team in five.
Pick the away team in four
If the away team is 2.83 or more times better, meaning they'll win at least 90.3% of the time, then pick them to sweep. This has probably never happened, and probably never will.

Summary (for lazy readers):
If you think the home team will win pick them in 5 games, unless if you think it's close than go with 7 games. If you think the away team will win, pick them in 6 games pretty much no matter what. Importantly, while it's often tempting it's never smart to pick the home team in 6 or the away team in seven. There will of course be sweeps this year, and home teams that win in six, but from a purely mathematical perspective, that's not a smart pick going in.
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