Tyler's piece on the higher-seed's winning percentage got me thinking a bit more about this question.  Using schedule data from 1986-87 (when the NHL moved to seven-game opening round series) through last season, I wanted to compare the home team's expected winning percentage to its actual winning percentage.  Let's start with the number of first-round series that got to each state, from the home team's perspective:

 Loss Loss Loss Loss 0 1 2 3 Win 0 184 75 66 32 Win 1 109 94 82 34 Win 2 24 63 77 70 Win 3 7 49 51 49

So the most unlikely path for the series to follow is for the home team to be up three games to none (bottom left corner, only seven occurrences.)  Back when the NHL was a 21-team league, there were some ridiculous mismatches in the first round, and it was very rare for the lower seed to sweep the series.

Now the next step here is to calculate the home team's expected winning percentage using the average of the Log5 winning percentage for all head-to-head matchups.  Each team's expected winning percentage was calculated using its goals for and goals against - in the aggregate, this is a reasonable estimate of team ability.  The higher seed has an expected winning percentage of .572 overall (Log5 breaks down a bit at this level, but it doesn't really impact the overall results here).  As we might expect, lower seeds that took a 2-0 lead in the series were substantially better (.444 expected winning percentage) than the teams that went down 2-0 (.419).

 Loss Loss Loss Loss 0 1 2 3 Win 0 0.572 0.571 0.419 0.416 Win 1 0.572 0.430 0.430 0.555 Win 2 0.444 0.432 0.569 0.419 Win 3 0.444 0.585 0.445 0.569

Now how did these teams do in each of these situations?  This table shows their actual winning percentage in each state:

 Loss Loss Loss Loss 0 1 2 3 Win 0 0.587 0.693 0.530 0.438 Win 1 0.615 0.500 0.561 0.706 Win 2 0.333 0.508 0.649 0.400 Win 3 0.857 0.592 0.588 0.571

It's more instructive to see this as a differential - the actual winning percentage minus the expected one:

 Loss Loss Loss Loss 0 1 2 3 Win 0 0.015 0.122 0.111 0.022 Win 1 0.043 0.070 0.131 0.151 Win 2 -0.111 0.076 0.080 -0.019 Win 3 0.413 0.007 0.143 0.002

The home team exceeded expectations the most in the must-win situations - down 1-0, 2-0, 2-1 and 3-1.  They did not perform particularly well when down 3-0.  And hey underperformed the most when they were up 2-0 at home as the lower seed.

Home-ice advantage appears to be relatively small in the first round of the playoffs - probably smaller than during the regular season - but it also appears to be much larger when a team needs a win.

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