it's been noted in numerous psychology studies that so called home field advantage plays little to no measurable role in performance among athletes. While crowd participation may boost performance in some cases, it can also decrease performance just as often.
Based on your statement, it appears what the research studies are suggesting:
Mean performance in competition at home (μ[SUB]home[/SUB]) = Mean performance in competition afield (μ[SUB]afield[/SUB]), although performance variance in competition at home (σ[SUP]2[/SUP][SUB]home[/SUB]) > performance variance in competition afield (σ[SUP]2[/SUP][SUB]afield[/SUB])
If that's indeed what the studies have shown, I would argue that the increase of variance could increase the chance of getting on the podium. Say, a skater competed three times abroad and three times on home ice and received the following ordinal scores or placement:
Abroad: 4, 5, 6 (μ[SUB]afield[/SUB] = 5, σ[SUB]afield[/SUB] = 1)
Home: 3 (crowd-boosted performance), 5, 7 (crumbled under stress) (μ[SUB]home[/SUB] = 5, σ[SUB]home[/SUB] = 2)
Although the two distributions have an identical mean performance, the skater had 33.33% chance of getting onto the podium while skating at home, whereas he had no chance while skating abroad.
Stefan LINDEMANN, a German skater who won the bronze medal at the 2004 World championships in Dortmund, Germany, seems to be a fitting example. He had the skate of his life on home ice, a performance that was not in his "normal" distribution when skating abroad.
The home field advantage in performance may not concern so much the mean as the increase of variance.....It's just my intuition or guess.
Of course, the home advantage in judging will further increase the skater's chance of getting onto the podium.