Here is a scholarly article on home advantage. It its introduction it notes that in the NBA, about 61% of the time the home team wins. The article does argue that due to the construction of the league schedule this number is inflated because the visiting team typically has had less time between games than the home team. For sake of argument we will assume home-court advantage is 61%.Consider a theoretical seven-game series between two evenly-matched teams. One team has home-court advantage, meaning they will have four out of the possible seven games in their home arena. We therefore assume that the home team has a 61% chance of winning any given game. What is the probability of the team with home-court advantage winning? The probability is about 53.5%. This implies that home-court advantage increases the probability of winning by about 3.5%.
As noted here and here, the Celtics focused their regular season on preparing for the playoffs and worried less about accumulating wins. In this case, it appears that the trade-off was worth it as they did make the finals even without home-court advantage for the last two rounds.
In the NHL the home team wins approximately 55% of the time. In a seven-game series between two evenly-matched teams, the home team will win with a probability of 51.6%. Home-ice in the NHL is therefore worth about a 1.6% percent increase in winning.
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