Ktom, sorry, I tried sending this by private message but I got an error message when I hit sent so I'm not sure if it made it to you.

When you've run melees I believe you have used a phantom player when necessary to have each table scored as though they all had an equal number of players. What is the power that you say the phantom player has for determining if the players at the table beat/tied it? Thanks.

The "phantom player" is still kind of a controversial idea. It doesn't really make winning a 3-person table equivalent to winning a 4-person table. What it does do is potentially make the 2nd and 3rd place at the 3-person table more equivalent to the 2nd, 3rd and 4th places at a 4-person table.

When I use the phantom player, I tend to make the threshold kind of low: 3 power. Remember that ranking in Melee is how far away you are from your (current) win condition, not your total power. So if someone at the table has a Treaty with the Isles Agenda, that 3-power phantom player (7 away from "winning") would "beat" the Agenda player if they had 7 or fewer power.

The use of the phantom player is not part of FFG's rules. If at all possible, equal tables is best. For example, with 15 players, I'd seriously consider running 5 tables of 3 instead of 3 tables of 4 and 1 table of 3 with a phantom player.