How many points the chess tournament player will get by winning a game or by making a game draw?

In a chess tournament, each participant plays with every other participant exactly once. Each participant gets 1 point for a winning a game, 0.5 points for a draw and no point for a loosing a game.
At most, how many of the 40 participants can score 24 points or more?

My attempt to answer this question:

There will be [math]\binom{40}{2}=780[/math]  games in this chess tournament. Now each player will play 39 game. The probability of winning a game is [math]\frac13[/math]. Probability of loosing a game is [math]\frac13[/math] and the probability of making a game draw is [math]\frac13[/math]. So, out of 780 games, 260 games will be won by some players, 260 games will be lost and 260 games will be drawn.

How can we proceed from here to answer this question?