So I finally had some time to look into this. The reason luck is always under 50% is because there is an error averaging luck for the day and month (luck per game seems accurate though).

The mistake is that your luck for the day is simply an average of all your games. So if you had 50% luck one game and 40% luck the next your daily average is 45%. Sounds ok to me so far. Right?

Oh Nooo! It's not! To see why think of how luck would be when you win and when you lose. When you lose you're out pretty quickly and don't have many battles. Therefore you're luck can be pretty low (10-50%). But when you win you have substantially more battles and your luck averages out around 50%. This means you don't have any high luck games to average out the low luck and your daily luck average will always be low.

Now its obvious how to fix this. Instead of averaging per game luck needs to be a weighted averaged base on the number of battles.

For example, instead of:

total_luck/total_games

it would be:

game_luck*game_battles/total_battles

Look for this update August 1.