Slight "fuzzyness" to game on external display.

Hello!
I have an external display connected to my macbook pro, when I play LoL, just when the game starts, i can see the loading screen for about half a sec. After that, my screen turns black, and then it returns after about 2 seconds, just now it's slightly fuzzy and not as clear looking as before. It's fully playable, but it just doesn't look as crisp as during that brief moment. So i know my display is capable of looking nice while in game, since it does for a short time. And this blackout thing happens every time I cmd tab out of the game. Everything looks fine when i'm not in the game and still on the external display.

Does anyone know why it does this? When im on the built in screen, there is not time lag when tabbing in and out of the game, and no fuzzyness on the display. It's an early 2011 model and connected via hdmi.

Thanks in advance!

 

Thanks for your reply,
Yes, I believe so. The res of my external display is 1920x1080, and so are my in-game settings. So you think the game isn't showing the correct resolution?