Well the idea seems nice - but I agree with general consensus this WILL be abused by people who don't like their team comp to play once a day...
On the other hand an ARAM-Reroll Esk version of this...
Whenever you complete a game win or lose you get emergancy dodge points - say some base value (numbers for numbers sake) of 3 for a loss or 20 for a win (those that are actively trolling the hell out of their team are less likely to actually win so) Plus a multiplier based off the number of minutes in game (Say oh x1.5 for ten, x2 for 20, x3 for 25, x5 for 30, x7.5 for 35 the longer the game IS the more points you get.) anyone who leaves in the middle of the game loses all points based on that game plus either 1 emergency dodge worth of points or all their remaining points (Because those people who start RANKED games without necessary time REALLY shouldn't be getting points - but on the other hand using this same system if you actually DO have an emergency would seem fairly easy to implement however the cost of doing so should be fairly severe as to again avoid abuse as much as possible)
at 250 or so points (Average game being about 20 minutes for sake of math - that is ROUGHLY 8 games - 4 won and 4 lost) to have one emergency dodge, you can hold up to 2 at any given time
Anyone still watching this thread have anything that they want to say about my version of this? Thoughts/Concerns - I really do feel like this does hit a middle ground between being too punishing on a player who IS being held at ransom every now and then, and being free to someone who is actively trying to make lives miserable
Edit: Math major forgot the asterisk which is actually used more for multiplication than using an x is already being used in HTML ... in a post where he also uses it in the HTML ... [zombie-brand-facepalm]