Well, I think total kda is a more useful stat than average kda. Let me grab my stats from Silver V:
Game 1: 7/4/5 3.00 KDA
Game 2: 0/3/17 5.67 KDA
Game 3: 1/2/16 8.50 KDA
Game 4: 0/3/20 6.67 KDA
Game 5: 1/1/11 12.0 KDA
Game 6: 2/2/11 6.5 KDA
Game 7: 1/0/7 8.00 KDA
Game 8: 4/2/10 7.00 KDA
Total KDA: 16/17/97 6.65 KDA
Average KDA: 7.99 KDA
Now, because my KDAs are extremely consistent, there's not too much difference between average and total KDA.
However, looking at your Gold III stats, you have an average KDA of 8.38, and a total KDA of 3.70. This would be heavily influenced by some good games you've had. Despite the fact that my total KDA was almost twice as high as yours, our average KDAs are comparable.
I just think that average KDA rewards good games too much while not punishing you for bad games. There's a large difference between a KDA of .5 and a KDA of 1, but average KDA doesn't weight them too differently over the long run. On the other hand, the difference between a game of 5 KDA and 6 KDA isn't that much (you did a bit better, but they're really not all that different -- probably 2/3 kills or assists would make the difference), but this difference is weighted more in average KDA.
I'm pretty sure LCS and other professional leagues use total KDA, not average KDA, as their statistic.