Building a better ranking system (probability)

[ibn_sina76]

Suppose we have four games and the probability that a player will win the game are as follows:

Game 1: 71%
Game 2: 55%
Game 3: 58%
Game 4: 16%

Suppose player b won these games with the following percentages of time:
Game 1: 100%
Game 2: 96%
Game 3: 87%
Game 4: 67%

In other words, he's a very good player. What is the probability that a player chosen at random will play these games with more skill than player b? A random player will play these games with the same skill as the average player.

I really have no idea where to begin on solving this problem. Any help would be appreciated. For the even more advanced, we can add in draws:Game 1: 71%, draw 9%
Game 2: 55%, draw 8%
Game 3: 58%, draw 6%
Game 4: 16%, draw 3%

Player b:
Game 1: 100% wins, 0% draws
Game 2: 96% wins, 3% draws
Game 3: 87% wins, 3% draws
lGame 4: 67% wins, 6% draws

 

[Stephen Tashi]

What is the probability that a player chosen at random will play these games with more skill than player b?

You must specify what "play these game with more skill means". Are you referring to a contest where the skilled player and the randomly chosen player play each of the 4 games once. What counts as "more skill"? Suppose the randomly chosen player wins 2 games and the skilled player only wins game 1. Do we say the randomly chosen player had "more skill" than the skilled player?