This is a very useful method for determining how often Team A, with a winning percentage of X, will beat Team B, with a winning percentage of Y. It can be modified to account for other factors, such as home court advantage, etc. (This all comes from Bill James' Baseball Abstracts.)
This method applies explicitly to teams, but there is no obvious reason that it cannot be applied to individuals once winning percentages have been evaluated for them.
In a 0.500 league, i.e., where all we have are the overall records and no information about home court advantage, etc.:
Win%A_B = [Win%A*(1-Win%B)]/[Win%A*(1-Win%B)+(1-Win%A)*Win%B],
where Win%A_B is the chance that A will beat B, Win%A is A's winning percentage against the league, and Win%B is B's winning percentage against the league.
In a non-0.500 league, things are different. For example, if Team A is the home court team and Win%H is the percentage of times the home team wins, we have
Win%A_B = [Win%A*(1-Win%B)*Win%H]/[Win%A*(1-Win%B)*Win%H+(1-Win%A)* Win%B*(1-Win%H)]
For example, say the Lakers are 8-2 and the Celtics are 5-5 and they are playing on the Lakers' court. The league's home court teams win 60% of the time. Then, ignoring the home court advantage, we estimate the Lakers' chance of beating the Celtics as (0.8)*(1-0.5)/[0.8*(1-0.5)+ (1-0.8)*0.5]=0.8, or 80%. Incorporating the league home court advantage gives the Lakers' chance of winning as (0.8)*(1-0.5)*(0.6)/[0.8*(1-0.5)*0.6+(1-0.8)*0.5*(1-0.6)]=0.857, or 85.7%.