My favorite sports related board game is Strat-O-Matic Baseball. It also used real players but unlike All Star Baseball every player on the team is involved and games are played as teams. It also takes into account fielding, running, throwing, injuries, and most importantly pitching.
In every at bat, a batter card and a pitcher card is involved. One six sided dice (d6) is rolled. If it is 1-3, the corresponding column in the batters card is used. A 4-6 roll uses the column in the pitchers card. Then 2 d6 are thrown and the total is read in the column to reflect what happened in the at bat. Some results need a twenty sided dice rolled as there are two options. Also the d20 is used for stealing, plays where a fielder's rating is involved, base running, and injuries.
To show how a card would look, I took my daughter's stats from this year and created a card:
For example if the first die is a 2 and the total of the other two dice is 8, the result would be a walk.
A few notes: Since the card only reflects half the possible options, it does not match the stats. I adjusted the card to provide the results if her batters card went against an average pitchers card from her league. (In the game, no pitchers card had a hit by pitch (HBP) possibility)
Fielding ratings in the game went from 1 (best) to 4 (worst) and throwing ability was from +5 (worst) to -5 (best). I created a 5 fielding rating and +8 throwing to be honest.
In the game, there are power ratings of "N" and "W". A "W" rating would turn a home run on a pitchers card to a SINGLE**(runners advnace two bases) for those who regularly don't hit home runs. I created "VW" meaning all hits on a pitchers card would become SINGLE* (all runners advance one base).
Also, I matched column 3 on my daughter's card with the column 3 on the card from Barry Bonds 2001 season where he hit 73 home runs.