|What kind of racing are you keeping track of?|
Here's one way. Look at the Help files for VLOOKUP to see how it works.
Let's put your Race Results example in Sheet1!A1:D4.
Let's put your Points Table in Sheet2!A1:B8.
In Sheet1:E1 enter this formula and drag it down to E4:
That formula gave me the results you showed in your example.