Count first occurrence of one criterion based on a second criterion

Sounds like a job for pivot table!

Highlight your table and go to Insert → pivot table and arrange it how you want. I'd do the following -

Thanks to Raystafarian's comment, I am able to provide a detailed answer to my own question. Using a pivot table, I select my entire table range. In the PivotTable Field List dialogue, I add Person to the report, then drag each year (i.e. 2011, 2012, 2013) unchecked into the Values field. Doing so gives me this initial result:

Row Labels     Count of 2011    Count of 2012   Count of 2013
A              2                1               2
B              1                                1
C              2                2   
D              1        
Grand Total    6                3               3

This is fantastic as it not only enables me to COUNT the number of values per row, indicating how many years each person participated, but it also tells me how many scores were given per year for each person.

So in my final step, I simply add the formula =COUNT(B2:D2) in cell E2 whereby Column A = Row Labels, Column B = Count of 2011, Column C = Count of 2012, Column D = Count of 2013, Column E = Years and get this result:

Row Labels     Count of 2011    Count of 2012   Count of 2013     Years
A              2                1               2                 3
B              1                                1                 2
C              2                2                                 2   
D              1                                                  1  
Grand Total    6                3               3