Index/Aggregate formula calculates correct row but does not yield name from Index array

[FivestarMac]

I have entered the following equation in L3 of the REPORT sheet to find the player with the highest average score, but although ALT-F9 calculation key gives me 25 for the row (correct - Carver, Graham with an average score of 40) I cannot make the equation give me his name in cell L3.
=INDEX($H:$H,AGGREGATE(15,6,ROW($H$2:$H$136)/((J$2:J$136=LARGE(J$2:J$136,ROWS($1:1)))*(COUNTIF(L$2:L2,$H$2:$H$136)=0)),1))

[tim201110]

for L2
=INDEX($H:$H,AGGREGATE(15,6,ROW($H$2:$H$136)/((J$2:J$136=LARGE(J$2:J$136,ROWS($1:1)))/(COUNTIF(L$1:L1,$H$2:$H$136)=0)),1))
all names are unique. why this part COUNTIF(L$1:L1,$H$2:$H$136)=0)

[FivestarMac]

Thanks for the quick and correct reply!

[FivestarMac]

Tim, you solved the problem as I described it but, when I pull down on your equation to get the top 10 performers (a part of the problem I failed to delineate) I get duplicates...how can we adjust the equation to differentiate duplicate scores?
Jim