Simple Formula Question

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Apologies right off the bat for asking a question that I assume will have a simple answer, but I just cannot figure it out. So I'm in a bowling league and am keeping a spreadsheet of my team's scores. I need a formula that will find the max score for game 1 (for example), and then convert that score into the name of the player who bowled it (trying to see who bowled the highest score for each game). So, the spreadsheet looks like this:
Player____Game 1 Score__Game 2 Score...
John__________200_________245...
Jane__________209_________214...
Jack __________253_________231...
Jules __________221________ 220...
Highest Scorer__Jack________ John...

I know how to use a formula to find the highest score for each game (=MAX(B2:B5)), but not how to tell excel to convert that number to the name of the player who bowled it from the A2:A5 list. Help would be greatly appreciated! Thank you
 
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