Find address of max value, sports stats

[Rikib1999]

Hi,
I have a table of sport team, which shows, how many goals (with assissts) 2 players scored together (so if player 5 scored a goal and player 16 assisted on this goal they will have one common goal).
There is an example of the table, players numbers are in the first column and row, common goals are for the player from the column and row:

	5	7	16	23
5		3	0	2
7			2	0
16				1
23

Now, I need in another 3 cells, the amount of most goals of a pair, so the max value of the table (can be done with MAX formula), then the numbers of the 2 players which have that most common goals.
I tried to find them out by INDEX, MATCH, MAX, ADDRESS, CELL... but nothing worked.
Do somebody know, how should I approach this problem?
Thanks!

 

[jasonb75]

Such tasks are never as simple as you would like them to be, I think that the method I've used below eliminates all possible errors in the results. I've deliberately set a tie for the max to further test the formulas. Tested with a 3 way tie with no apparent issues.

Book1
	A	B	C	D	E	F	G	H	I
1		5	7	16	23		MAX	First Player	Second Player
2	5		3	0	2		3	5	7
3	7			3	0			7	16
4	16				1
5	23
Sheet9

Cell Formulas
Range	Formula
G2	G2	=MAX($B$2:$E$5)
H2:H4	H2	=IFERROR(INDEX($A$1:$A$5,AGGREGATE(15,6,ROW($B$2:$E$5)/($B$2:$E$5=$G$2),ROWS(H$2:H2))),"")
I2:I4	I2	=IFERROR(INDEX($A$1:$E$1,AGGREGATE(15,6,COLUMN($B$2:$E$5)/(INDEX($B$2:$E$5,MATCH($H2,$A$2:$A$5,0),0)=$G$2),COUNTIF(H$2:H2,H2))),"")