How to convert a data matrix into a relational table using Google Sheets formula?

Question

I've got a set of data in a matrix form and I'm trying to use a formula to generate a relational table from that matrix. Here's an illustration of what I'm trying to achieve:

Matrix:

        | 3/5 | 4/5 | 5/5 |
---------------------------
Player1 |  1  |  0  |  1  |
Player2 |  0  |  1  |  2  |
Player3 |  1  |  1  |  2  |

Goal:

Player  | Date | Value |
------------------------
Player1 | 3/5  |   1   |
Player3 | 3/5  |   1   |
Player2 | 4/5  |   1   |
Player3 | 4/5  |   1   |
Player1 | 5/5  |   1   |
Player2 | 5/5  |   2   |
Player3 | 5/5  |   2   |

See the real data here: https://docs.google.com/spreadsheets/d/1DNaoBnYMNbznUoAJahW9-UfGq6LbTG3TXgXPz90bWas

Anyway, I followed the instructions in this answer and came up with this formula:

=ArrayFormula(QUERY(VLOOKUP(HLOOKUP(matrix!A3,matrix!A3:A,INT((ROW(matrix!A3:A)-
 ROW(matrix!A3))/COLUMNS(matrix!B1:Z1))+1,0),{matrix!A3:T, IF(ROW(matrix!A3:A), 
 matrix!B1:Z1)}, {SIGN(ROW(matrix!A3:A)), MOD(ROW(matrix!A3:A) - 
 ROW(matrix!A3), COLUMNS(matrix!B1:Z1)) + {2, 2+COLUMNS(matrix!B1:Z1)} }, 0 ), 
 "select Col1, Col3, Col2 where Col2 is not null and Col2 != 0 order by 
 Col3,Col2", 0))`

It does work, sort of, but with the downside that to generate the rows it uses a lot of empty rows in the matrix sheet, and practically requires that the matrix sheet have at least numCols*numRows number of rows. Now I could just add 3500 empty rows to the matrix and be done with it, but somehow it feels like there should be a better way. Any ideas on how to improve it?

Answer 1

=ARRAYFORMULA({"Player", "Date", "Value"; 
 SORT(SPLIT(TRANSPOSE(SPLIT(TRIM(QUERY(TRANSPOSE(QUERY(TRANSPOSE(
 IF(Sheet1!B2:Z<>"","♠"&Sheet1!A2:A&"♦"&Sheet1!B1:1&"♦"&Sheet1!B2:Z,)),,999^99)),,999^99)),
 "♠")), "♦"), 2, 1, 1, 1)})