Let’s say we have a table team_person as below:

+======+===========+
| team |    person |
+======+===========+
|   A  |      John |
+------+-----------+
|   B  |     Smith |
+------+-----------+
|   A  |    Walter |
+------+-----------+
|   A  |     Louis |
+------+-----------+
|   C  | Elizabeth |
+------+-----------+
|   B  |     Wayne |
+------+-----------+

CREATE TABLE team_person AS SELECT 'A' team, 'John' person
UNION ALL  SELECT 'B' team,  'Smith' person
UNION ALL  SELECT 'A' team,  'Walter' person
UNION ALL  SELECT 'A' team,  'Louis' person
UNION ALL  SELECT 'C' team,  'Elizabeth' person
UNION ALL  SELECT 'B' team,  'Wayne' person;

To select the table team_person with additional row_number column, either

SELECT @row_no := @row_no+1 AS row_number, team, person
FROM team_person, (SELECT @row_no := 0) t;

OR

SET @row_no := 0;
SELECT  @row_no := @row_no + 1 AS row_number, team, person
FROM team_person;

will output the result below:

+============+======+===========+
| row_number | team |    person |
+============+======+===========+
|          1 |   A  |      John |
+------------+------+-----------+
|          2 |   B  |     Smith |
+------------+------+-----------+
|          3 |   A  |    Walter |
+------------+------+-----------+
|          4 |   A  |     Louis |
+------------+------+-----------+
|          5 |   C  | Elizabeth |
+------------+------+-----------+
|          6 |   B  |     Wayne |
+------------+------+-----------+

Finally, if we want to get the row_number group by column team

SELECT @row_no := IF(@prev_val = t.team, @row_no + 1, 1) AS row_number
   ,@prev_val := t.team AS team
   ,t.person  
FROM team_person t,
  (SELECT @row_no := 0) x,
  (SELECT @prev_val := '') y
ORDER BY t.team ASC,t.person DESC; 

+============+======+===========+
| row_number | team |    person |
+============+======+===========+
|          1 |   A  |    Walter |
+------------+------+-----------+
|          2 |   A  |     Louis |
+------------+------+-----------+
|          3 |   A  |      John |
+------------+------+-----------+
|          1 |   B  |     Wayne |
+------------+------+-----------+
|          2 |   B  |     Smith |
+------------+------+-----------+
|          1 |   C  | Elizabeth |
+------------+------+-----------+