How do I MELT a SQL table?

I have the following SQL table, lets call it teams_score which shows teams of 2 players for a game and their score. I need to observe the score for each player each time they appear on a team as either Player1 of Player2. I think this is like melting.

Player1,         Player2,          TeamScore
"Johnny Onspot", "Pat Magroin",     95
"Pepe Roni",     "Cole Kutz",       78
"Ben Dover",     "Ibin Yerkinoff",  76
"Johnny Onspot", "Frumunda Mabalz", 69
"Sal Lami",      "Cole Kutz",       65
"Pat Magroin",   "Frumunda Mabalz", 63

I want to find the top 3 players with the highest average score.

For example, "Pat Magroin" appeared on 2 teams with scores 95 and 63 for and average score of 79

So I need to display the table "player_score" as shown below and then aggregate by the average score. HOW DO I GET THE TABLE player_score SHOWN BELOW?

Player,            Score
"Ben Dover",       76
"Cole Kutz",       78
"Cole Kutz",       65
"Frumunda Mabalz", 69
"Frumunda Mabalz", 63
"Ibin Yerkinoff",  76
"Johnny Onspot",   95
"Johnny Onspot",   69
"Pat Magroin",     95
"Pat Magroin",     63
"Pepe Roni",       78
"Sal Lami",        65

Once I have player_score, I should be able to run the query (shown below) to get the table result_table as shown below.

SELECT Player, AVG(Score) AS Avg_Score FROM player_score
GROUP BY Player
ORDER BY Avg_Score DESC
LIMIT 3;

Player,            Avg_Score
"Johnny Onspot",   82
"Pat Magroin",     79
"Pepe Roni",       78

Solution

CREATE TABLE player_score AS SELECT Player1 AS Player, TeamScore AS Score FROM(
SELECT Player1, TeamScore
FROM teams_score
UNION ALL
SELECT Player2, TeamScore
FROM teams_score);

-- Delete duplicate rows where player and score are the same in both rows
DELETE FROM player_score WHERE rowid NOT IN 
(SELECT min(rowid) FROM player_score GROUP BY Player, Score);