SQL Server Averages/Sums/Groups/Counts Query Issue

Question

I have the following table:

╔══════════╦════════╦═══════╦═══════╗
║ PlayerID ║ GameID ║ Stat1 ║ Stat2 ║
╠══════════╬════════╬═══════╬═══════╣
║        1 ║ A      ║     2 ║     1 ║
║        1 ║ B      ║     4 ║     2 ║
║        1 ║ C      ║     6 ║     5 ║
║        2 ║ A      ║     2 ║     4 ║
║        2 ║ B      ║     2 ║     6 ║
║        2 ║ C      ║     2 ║     8 ║
║        2 ║ D      ║     4 ║     2 ║
║        2 ║ E      ║     6 ║     1 ║
║        3 ║ A      ║     5 ║     9 ║
║        3 ║ G      ║     6 ║     4 ║
║        3 ║ H      ║     4 ║     2 ║
║        3 ║ N      ║     8 ║     6 ║
╚══════════╩════════╩═══════╩═══════╝

What I am trying to achieve is the following:

╔══════════╦═══════════╦═══════════════════╦═══════════════════╗
║ PlayerID ║ GameCount ║ Stat 1 Avg / Game ║ Stat 2 Avg / Game ║
╠══════════╬═══════════╬═══════════════════╬═══════════════════╣
║        1 ║         3 ║ 4                 ║ 2.66              ║
║        2 ║         5 ║ 3.2               ║ 4.2               ║
║        3 ║         4 ║ 5.75              ║ 5.25              ║
╚══════════╩═══════════╩═══════════════════╩═══════════════════╝

The game count should be the total number of games played per player and the stats should be the average per game. Basically the calculation for PlayerID 1 is the following:

"Stat1 Avg / Game" = (2 + 4 + 6) / 3 "Stat2 Avg / Game" = (1 + 2 + 5) / 3

I have tried numerous variations of the same query with a combination of SUMS and COUNTS but the GameCount never comes out correct. An example of what I have tried is below

SELECT PlayerID, 
COUNT(GameID) AS GameCount, 
SUM(Stat1) / COUNT(GameID)  "Stat 1 Avg / Game",
SUM(Stat2) / COUNT(GameID)  "Stat 2 Avg / Game"
FROM PublishedStats A
GROUP BY PlayerID

SELECT PlayerID, 
COUNT(GameID) OVER (PARTITION BY PlayerID) AS GameCount, 
SUM(Stat1) /  COUNT(GameID) OVER (PARTITION BY PlayerID) "Stat 1 Avg / Game", 
SUM(Stat2) /  COUNT(GameID) OVER (PARTITION BY PlayerID) "Stat 2 Avg / Game", 
FROM Stats
GROUP BY PlayerID, GameID

Answer 1

So just add the DISTINCT keyword.

SELECT PlayerID, 
COUNT(DISTINCT GameID) AS GameCount, 
AVG(Stat1)  "Stat 1 Avg / Game",
AVG(Stat2)  "Stat 2 Avg / Game"
FROM PublishedStats A
GROUP BY PlayerID