In Hearts, is there a way to calculate an average score that is weighted based on the number of games that are played?

I have put together an advanced Excel spreadsheet that I use to keep score.

I currently track a year to date average which is a raw average. A yearly average that has a minimum of 12 games played to tabulate and a lifetime average that uses the yearly averages to show your average of all time.

I would like to have a sheet that tracks your average based on the number of games you play, but I am not sure how to do this.

David plays the most games and statistically I think his score would be the greatest risk/reward and in some cases he plays hundreds more games than another player.

Is this assumption correct?
If so how would be the best way to look at this?

Here is a copy of the current sheet: Scoresheet

• I did not understand, can you explain a bit more what are you asking? Are you looking for something else than average? Do you wish to give players that play more often more or less points? Are you looking for some Ranking criteria? If so, you can look at ELO or GLICKO rating systems. Jan 16 at 20:06
• I may be looking for a "weighted average" although I am not sure. Jan 17 at 2:18
• Are you looking for something else than average? Maybe I am, I am not sure. I just want to have the most accurate information on player "ranking" Do you wish to give players that play more often more or less points? Not more or less points just looking to tabulate a ranking on the players based on scores and games played. Are you looking for some Ranking criteria? If so, you can look at ELO or GLICKO rating systems. Those look interesting but I am not sure how to incorporate that into my sheet Jan 17 at 4:05

From what I understand, I think that you are looking for some players-rating system. The most known system is ELO. In a nutshell, the ELO compute the probability for player A to win player B (and players C & D).

I would start by reading Understanding the Elo Rating System. If you want a bit more theory, check wikipedia.

BGA explains well their implemented of ELO that takes into account multi-player games:

A player's ELO score on BGA is based on the ELO formula, which is one of the most popular ways to evaluate a player's level.

• When you have never played a game, your ELO is zero.
• When you finish a game, the number of points you gain/lose depends on the level of your opponents, and more precisely on the ELO difference between you and your opponents.
• The easiest situation is a 2 player game. You will gain a number of ELO points equal to K x (W - p(D)) where:
• W is the result of the game: 1 for a victory, 0 for a defeat, 0.5 for a tie.
• D is the difference of ELO between you and your opponent.
• p(D) is the probability of victory considering the previous difference (see Wikipedia for details).
• K, the 'elasticity factor,' has a value that depends on the number of games you have played: 60 for your first 10 games, 40 between your 11th and 20th games, 20 for your 21st onwards.

Some more details and specific cases:

• On your very first game, you always win at least 1 ELO point, even if you lose the game. Until you reach 100 ELO (beginner), you can never lose ELO points. After that you can never go back below 100 ELO.
• When you play with more than 1 opponent, we consider that you win against each opponent who scores lower than you during this game, and lose against each opponent who scores higher than you. For example, if you place 2nd in a 4 player game, you gain ELO points as if you won against the 3rd and 4th players, and lost against the 1st.