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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

Excel sheet

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    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.
    – Cohensius
    Jan 16 at 20:06
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    I may be looking for a "weighted average" although I am not sure. Jan 17 at 2:18
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    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

2 Answers 2

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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.
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Like Cohensius, I will assume you are looking to create a player rating for your group's hearts games. I assume that an Elo based system is more complicated than you need/want. Recommend the following:

  1. Rate player based on game results, instead of hand results. The goal in hearts is to win the game and this greatly reduces your data entry.
  2. Need a score to rate each players result in each game. The scoring method I chose for a tournament I ran was: [player's points] - [winner's points] + (constant between 0 and 100, if not the winner). For my elimination tournament I chose a fairly high constant, but point differential alone may be good enough for your group. It is easier to explain as "the average number of points the player looses by".
  3. Player rating is the average of their game scores.

Unlike an Elo system, this system doesn't address the following issues:

A. Some players improving over time.

B. Stronger (or weaker) players playing each other more often. This type of rating is likely good enough for a social group of under 15 players, especially if games are NOT arranged by skill level.

If you do want to account for a larger group with a wider range of skills, I recommend the following:

  1. Instead of the constant referenced in item 2, calculate extra points given to non-winners as [Sum of ratings of players in game]/4.
  2. New players should start with a rating at or above the group's average rating.

One additional scoring rule I recommend:

  1. Any score above 100 is considered 100 when calculating point differential with winner. This rule helps minimize the penalty for final desperate attempts to win via a run.
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    Any rating system that accounts for other than strict Win-Loss will be gamed. This system you propose punishes players who take a late hit in attempting to stop a Moon Shoot. Do you really want to introduce that dynamic into your games? I wouldn't. Sep 25 at 17:34
  • @Forget Evaluating solely on game win% ignores information on the performance of the 2nd-4th place finishers. This is important if some players don't play many games. Win% should also be tracked with the same spreadsheet. The hearts scoring model does punish a player who stops a run, so the dynamic you describe is already part of the game. An end-game stopper with a big lead still scores a 0 by stopping and winning. If winning is not possible, deciding to stop or not allows the player to pick the game winner. This is a situation common to most multiplayer games.
    – Lee
    Sep 27 at 12:59
  • Don't be absurd. You seem to think the game is Diplomacy. It's not; it's Hearts. There is no second place in the game. Your ranking system makes it better to come second every game than to win half the games and come 4th in the other half. That's silly. Sep 27 at 15:39
  • @Forget Hearts includes situations where a player without a shot of winning can determine who wins. So like other multiplayer games, there is an element of diplomacy. Always 2nd player would have a below average rating compared to the group he plays with. Winning is the only way to score better than the group average. Multiplayer Elo has the always-2nd beating 2/3 of his competition, while the 1st-4th player beats only 1/2 of his competition. Do you have a better answer to the question? Win % alone can be gamed by choosing weaker opponents. This solution worked well enough for my group.
    – Lee
    Sep 28 at 17:39

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