By: Glenn E. L. Petroski, A.R.E.A. administrator. September 25, 2001 updated May 1, 2002
For A.R.E.A. purposes, games fall into five classes or types: Two-player (TWO), Winner-Take-All (WTA), Team (TEAM), Solitaire (SOL), and Race (RACE). Each type uses a slightly modified scoring technique of it's own to calculate the rating.
In a tournament or club gathering any recognized GameMaster, Tournament Official, or Club Officer, may turn in the results for any game as usual. It is recommended that such a submission have a second signature or verification such as a recognized assistant or prominent player. For individual TWO games, both players must verify the result. All independent WTA, TEAM, and RACE games require verification by a minimum of three participants, although it is strongly preferred that ALL participants sign or verify the outcome. Solitaire games, which actually are solitaire, are dependant upon the honor system of each individual player.
Calculations for all types are based on the usual A.R.E.A. two-player formula, so we had better review that here, before examining multi-player calculations further.
Formula: @round(((defeated player rating - victor's rating)x0.05),0)+100 Minimum of one point, maximum of 200 points. Winner's score = Victor's beginning rating + formula result. Loser's score = Defeated player's beginning rating - formula result.
In event of ties:
Formula: @round(((lower player rating - higher player rating)x0.05),0) Note that there is no 100-point baseline added on the end. No minimum points. Tied players may have a zero change in scores. The maximum 200 points still applies. Lower rated player: Lower player's beginning rating + draw formula. Higher rated player: Higher player's beginning rating - draw formula.
To translate the formula into English:
Subtract the lower player rating from the higher. Multiply the difference by 5% (.05). Round this figure to the nearest whole number. If the higher rated player has won, subtract the result of #2 from 100. If the lower rated player has won, add the result of #2 to 100. Add the result of #3 to the winner's rating. Subtract the result of #3 from the loser's rating.
To calculate WTA games, begin at the basic A.R.E.A. two-player formula: round(((defeated player rating - victor's rating)x0.05),0)+100. Apply this to one individual loser against the winner. Divide this by the total number of opponents in the game. If there is only one winner, this means divided by the number of losers. The resulting quotient is then subtracted from the individual loser's rating and set aside to the winner's credit. Do not actually add this to the winner's rating yet.
Repeat this process for each loser in the individual game being calculated. For each calculation within the same game, use the winner's rating prior to the beginning of the game. Do not readjust the winner's rating until all of the loser's ratings have been calculated, and the full list of credits has been determined for the winner.
After all of the losers ratings have been calculated and debited, add all of the winner's credits to his beginning rating.
EXAMPLE: Assume player A with a rating of 5100 wins a four-player game of KREMLIN. The losers are rated 5200, 4800 and 4600 respectively. Player B loses 35 points (.33 of 105), player C loses 28 (.33 of 85), and player D loses 25 (.33 of 75). Player A will gain 35 points from B, 28 from C, and 25 from D for a total gain of 88 points in one game.
Create a debit list for each loser, and a credit list for each winner, until all calculations are complete. Calculate each individual loser against each individual winner, using only beginning scores for all players. Divide the formula result by the total number of opponents. Round to the nearest whole number. Note here that even if the end result is less than one, the loser will be debited a minimum of one, and the winner credited with a minimum of one. For each calculation place the result in the appropriate winner's credit and loser's debit list.
Now go to the tie formula: @round(((lower player rating - higher player rating)x0.05),0). Apply this to each winner verses every other winner. Divide by number of opponents. Round to nearest whole number. In tie calculations, if the result is zero, it remains zero. The minimum one does not apply. Place the result as a debit to the higher rated player, and as a credit to the lower rated player in each calculation.
Finally, calculate all of the debits and credits for all players and adjust their ratings accordingly.
These games are calculated exactly the way that the winners verses the losers are calculated in tie games. The difference comes in that there are no tie calculations between winners. The winners did not tie. They worked together for the win. As such, they do not credit or debit each other in any way toward their ratings.
To calculate, set up a debit and credit account for each player and pull out the TWO formula again. Begin by rating the winner of the race or game winner against whomever came in second and divide by number of opponents. Place this number as a credit to the winner and a debit to the second-place player. Do the same for first verses third, first verses fourth, and all the way down. The minimum one point applies to each calculation, as does the maximum 200 points.
This will give a full list of credits, with no debits, for the winner. Calculate his score accordingly.
Go to the second place player. He already has one debit on his account. Start with that. Now calculate his score against the third, fourth, fifth, and every other player in the game. Use the TWO calculation, and continue to divide by the number of opponents. Each result is given as a credit to the second place player, and a debit to each below him.
Do the same for each player in the game. Give a debit for each player that places ahead of the one being calculated, and a credit for each player placing below. Any tied positions are calculated as ties using the tie formula. Subtract the debits, add the credits. Use the beginning ratings for all players until full calculation for the entire game is complete.
It is possible, even probable, that some players will actually gain more points than those that finish a particular game ahead of them, or lose more than those finishing behind. A.R.E.A. is not calculating a particular game, but an overall history for each player, a long-term record. This is all taken into account. Over the course of as few as five games, an individual's true ability will begin to show itself. This is true of all games in the system.
These games are calculated exactly the way that the winners verses the losers are calculated in WTA games. The only difference is that the game itself is included in every game as another player. In a true solitaire game, such as B-17, it can be calculated as TWO with the individual player against the game. It will come out the same as using the WTA method with only two players. In games with two or more players it becomes WTA, with the game becoming another player, win or lose. In these games, the game itself has a rating, and it will show up on the A.R.E.A. rating sheets.
At your service, -----Glenn Glenn E. L. Petroski A.R.E.A. Administrator 6829 23rd Avenue Kenosha, Wisconsin 53143.1233 Home phone: 262-654-5044 Email: AREA1@ATT.net