JP2007319384A - Rating program, method and device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To calculate new rating by adding a content of winning or losing (with a big difference or a small difference) even in a game where three or more players play a match against each other. <P>SOLUTION: A storage device 1 stores n ratings and n scores. Then, a CPU 4 calculates a rating deviation a<SB>k</SB>about k-th rating x<SB>k</SB>in the n ratings, calculates a score deviation b<SB>k</SB>about a score P<SB>k</SB>corresponding to the rating x<SB>k</SB>, and calculates new rating X<SB>k</SB>by formula (I) X<SB>k</SB>=x<SB>k</SB>+(b<SB>k</SB>-a<SB>k</SB>). (where, n is a natural number of ≥2, and k is a natural number of ≥1 and ≤n). <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a rating program, a method, and an apparatus for evaluating a player's ability based on a game match result or the like.

In the field of games such as chess and shogi, an ability evaluation method called a rating system is known. For example, in chess, the Iro rating system developed by Professor Iro is prominent (see Non-Patent Document 1, for example).
“Rating of the past and present (TheRating of Chessplayers, Past and Present)” by Arpad Elo, published by Arco Publishers

  In the conventional rating system, a new rating can be calculated based on the win and loss of the game and the ratings of both players in a game in which two players play one-on-one. However, it cannot be applied to a game in which three or more players play. In addition, it is not possible to calculate a new rating taking into account the contents of the win or loss (whether it was a big difference or a small difference).

  Therefore, the present invention can be applied to a game in which three or more players participate, and provides a program, method, and apparatus capable of calculating a new rating in consideration of contents of wins and losses. Objective.

A first feature of the present invention is a rating program, comprising:
storage means for storing n ratings and n scores;
A rating deviation value a _k is calculated for the k-th rating x _k out of the n ratings, and a score deviation value b _k is calculated for the score P _k corresponding to the rating x _k . Means for calculating a new rating X _k ,
It is to function as.
X _k = x _k + (b _k −a _k ) (I)
(However, n is a natural number of 2 or more, and k is a natural number of 1 or more and n or less.)

“N ratings” means, for example, in a game in which n people participate, the rating of the first participant before the game starts, the rating of the second participant,..., The rating of the nth participant Means. “Rating deviation value a _k ” means, for example, a deviation value of the rating x _k of the kth participant before the game starts.

The “score P _k corresponding to the rating x _k ” means, for example, the points of the kth participant at the end of the Mahjong game. “Score deviation value b _k ” means, for example, the deviation value of the score of the kth participant at the end of the game.

According to a second feature of the present invention, the storage means stores m score elements for each of the n scores.
It said calculating means, scoring elements deviation b _k1, for each of the m-th score elements from the first of said k-th score ..., calculates b _miles, calculates a new rating X _k by the following formula (II) There is to do.
X _k = x _k + (b _k1 +… + b _km −a _k ) (II)
(However, n is a natural number of 2 or more, k is a natural number of 1 or more and n or less, and m is a natural number of 2 or more.)

  For example, in the case of a mahjong game, the “score element” means “the score at the end of the game”, “the number of transfers”, “the number of climbs”, and the like. “M score elements for each of n scores” means, for example, “the number of points at the end of the game” for each of the first participant, the second participant,. "Point", "Number of transfers", "Number of climbs", etc. Alternatively, information such as the number of consecutive wins and the number of consecutive losses may be used as a score element.

“Score element deviation values b _k1 ,..., B _km for each of the 1st to m-th score elements of the score P _k corresponding to the rating x _k ” are, for example, “the end of the game” It means a deviation value of “point”, a deviation value of “number of transfers”, a deviation value of “number of climbs”, and the like.

A third aspect of the present invention, the storage means, said scoring element deviation b _k1, ..., each of the weighting of b _miles w _k1, ..., stores w _miles,
The calculating means is to calculate a new rating X _k by the following formula (III).
X _k = x _k + (w _k1 × b _k1 +… + w _km × b _km −a _k ) (III)

  According to the first feature of the present invention, for example, the first participant, the second participant,..., The nth participant's “rating at the start of the game”, “the rating at the start of the game” By calculating a new rating based on “deviation value” and “deviation value of points at the end of the game”, a highly accurate rating is possible.

  Further, according to the second feature of the present invention, the deviation value of “the score at the end of the game” for each of the first participant, the second participant,. The rating accuracy can be further improved by taking into consideration the deviation values of a plurality of elements such as the deviation value of “the number of transfers” and the deviation value of “the number of climbs”.

  Furthermore, according to the third feature of the present invention, it is possible to further improve the accuracy of the rating by weighting the deviation values of a plurality of elements for rating.

  The best mode for carrying out the present invention will be described below with reference to the drawings. The following description is merely an example, and the technical scope of the present invention is not limited to the following description.

  FIG. 1 shows an example of a hardware configuration of a rating calculation apparatus according to an embodiment of the present invention.

  The input device 2 is a pointing device such as a keyboard or a mouse. The display device 3 is, for example, a liquid crystal display device or a CRT (Cathode Ray Tube). The player inputs an instruction using the input device 2. For example, a plurality of characters that are opponents are displayed on the display screen of the display device 3. The player can use the mouse to move the pointer displayed on the display screen over an arbitrary character and click that character to select that character as an opponent. Then, after the player finishes selecting a character necessary for starting the game, the player clicks the “PLAY” button displayed on the display screen to start the game.

  The CPU 4 controls the entire system, executes the game according to the game program, and outputs a game result. The game includes, for example, a mahjong game and a racing game. The game result includes, for example, the score of each player in the case of a mahjong game, and the time difference from the top in the case of a racing game. Then, the CPU 4 calculates a rating based on a calculation formula described later.

  The storage device 1 is, for example, an HDD (Hard Disk Drive), a RAM (Random Access Memory), or the like. The storage device 1 stores a game program 10 including a battle result calculation program 11 and a rating calculation program 20 including a deviation value calculation program 21 and a new rating calculation program 22. Further, the storage device 1 stores a player rating value 33 and an opponent character rating value 34 at the start of rating calculation. Furthermore, the storage device 1 temporarily stores a rating deviation value 31 and a score deviation value 32 during rating calculation.

  FIG. 2 shows an example of the flow of rating calculation processing in the embodiment of the present invention. As shown in FIG. 2, when the game is over (step S13), the CPU 4 calculates a battle result (scores of the player and the opponent character) according to the battle result calculation program 11 (step S15). Subsequently, according to the deviation value calculation program 21, a score deviation value 32 based on the score (denoted as a score deviation value b in the embodiment described later) is calculated (step S17). Further, according to the deviation value calculation program 21, a rating deviation value 31 (denoted as a rating deviation value a in the embodiment described later) based on the player rating value 33 and the opponent character rating value 34 is calculated (step S11). Then, according to the new rating calculation program 22, the CPU 4 calculates a new rating based on the original rating (current player rating value 33 and opponent character rating value 34), the rating deviation value 31, and the score deviation value 32. (Step S19). The player rating value 33 and the opponent character rating value 34 are updated with the new rating calculated here (step S21).

The contents of FIG. 2 will be described more specifically.
(1) First _, a deviation value a of each original rating (rating before the battle: x1 _, x2 _, ..., _xn ) is calculated. The calculation of the deviation value is performed using a known method. That is,
(1-1) Calculate the average value x _μ of n people's ratings,
x _μ = (x ₁ + x ₂ +… + x _n ) / n
(1-2) Calculate the standard deviation x _σ of the rating of n people,
x _σ = [{(x ₁ −x _μ ) ^ ² + (x ₂ −x _μ ) ^ ² +… + (x _n −x _μ ) ^ ² } / n] ^ ^(1/2)
(1-3) Rating values a ₁ to a _{n of} each person's rating
a ₁ = Cs × {(x ₁ −x _μ ) / x _σ } + Cm
a ₂ = Cs × {(x ₂ −x _μ ) / x _σ } + Cm
:
a _n = Cs × {(x _n −x _μ ) / x _σ } + Cm
Is calculated. For simplification of description, Cs is 10 and Cm is 50 so that the average value is 50 and the standard deviation is 10 in the calculation formula described later. However, it is not always necessary to correct the average value to be 50 and the standard deviation to be 10. For this reason, Cs and Cm can be arbitrary numerical values.

(2) Next, the deviation value b of each score (y _1, y _2, ... _, Y _n ) is calculated. The calculation of the deviation value is performed using a known method. That is,
(2-1) Calculate the average value y _μ of n scores,
y _μ = (y ₁ + y ₂ +… + y _n ) / n
(2-2) Calculate the standard deviation y _σ of n scores,
y _σ = [{(y ₁ −y _μ ) ^ ² + (y ₂ −y _μ ) ^ ² +… + (y _n −y _μ ) ^ ² } / n] ^ ^(1/2)
(2-3) Deviation value b ₁ to b _{n of} each person's score
b ₁ = 10 × {(y ₁ −y _μ ) / y _σ } +50
b ₂ = 10 × {(y ₂ −y _μ ) / y _σ } +50
:
b _n = 10 × {(y _n −y _μ ) / y _σ } +50
Is calculated.

(3) And the following formula
X ₁ = x ₁ + (b ₁ −a ₁ )
X ₂ = x ₂ + (b ₂ −a ₂ )
:
X _n = x _n + (b _n −a _n )
The value calculated by is used as a new rating (X _1, X _2, ... _, X _n ).

  Examples 1-3 of the present invention will be described below. In the following examples, it can be said that the rating changes significantly when the rating increases or decreases by 20 or more.

Player A and opponent characters B, C, and D prepared in advance by the game program played a mahjong game. Player A has a low rating (x ₁ = 1500), opponent character B has a high rating (x ₂ = 2500), and opponent characters C and D have a rating between player A and partner character B (x ₃ = 2000 _, x ₄ = 2000). At the end of the game, the scores of player A, opponent characters B, C, and D were y ₁ = 6000, y ₂ = 92000, y ₃ = 1000, and y ₄ = 1000, respectively.

(1) First, when calculating the deviation value a of each original rating,
(1-1) The average value x _μ of the ratings of four people is
x _μ = 2000
And
(1-2) The standard deviation x _σ of the rating of four people is
x _σ = 353.5534
And
(1-3) Deviation values a ₁ to a ₄ of each person's rating are
a ₁ = 35.85786
a ₂ = 64.14214
a ₃ = 50
a ₄ = 50
It becomes.

(2) then calculating the deviation value b of each of the scores _{(y 1, y 2, y} 3, y 4),
(2-1) The average value y _μ of the scores of four people is
y _μ = 25000
And
(2-2) The standard deviation y _σ of the scores of four people is
y _σ = 38736.29
And
(2-3) Deviation values b ₁ to b ₄ of each person's score are
b ₁ = 45.09504
b ₂ = 67.29644
b ₃ = 43.80426
b ₄ = 43.80426
It becomes.

(3) So the new rating is
X ₁ = 1509.237
X ₂ = 2503.154
X ₃ = 1993.804
X ₄ = 1993.804
It becomes.

The above contents are summarized in [Table 1]. As described above, in the first embodiment, the player A with a low rating may rise without decreasing the rating even if the player B loses the opponent character B with a high rating. In addition, even if the opponent character B with a high rating wins the player A with a low rating by a large difference, the rating increases only slightly.

Player A and opponent characters B, C, and D played a mahjong game. The ratings of player A and opponent characters B, C, and D are the same as in the first embodiment. At the end of the game, the scores of player A, opponent characters B, C, and D were y ₁ = 92000, y ₂ = 1000, y ₃ = 6000, and y ₄ = 1000, respectively.

(1) First, when the deviation value a of each original rating is calculated, the average value x _{μ of} the rating of four people, the standard deviation x _σ of the rating, and the deviation value a ₁ of the rating of each person
A ₄ is the same as in Example 1 from.

(2) then calculating the deviation value b of each of the scores _{(y 1, y 2, y} 3, y 4),
(2-1) The average value y _μ of the scores of four people is
y _μ = 25000
And
(2-2) The standard deviation y _σ of the scores of four people is
y _σ = 38736.29
And
(2-3) Deviation values b ₁ to b ₄ of each person's score are
b ₁ = 67.29644
b ₂ = 43.80426
b ₃ = 45.09504
b ₄ = 43.80426
It becomes.

(3) So the new rating is
X ₁ = 1531.439
X ₂ = 2479.662
X ₃ = 1995.095
X ₄ = 1993.804
It becomes.

The above contents are summarized in [Table 2]. As described above, in Example 2, when the player A having a low rating wins the opponent character B having a high rating with a large difference, the rating greatly increases. If the opponent character B with a high rating loses the player A with a low rating by a large difference, the rating greatly decreases.

Player A and opponent characters B, C, and D played a mahjong game. The rating of player A is high (x ₁ = 2500), the rating of opponent character B is low (x ₂ = 1500), and the rating of opponent characters C and D is between player A and opponent character B (x ₃ = 2000 _, x ₄ = 2000). At the end of the game, the scores of player A, opponent characters B, C, and D were y ₁ = 30100, y ₂ = 29900, y ₃ = 30000, and y ₄ = 10000, respectively.

(1) First, when the deviation value a of each original rating is calculated, the average value x _{μ of} the ratings of the four people and the standard deviation x _{σ of the} rating are the same as in the first embodiment.
(1-1) Each person's rating deviation values a ₁ to a ₄ are
a ₁ = 64.14214
a ₂ = 35.85786
a ₃ = 50
a ₄ = 50
It becomes.

(2) then calculating the deviation value b of each of the scores _{(y 1, y 2, y} 3, y 4),
(2-1) The average value y _μ of the scores of four people is
y _μ = 25000
And
(2-2) The standard deviation y _σ of the scores of four people is
y _σ = 8660.542708
And
(2-3) Deviation values b ₁ to b ₄ of each person's score are
b ₁ = 55.88878
b ₂ = 55.65784
b ₃ = 55.77331
b ₄ = 32.68007
It becomes.

(3) So the new rating is
X ₁ = 2491.747
X ₂ = 1519.8
X ₃ = 2005.773
X ₄ = 1982.68
It becomes.

The above contents are summarized in [Table 3]. As described above, in the third embodiment, even if the player A having a high rating wins the opponent character B having a low rating, if the score difference between the player A and the opponent character B is small, the rating is lowered. As a result, the player can develop a game with a sense of tension even when fighting against an inferior opponent.

Player A and opponent characters B, C, and D played a mahjong game. Player A has a slightly higher rating (x ₁ = 1900), opponent character B has a slightly lower rating (x ₂ = 1899), opponent character C has a slightly lower rating (x ₃ = 1895), The rating was the same as opponent character B (x ₄ = 1899). At the end of the game, the scores of player A, opponent characters B, C, and D were y ₁ = 30100, y ₂ = 29900, y ₃ = 30000, and y ₄ = 10000, respectively.

(1) First, when calculating the deviation value a of each original rating,
(1-1) The average value x _μ of the ratings of four people is
x _μ = 1898.25
And
(1-2) The standard deviation x _σ of the rating of four people is
x _σ = 1.920286437
And
(1-3) Deviation values a ₁ to a ₄ of each person's rating are
a ₁ = 59.11322
a ₂ = 53.90567
a ₃ = 33.07544
a ₄ = 53.90567
It becomes.

(2) then calculating the deviation value b of each of the scores _{(y 1, y 2, y} 3, y 4),
(2-1) The average value y _μ of the scores of four people is
y _μ = 25000
And
(2-2) The standard deviation y _σ of the scores of four people is
y _σ = 8660.542708
And
(2-3) Deviation values b ₁ to b ₄ of each person's score are
b ₁ = 55.88878
b ₂ = 55.65784
b ₃ = 55.77331
b ₄ = 32.68007
It becomes.

(3) So the new rating is
X ₁ = 1896.776
X ₂ = 1900.752
X ₃ = 1917.698
X ₄ = 1877.774
It becomes.

The above contents are summarized in [Table 4]. As described above, in Example 4, the difference between the scores of player A and opponent character B is that player A who has a slightly higher rating wins opponent character B who has a slightly lower rating. If it is small, the rating is lowered. In other words, when playing against an opponent whose ability is antagonizing, if the score difference is small, the rating may be negative even in the first place. In other words, simply winning may not increase the rating, but may decrease.

  In Examples 1 to 4, a new rating is calculated using the original rating, the rating deviation value, and the score deviation value. However, instead of the score deviation value, a new score is used using a plurality of score element deviation values. An appropriate rating may be calculated. In this case, for example, each value of “the score at the end of the game”, “the number of times of transfer”, and “the number of times of lifting” is calculated as a score element based on the result of the battle, and is stored in the storage device 1. . Then, instead of the score deviation value in the first to fourth embodiments, the deviation value of each score element, that is, the deviation value of “the score at the end of the game”, the deviation value of “the number of times of transfer”, and the “number of rising times” Use the sum of the deviation values.

Specifically, as in the above-described embodiment, (1) the deviation value a of each original rating (rating before the battle: x1 _, x2 _, ..., _xn ) is calculated. Then (2) Each of the scores _{(y 1, y 2, ...} , y n) for each, the score regarding the m scoring Element deviation _{b 11, ..., b 1m,} b 21, ..., b 2m, b _{n1 to bnm} are calculated. And the following formula
X ₁ = x ₁ + (b ₁₁ +… + b _1m −a ₁ )
X ₂ = x ₂ + (b ₂₁ +… + b _2m −a ₂ )
:
X _n = x _n + (b _n1 +… + b _nm −a _n )
The value calculated by is used as a new rating (X _1, X _2, ... _, X _n ).

  Thereby, a more accurate rating is possible.

  In addition, when calculating a new rating using multiple score element deviation values, an even more accurate rating can be obtained by increasing the weight of a specific score element deviation value and lowering the weight of other score element deviation values. Is possible. This weight may be a value determined for each scoring element, or may change as the game progresses, and is set as appropriate.

Specifically, each of the score element deviation values b ₁₁ , ..., b _1m , b ₂₁ , ..., b _n1 , ..., b _nm is weighted (weight) w ₁₁ , ..., w _1m , w ₂₁ , ... , w _n1 ,..., w _nm are stored in the storage device 1. Then, similarly to the above-described embodiment, (1) the deviation value a of each original rating (pre-match rating: x _1, x _2, ..., X _n ) is calculated. Subsequently, (2) for each score (y _1, y _2, ... _, Y _n ), the score element deviation values b ₁₁ ,... B _1m , b _{21 ,.} Calculate _nm . And the following formula
X ₁ = x ₁ + (w ₁₁ × b ₁₁ +… + w _1m × b _1m −a ₁ )
X ₂ = x ₂ + (w ₂₁ × b ₂₁ +… + w ₂₁ × b _2m −a ₂ )
:
X _n = x _n + (w _nm × b _n1 +… + w _nm × b _nm −a _n )
The value calculated by is used as a new rating (X _1, X _2, ... _, X _n ).

  Examples 1 to 4 are ratings in a Mahjong game where four players play against each other. However, the present invention can also be applied to a game where less than four or five or more players play, for example, ratings in a racing game.

  Moreover, although Examples 1-4 were the battle | competition (so-called CPU battle | competition) of one player and three characters, this invention is not limited to such a CPU battle | competition, A some player is Internet etc. The present invention can be similarly applied to an interpersonal battle such as a network battle that competes via the network.

  As described above, according to the present invention, a rating can be calculated even in a game in which three or more players or characters that are virtual players play simultaneously. In addition, not only the results of each player or character's victory or defeat, but also the contents of the win (defeat or defeat or win or defeat with a small difference) can be added to calculate a new rating. It becomes possible to evaluate each player or character's ability more accurately and quickly. This avoids a situation where, for example, a player with high ability mistakenly has a low rating (that is, a low rating), the player feels dissatisfied with the rating, and eventually loses interest in the game itself. Can do.

The block diagram which shows an example of a function structure of the rating calculation apparatus in embodiment of this invention. The figure which shows an example of the flow of the rating calculation process in embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Memory | storage device 2 ... Input device 3 ... Display apparatus 4 ... CPU

Claims (5)

Computer
storage means for storing n ratings and n scores;
A rating deviation value a _k is calculated for the k-th rating x _k out of the n ratings, and a score deviation value b _k is calculated for the score P _k corresponding to the rating x _k . Means for calculating a new rating X _k ,
A rating program characterized by functioning as
X _k = x _k + (b _k −a _k ) (I)
(However, n is a natural number of 2 or more, and k is a natural number of 1 or more and n or less.) The storage means stores m score elements for each of the n scores.
The calculation means calculates score element deviation values b _k1 ,..., B _km for each of the first to m-th score elements of the score P _k and calculates a new rating X _{k according} to the following formula (II). The rating program according to claim 1.
X _k = x _k + (b _k1 +… + b _km −a _k ) (II)
(However, n is a natural number of 2 or more, k is a natural number of 1 or more and n or less, and m is a natural number of 2 or more.) Said storage means, said scoring element deviation b _k1, ..., each of the weighting of b _miles w _k1, ..., stores w _miles,
The rating program according to claim 2, wherein the calculation means calculates a new rating X _k by the following formula (III).
X _k = x _k + (w _k1 × b _k1 +… + w _km × b _km −a _k ) (III) memorize n ratings and n scores,
A rating deviation value a _k is calculated for the k-th rating x _k of the n ratings,
A score deviation value b _k is calculated for the score P _k corresponding to the rating x _k ;
A rating method characterized by calculating a new k-th rating X _k by the following formula (I).
X _k = x _k + (b _k −a _k ) (I)
(However, n is a natural number of 2 or more, and k is a natural number of 1 or more and n or less.) storage means for storing n ratings and n scores;
A rating deviation value a _k is calculated for the k-th rating x _k out of the n ratings, and a score deviation value b _k is calculated for the score P _k corresponding to the rating x _k . Means for calculating a new rating X _k ,
A rating device comprising:
X _k = x _k + (b _k −a _k ) (I)
(However, n is a natural number of 2 or more, and k is a natural number of 1 or more and n or less.)

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