Point system

Many times in powerful closed chess tournament with double meetings the system of points (3-1-0) is applied eg. Bilbao 2008 until 2011 and is the usual reason of discussions for whether is fair the relation of victory with the draw. Previous experience also exists from the football that roughly twenty years ago changed the point system from (2-1-0) in (3-1-0). Before this change the average probability for each result 1-X-2 was 0,5-0,3-0,2 and afterwards the change it became 0,5-0,2-0,3, that is to say "woke up the guest". The change surely did not become based on the average probability of each result, because for the average probability that the home has to win, the 3 points are excessive, but the championships they are carried out with double meetings.

With the (3-1-0) system in the double meetings two opponents can agree a victory and a defeat for each and both take 3 points. Two others if they have made a played draw, then one of them wins the second game takes in total 4 points. If the second game end also draw then finally both opponents take 2 points! Something more reasonable that is applied in multiple games of opponents or meeting of teams, it is if the sums of points at both sides is same, the result is draw, otherwise the victory corresponds in the bigger sum. In tournaments with simple meetings three “opponents” are needed and each one of them loses from the one and wins the other "opponent" so all the three “opponents” make 3 points.

Each result in a game has her own average probability. Αverage probability ιs reported because is altered in combination with profit, difference or the capacity of players since also them has variable output. For the fair points in a game, the average probability multipled by the profit should be the same for each result (can also be roughly the same, because of breadth of solutions). ex.

Result              | 1-0 | 1/2 | 0-1 |    | 1-0 | 1/2 | 0-1 |

Average probability | 0,3 | 0,5 | 0,2 |    | 0,3 | 0,45| 0,25|

Profit              |  10 |   6 |  15 |    |  15 |  10 |  18 |

Expected value      |   3 |   3 |   3 |    | 4,5 | 4,5 | 4,5 |

Does exist system of points for the all levels of capacity that would have fair relation of points with the result and it mainly decreases the without battle draws? Various other metres or rules that face the causes of the short or all draws, concern bigger base of discussion but in the present it becomes report only in the points of played games.

In most systems of points the draw takes one point and the defeat no one. The points of victory are calculated if is determined her relation with the draw.

The system (2-1-0) (average probability 0,5 victory, 0,5 draw) considers that 2 victories = 4 draws.
The system (3-1-0) (average probability 0,4 victory, 0,6 draw) considers that 2 victories = 6 draws.

In big sample of played games of roughly equivalent powerful players, the statistical elements can indicate a system of points. In the overwhelming majority however the games became with system (2-1-0).

The truth can find somewhere in the middle that is to say 2 victories = 5 draws and thus result a intermediary system (5-2-0) (medium probability 0,444 victory, 0,555 draw) precisely in the middle between two mentioning before.

In this are in effect the inequalities:
2 draws  < 1 victory  < 3 draws
the truth of that appears very near the reality. This relation helps the comparison of sums of results.

Apart from the probabilities it is also examined if the players are fighting to succes the result. In a lot of sports for if and how the players are fighting exist also technical sentences and disapprovals of spectators and much more badly.

In even number of games the player that makes the half victories and the half defeats, sure dedicates time and labour in the all games. This can be considered bigger than if he makes them all draws because at least one of all can become in enough cases with null until minimal effort (agreement fast or that it does not involve from the position, known or necessarily triple repetition in the opening, moves of theory multiple rests moves, from the opening in simple final etc). Thus the player relax and has time of preparation for the next round or avoids game with blacks etc. In the case of stalemate, where it is usually escape from very unfavourable position, the one that did not have legal moves (centuries) older was lost, now in tie he is not calculated if he had the disadvantage or the advantage. Fortunately however the case of stalemate except that it happens in minimal percentage of games, the half probabilities would be in favour the player and other half against the player.

However any value that the victory has from 2,1 up to the 2,9 (step 0,1) the final ranking remains the same. In value 3,0 the final ranking is globally differentiated little, but afterwards the first places of ranking. ex. 9 and 11 rounds:

| SN | W D L | x2 | x2,5 | x3 |  | SN |  W D L | x2 | x2,5 | x3 |

|  1 | 9 0 0 | 18 | 22,5 | 27 |  |  1 | 11 0 0 | 22 | 27,5 | 33 |

|  2 | 8 1 0 | 17 | 21,0 | 25 |  |  2 | 10 1 0 | 21 | 26,0 | 31 |

|  3 | 8 0 1 | 16 | 20,0 | 24 |  |  3 | 10 0 1 | 20 | 25,0 | 30 |

|  4 | 7 2 0 | 16 | 19,5 | 23 |  |  4 |  9 2 0 | 20 | 24,5 | 29 |

|  5 | 7 1 1 | 15 | 18,5 | 22 |  |  5 |  9 1 1 | 19 | 23,5 | 28 |

|  6 | 6 3 0 | 15 | 18,0 | 21 |  |  6 |  8 3 0 | 19 | 23,0 | 27 |

|  7 | 7 0 2 | 14 | 17,5 | 21 |  |  7 |  9 0 2 | 18 | 22,5 | 27 |

|  8 | 6 2 1 | 14 | 17,0 | 20 |  |  8 |  8 2 1 | 18 | 22,0 | 26 |

|  9 | 5 4 0 | 14 | 16,5 | 19 |  |  9 |  7 4 0 | 18 | 21,5 | 25 |

| 10 | 6 1 2 | 13 | 16,0 | 19 |  | 10 |  8 1 2 | 17 | 21,0 | 25 |

| 11 | 5 3 1 | 13 | 15,5 | 18 |  | 11 |  7 3 1 | 17 | 20,5 | 24 |

| .. | . . . | .. | .... | .. |  | .. |  . . . | .. | .... | .. |

| 55 | 0 0 9 |  0 |  0,0 |  0 |  | 78 | 0 0 11 |  0 |  0,0 |  0 |

In columns SN if the rounds are n, the count of different total points is (n+1) * (n+2) /2.
In columns "W D L" they are the victories, the draws and the defeats, essential they are presented with the points.
The point groups in swiss system of draw they can become with not only with the points but also the number of victories or draws proportionally who is criterion of tie. Similar possibilities exist already in programs of draw where only for the draw the ranking is considered with various ways.
In columns x2 where it exists tie then is used the criterion of number of victories (1 victory  > 2 draws).
In columns x2,5 does not exist tie in the first places only that in very few cases in following places.
In columns x3 where the tie exists the criterion that is used is the number of draws (3 draws  > 1 victory).

The ranking with system (2-1-0) with first criterion number of victories is exactly the same with system (5-2-0) with first criterion the number of draws. Thus does not exist reason of differentiation from system (2-1-0), but simply can set as first criterion the number of victories. Absolute tie is considered when somebody makes the same number of victories and draws with another. The rewards can be shared equally after the criterion of number of victories.

In system (2-1-0) in high level of players the victory is not rewarded well in combination with her average probability because the most likely result is the draw. Consequence of this is the player in last two rounds if it needs one point, it prefers for sure two draws from to play at least for a victory. Also a player in ambivalent position does not undertake the danger to lose, if the victory does not deserve something more.

In system (3-1-0) the one point of draw resembles with defeat and the victory is rewarded too much in combination with her average probability unless is very high the level of players. In lower level it focuses in the fighting spirit of players, despite in the right of points because the final ranking is not differentiated and a lot from that with system (2-1-0). It is very likely when it is applied become different statistical results for the game. It has repercussions in the calculation of ELO that is other chapter.

The priority of criteria of equivalence in points

In order the tournaments are with more quality a parameter is if are shared the rewards in case of tie. The proclamations refer in the criteria of tie which can be analyzed many days. Some small details (as what it becomes with the points without game) in the criteria of tie can they correspond in high pecuniary rewards. With various criteria, the rewards could be not shared but the players would find way to be shared.

Most criteria have relation with the draw, that is to say who similar opponents happened, with who similar order they happened, oh which colours happened. Usually those that they tied on certain criteria depend from the results of their few opponents and on other criteria have also very small differences. The importance of difference in these criteria, does not justify the priority against the number of victories (draws). The criterion of number of victories (draws) has absolute priority only in round robin tournaments because it is direct related with the system of points and the results of player. The points are afterwards compared real first and after the other criteria are compared.

Usually the first criterion is the points between the tied players. In this criterion does not taken into account the colours which in high level is important. It is strange to have a priority that supersedes in this criterion, while has less points against the other no tied opponents, which usually is much larger sample of games. It can happen in a tournament of 7 rounds in the last round the first with 6 points (6 wins) and his opponent as second with five points (four wins and two draws). It is very likely the player with 6 wins, except the most wins maybe has and other better criteria, but if he will lose the game, he will lose the first place.

In a lot of international tournaments are reported in the proclamation the criteria of tie for swiss system and "are repeated" also in proclamations of other local tournaments ex.
a) Direct encounter.
b) Sum of progressive score (and fine criteria).
c) The criterion Boucholtz (sum points of opponents)
d) The criterion Sonneborn-Berger (sum points of opponents depending on the result).
e) Greater number of victories.
But if it is applied completely the (b) and is not raised the tie means that tied they have the same results in the same rounds. Thus from the erroneous priority it involves that the criterion of number of victories (e) not needed.

The criterion of progressive score in many times is contrary to greater number of victories ex.

1.| 1 1 1 1 1 1 1 ½ ½ | 8 | 43,5

2.| 1 1 1 1 1 1 1 0 1 | 8 | 43,0

3.| 1 1 1 1 1 ½ ½ ½ ½ | 7 | 40,0

4.| 1 1 1 1 1 0 1 0 1 | 7 | 39,0

5.| 1 1 1 ½ ½ ½ ½ ½ ½ | 6 | 34,5

6.| 1 1 1 0 1 0 1 0 1 | 6 | 33,0

In the draw becomes a lot of reason for colours while in the criteria of equivalence in grade is not given the proportional importance in tournament powerful players.

Usually the criterion "more blacks" if it exists, is found below by other more lucky criteria ex. In two types of tie with 8 points can be the same progressive score as follows:

Α) 1 1 1 ½ 1 ½ 1 1 1 = 8 (40)

Β) 1 1 1 1 0 1 1 1 1 = 8 (40)

The phenomenon the three successive (in example 4,5,6) rounds can happen in anyone round. When is applied the sum of progressive score (and the criteria of lifting) in the B) case the player while it appears sure that he fights, unfortunately flawed on the criteria.

The criterion sum of the scores of opponents (Buchholz) it not remove the tie if the players have played the same opponents. The criterion sum of the scores of opponents depending on the result (Berger) it not remove the tie if the players have played the same opponents and have had the same result with each. But the criterion of the progressive score can present them unfairly with huge difference:

A) 1 1 1 1 1 1 1 1 0 = 8 (44)

B) 0 1 1 1 1 1 1 1 1 = 8 (36)

The criterion progressive score sum can be calculated before the last round and this helps some of the pioneers to "set up" the final ranking.

When all the criteria fail then there is the draw as criterion of tie. The players dont like it but the criterion has the advantage that it can be unique and reverse the tie 100%. Instead of using any way of draw for the ranking in swiss system can become the following: The tied that can be several, they are ranking according to the draw of next round and in priority the white in smaller table number wins. The program of draw for the pairs can make also the draw for the ranking that also are tied.

Because the subjects are complex and because exist also points that do not emanate from played games, that it was written and has any resemblance with the reality of game it can be completely coincidental! Somebody can play for amusement in the internet or friendly games without it measures points!

28-9-2012

Result depending on the ELO difference
Sample 3500000 games

ELO white‑black less than	probability %
	white wins	draw	black wins
-700	3	7	90
-650	4	9	87
-600	5	11	84
-550	6	12	82
-500	8	14	78
-450	9	17	74
-400	10	20	70
-350	13	23	64
-300	14	28	58
-250	17	32	51
-200	21	37	42
-150	24	42	34
-100	29	44	27
50	36	42	22
100	45	37	18
150	53	32	15
200	61	26	13
250	67	22	11
300	71	19	10
350	76	15	9
400	80	12	8
450	83	10	7
500	85	9	6
550	87	8	5
600	89	7	4
650	91	6	3
700	93	5	2

 

6-4-2016