A fragment of the book

rating in the sport: yesterday, today and tomorrow / A.A.Polozov. – Moscow: Soviet sport, 2007 – 316s.

Sport was among the first life spheres where ratings appeared. Moreover, ratings in sports managed to come to a more formal level in comparison with economics and sociology, where expert assessments have traditionally played a special role. For instance, in public life the percentage of votes cast for the politician in the election has nearly always been considered his/her rating, whereas the citation frequency of publications in the printed matter has been considered a rating of an academic researcher, and so on. As far as sport is concerned, from the very start of the team sports competitions there existed a simple rating system in the form of scoring the winner of the match. However, here are some variations as well: the level of achievements in the Champions League or the number of wins in the Club National Championship can be added to the ranking of a football team due to the variety of tournaments conducted.
People have been competing with each other since ancient times. The desire to be cut above the rest, to outrun everybody, and the struggle for leadership in general – all this has been bred in the bone of every representative of the menfolk and reflected the spirit of the warrior and the hunter. The person who defeated more enemies in the battles between the tribes was considered the best warrior and was given honours and advantages in splitting the spoils. The best hunter had the right to be the first to take the share of kill, etc.
Later, people invented sports in which warriors and hunters were able to measure strength with each other not in a real battle with the enemy or in the fight with a wild animal, but by matching their skills, strength and agility in special exercises, which had earlier served just for practising martial arts or hunting, and by participating in conventional doubles or group fightings as well.
The rating problem in sports appeared after the number of competitors increased and the existing competition forms did not allow for their consistent ranking. There emerged a necessity for conducting international competitions, where dozens of millions of athletes or teams would participate. However, it is impossible to hold such a competition using round-robin system, because it may last longer than life. Thus, at the moment there emerged a necessity for conducting a global macrotournament in the system of sporting contests. However, the procedure of conducting it requires some clarification. This problem needs to be solved, but reaching consensus on the form of such a macrotournament appears to be problematic due to the large number of participants.
“Plus-minus” (an efficiency statistic), reflects the difference between the team’s total scoring versus their opponent’s, for each of those players on the ice both scoring and allowing the goal. This parameter does not apply to goaltenders. When an even-strength goal or shorthanded goal is scored (penalty shot goals are not counted), the plus–minus statistic is increased by one (“plus”) for those players on the ice for the team scoring the goal. The “Montreal Canadiens” were the first team to track the plus−minus of its players, starting sometime in the 1950s. Other teams followed in the early 1960s, and the NHL started officially compiling the statistic in 1968. While a famous player and coach Emile Francis is often credited with devising the system, he only popularized and somehow adapted the system invented in Montreal. The statistic is influenced by both the offensive and defensive performance of the team as a whole – you will get different statistics depending on whether you place a player in the 4th line of the “weakest” club or in the 1st line of the strongest club of the Kontinental Hockey League (KHL).

The method of determining the tournament results is described in the regulations. However, I would like to dwell on this point due to the large number of questions about what rating is and how it is calculated.
The number of points received by the team is considered to be the basic criterion for assessing its success in the tournament. The team gets 1 point for each correct answer. Thus, the number of correct answers is the number of points. There are often situations when several teams receive the same number of points by the end of the tournament. In this case, the standings are distributed according to the rating.
A rating is an auxiliary option, which takes into account the difficulty of the questions asked. There are two types of rating: the rating of the question and the rating of the team. The rating of the question is the number of teams that gave an incorrect answer to the question. The rating of the team is equal to the sum of the ratings of the questions correctly answered by this team.
Let’s illustrate this with an example. Let us assume that 5 teams participate in the tournament and 10 questions were asked.
Table 6.3. The standings are as follows:
Question No. 1 2 3 4 5 6 7 8 9 10 Points Rating Place
Team 1 + + – + – – + + + + 7 13 1
Team 2 – + + + + – – + – – 5 9 3
Team 3 – + + – – – + – + – 4 6 5
Team 4 + + – + – – + – + – 5 7 4
Team 5 – + – + + + – + + – 6 11 2
Rating of the question 3 0 3 1 3 4 2 2 1 4
The “+” sign indicates a correct answer, and the “-” sign indicates a wrong answer
As it can be seen from the table, teams No.2 and No.4 got the same number of points. In this case, we must consider rating.
Three teams gave a wrong answer to the first question (there are three “-” signs in column 1), that is why its rating is equal to 3. All teams answered the second question correctly, and its rating is equal to 0. Three wrong answers were given to the third question, its rating being equal to 3. And so on, and so forth.
After that the ratings of teams are defined. Team 1 gave a correct answer to the questions number 1, 2, 4, 7, 8, 9, and 10. Thus, their rating is equal to 3+0+1+2+2+1+4 = 13. The second team gave a correct answer to the questions number 2, 3, 4, 5 and 8, and their rating is equal to 0+3+1+3+2 = 9, respectively. Similarly for the third team the rating is equal to 0+3+2+1 = 6, and for teams 4 and 5 the ratings are equal to 3+0+1+2+1 = 7 and 0+1+3+4+2+1 = 11 respectively.
Thus, the standings in our hypothetical tournament have been distributed as shown in the “Place” column.
The “point-rating” system was developed more than 10 years ago, was successfully tested in many tournaments for children and adults in many cities, and is widely used nowadays. It is convenient because the difficulty of the question is determined, firstly, for the playing teams, and, secondly, automatically. Such an approach allows you to more accurately define the standings of the teams in accordance with their playing strength.

The O’Neill Rankings for Olympic Classes adopted by ISAF were taken as a basis for the suggested technique. Taking part in regattas, an athlete gets points which are summarised to calculate the actual rankings. FIVE best results for the previous calendar year are summarised for each of the participants. The formula for calculating the regatta ranking points will be P=RxFxQxY.
Where P stands for bonus points, and R stands for the points received for the place taken in the regatta. The first place is credited with 100 points; the second one is credited with 99 points, and so on. Only the first 100 participants receive points for participation. F is a significance factor. Each regatta is assigned a certain level of significancefor athletes starting from 1 up to 5, the first level being assigned to the regattas of the highest level. The significance of the regatta should be determined by some panel.
Table 6.4. Factors
Level of significance Value of F factor Proportion of participants receiving points
1 5 The first 80%
2 4 The first 80%
3 3 The first 60%
4 2 The first 40%
5 1 The first 20%
It is obvious that the official National Championships must have a significance factor higher than all other regattas, no matter how popular and representative they are. The F factor is determined depending on the level of the regatta significance. In addition, the significance of the regatta is also determined by the proportion of the regatta participants, who will receive ranking points for participation. Q is the factor of representativeness. A factor of representativeness, “Q”, is assigned to each regatta. It is calculated after the regatta ends, on the basis of the number of the regatta participants that ranked among the first thirty before the regatta started. Q is defined by the formula Q = 1 + n/30, where n is the number of participants who ranked among the top 30 before the regatta started. Q must be in the range of 1.0 – 1.5. For the official national championships Q is always equal to 1.5. Y is the annual factor. For the results of the current calendar year (the previous 12 months) the annual factor Y is equal to 1. So the ranking points are calculated for each of the participants for all the regattas in which they participated, and seven largest values are summarised The participant with the highest number of points takes the first place in the ranking.

First published in August 1993 by the FIFA and the Coca-Cola Company, the FIFA / Coca-Cola World Ranking is a monthly status list of the world’s current senior national teams. At the moment, the ranking concerns about 180 teams (on the whole FIFA involves 203 national associations).
The ranking takes into account the results of all international matches over the past eight years: the World Cup finals matches, the World Cup qualification matches, the final matches of the continental championships, the qualification matches of the continental championships, the FIFA Confederations Cup matches, and the friendly matches.
The ranking list is the result of calculations made by a computer programme that calculates the team points for each match, according to clearly defined criteria. The following values are taken into account:
1. Result (win, draw or defeat)
2. Number of goals scored or conceded
3. Venue of the match (whether it was played at home or away)
4. Importance of the match (multiplication factor)
5. Opponents’ strength
6. Regional strength (multiplication factor)
The basic idea underlying the FIFA / Coca-Cola Ranking is the same as for an ordinary championship: depending on the result, the team gains a certain number of points in each match. The number of the points gained is calculated, and the teams are placed in descending order of the number of the points gained. A win over a weaker opponent will bring fewer points than a win over an equal or a stronger one. Thus, there appears an incentive for a weaker team that can gain points in the match against the stronger opponent even in case of defeat.
The next factor taken into account is the number of scored and conceded goals during the match. The distribution of these points depends on the relative strengths of the opponents team. In other words, the goal scored by the weaker team will mean more than a goal scored to it by a stronger opponent. On the other hand, the points are deducted for the conceded goals. The conceded balls have a smaller value than the scored ones in order to encourage the attack. In order to take account of additional difficulties connected with the away match, the guest team is given a small bonus of 3 points. No points are given for the matches that are played on neutral ground or for the World Cup finals.
The importance of the game is also taken into account. The most significant are the World Cup matches, and the lowest weighted are the friendly matches. The method used for this purpose
Table 6.7.FIFA / Coca-Cola factors
Match status Factor
Friendly match 1.00
Continental Championships qualifying matches 1.50
World Cup qualifying matches 1.50
Continental Championships finals 1.75
World Cup Finals 2.00

is to use a factor that is multiplied by a total number of points of the given match. This means that the qualifying matches “weigh” 50% higher than the match between the teams of Uzbekistan and Turkmenistan, the continental finals weigh 75% higher, and the World Cup finals finals weigh twice as high, respectively.
With the account of the abovementioned considerations, the total number of points given to the team after the match will depend on the following criteria:
1. Points for the result (win, draw or defeat)
2. Plus points for the goals, scored in a match
3. Minus points for the goals, conceded in a match
4. Plus bonus for the guest team
5. Multiplication by a factor that takes into account the match status
6. Multiplication by a factor that takes into account the regional strength
The number of points for a win, a draw, or a defeat, and for the ratio between the scored and conceded goals as well, depends on the opponent strength. In order not to punish the team for the lack of success too strictly, a negative total of points is rounded to 0.00.
Some actual examples should help to make methods from the clear calculation. In this case, three teams of different strength are involved in a small friendly tournament on neutral ground. For the sake of clarity, neither guest team bonus, nor continental and status multiplication factors are applied.
Before the tournament, these three teams have the following total numbers of points:
Team A: – 630 points: Team B: – 500 points: Team C: – 480 points
Thus, Team A,the strongest of all three, is somehow distanced from the other two teams B and C, whose strengths are approximately equal. The following table shows the distribution of points for three possible results of match between the strongest team A, and the weaker team B:
Table 6.8. Practical example
Score 3 : 1 1 : 3 2 : 2
Team A B A B A B
Points for the result +17.4 +2.6 -2.6 +22.6 +7.4 +12.6
Points for goals A +5.4 -3.6 +2.3 -1.6 +4.1 -2.7
Points for goals B -1.8 +2.7 -4.1 +6.2 -3.1 +4.7
Total points +21.0 +1.7 (0.00) +27.2 +8.4 +14.6
From the table it can be seen that in case of a 3:1 win, the team gets the total number of 21.0 points. But as it is a stronger team, their winning brings them directly only 17.4 of this amount. A weaker team B still earn 1.7 points. If the “weaker” Team B won the match 3 goals to 1, they would get 27.4 points, while the negative result for the team A just “returns to zero”. In case of a draw (2:2), team B as a weaker one, gets a bit more points than the team A, which is the stronger team.
We offer some excerpts from the articles written by the famous people, these excerpts describing their attitude to the problem of rating and ranking. All the articles are given in abridged form.