Increased Likelihood of Drawing Lots at World Cup
In the World Cups from 1974 to 2002, teams level on points in each first round group were ranked according to the following criteria:
a) Goal difference in all group matches.
b) Goals scored in all group matches.
c) Points obtained in matches between the deadlocked teams in question.
d) Goal difference in matches between the teams in question.
e) Goals scored in matches between the teams in question.
f) Drawing of lots.
But for the 2006 World Cup (in Germany), FIFA (the football governing body) had amended the competition regulations so that head-to-head results would take precedence over results in all group matches (as in the European Championship). Teams level on points in each first round group would be separated according to the following criteria:
a) Points obtained in matches between the teams in question.
b) Goal difference in matches between the teams in question.
c) Goals scored in matches between the teams in question.
d) Goal difference in all group matches.
e) Goals scored in all group matches.
f) Drawing of lots.
Unlike the European Championship, when teams are level according to all of the above criteria (points and a-e), the World Cup would then go straight to ‘lots’ without considering innovations such as qualifying or seeding ‘coefficient’, fair play quotient or even a penalty shoot-out at the end of the final group game. (If two teams completely level are third and fourth in their group, no ‘lots’ are necessary – they would just be given equal third place.)
The possibility of penalty shoot-outs at the end of the final group game is now available in three Continental championships – European, South American and Asian – as well as the Olympic football tournament. I am in favour of penalty shoot-outs between deadlocked teams at the end of the group phase even if the teams concerned are in different final group matches since the goalkeepers can be helicoptered over to the other game being played simultaneously and giant video screens can show them attempt to save their opponents’ penalties at the other game! In addition, deadlocked teams in the European Championship and the Olympic football tournament can now be separated by fair play quotient. But despite these ‘improvements’, neither penalty shoot-outs nor fair play would feature in the revised ranking rules for the group stage of the 2006 World Cup.
Amazingly, I have even written a fairly complicated computer program myself that makes thousands of simulations of the 32-team, 8-group, post-draw 2006 World Cup and tallies the number of times a 2-way, 3-way or even 4-way lottery draw is required in each of the 8 groups. After thoroughly checking for errors as far as I could and correcting them, I managed to run the program for 1,000,000 World Cups using both the old ranking rules and the new (with each simulation), and found the following results:
Table 1: Number of lottery draws under Old Rules.
Group Type of lottery draw Total
2-way 3-way 4-way
A 15,828 128 38 15,994
B 15,299 106 15 15,420
C 19,764 142 45 19,951
D 17,881 149 49 18,079
E 18,619 179 46 18,844
F 14,980 134 33 15,147
G 17,772 155 51 17,978
H 16,897 126 30 17,053
Total 137,040 1,119 307 138,466
Table 2: Number of lottery draws under New Rules.
Group Type of lottery draw Total
2-way 3-way 4-way
A 17,336 189 38 17,563
B 16,485 129 15 16,629
C 21,719 230 45 21,994
D 19,479 214 49 19,742
E 20,472 274 46 20,792
F 16,241 175 33 16,449
G 19,573 262 51 19,886
H 18,451 184 30 18,665
Total 149,756 1,657 307 151,720
Table 3: Percentage increase of lottery draws.
Group Type of lottery draw Total
2-way 3-way 4-way
A 9.5 47.7 0.0 9.8
B 7.8 21.7 0.0 7.8
C 9.9 62.0 0.0 10.2
D 8.9 43.6 0.0 9.2
E 10.0 53.1 0.0 10.3
F 8.4 30.6 0.0 8.6
G 10.1 69.0 0.0 10.6
H 9.2 46.0 0.0 9.5
Total 9.3 48.1 0.0 9.6
The above results mean that under the new rules, a drawing of lots would be required once in every 6.59 World Cups (on average) instead of once in every 7.22 under the old rules – an almost 10% greater likelihood. However, a three-way lottery draw would be around 50% more common using the new rules – once in every 600 World Cups as against once in every 900 – though the chances of all four teams in a group finishing the group stage completely level on points, goal difference and goals scored would remain unaltered (at once in every 3,000 to 3,500 World Cups – this is what exactly would have happened to England’s Group F in the 1990 World Cup if Egypt had equalised against England, for example, with a late penalty!!!). Pretty obviously, a lottery draw is considerably more likely in a ‘Group of Death’ (e.g. Group C in the above tables) than in the group containing the rank outsider (e.g. Group B in the above tables).
How the computer program works:-
Each of the 32 teams in the 2006 World Cup has been given a ‘strength factor’ estimated by the average odds of winning the World Cup of bookmakers that gave reliable prices on the Oddschecker website (www.oddschecker.com). The strength factor (S) for each team has been calculated using the formula S = K(B/AC)^0.14, where A is the average odds on the day before the finals draw (8 Dec 2005), B is the average odds on the day after the draw (10 Dec 2005), C is the latest average odds (calculated on 16 May 2006) and K is a constant in order to give the favourites (Brazil) an index of 1,000. (AC/B gives the closest estimate of what the World Cup odds would have been if the finals draw had not yet taken place – this gives an indication of the relative strength of the team.) For example, in England’s Group B, the strength factors are as follows, England 855, Paraguay 576, Trinidad and Tobago 432 and Sweden 683. In the England-Sweden game, the probability that England will score a goal in a given 10-minute period is 0.135*855/683 and likewise for Sweden 0.135*683/855, since my estimated average number of goals per game in the 2006 World Cup is 0.135*18 (= 2.43) in matches where the two teams involved have similar strength (the asterisk denotes the ‘times’ sign, as used in computer terminology). I have verified this program by making thousands of simulations and awarding ‘group’ scores (25, 10, 5 and 0 pts respectively for finishing top, 2nd, 3rd and 4th in their group) and ‘outright’ scores (for reaching a certain round of the tournament), and checking the averages of these against relevant data from ‘spread-betting’ bookmakers. I also counted the number of outright wins and checked the probabilities of each team winning the Cup against the 1/(C+1) values (which tend to be much greater than the true odds for the weakest teams). After much trial and error experimenting with the ‘strength’ formula, I decided on S = K(B/AC)^0.14 for the program.
A lottery draw is significantly more likely under the new ranking rules, possibly because when three teams in a group are level on points and two of these level also on goal difference and goals scored in all group matches, those two are more likely to be level on the basis of matches between the three teams level on points than them to have drawn the match between them. Also, when all four teams are level on points – as happened to Group E in the 1994 World Cup – matches between any teams level also on goal difference and goals scored are no longer taken into account and they would go straight to ‘lots’ instead. The 50% greater chance of a 3-way lottery draw is attributed to the fact that it is much more likely when all four teams in a group are level on points.
Another disadvantage of head-to-head results of teams level on points being made more important than results in all group matches is that when there are three teams level on points, those three might quite possibly have drawn all their matches between them and then the next consideration would then be the number of goals scored in the ‘mini-group’ between the three teams in question. Italy’s Group C in Euro 2004 has provided a classic example of this and Italy’s 0-0 and 1-1 draws against Denmark and Sweden respectively (who both beat Bulgaria) has meant that a 2-2 or higher scoring draw between the Scandinavians in their final group match would put Italy out of the next stage of the competition regardless of their result against Bulgaria, and there might be accusations of ‘match-fixing’. (In the event, Sweden and Denmark did draw 2-2 but their game had been nothing like the West Germany v Austria debacle of the 1982 World Cup. Italy, on the other hand, only managed to beat Bulgaria by one goal.) If Group C in Euro 2004 had been determined by the old World Cup rules, a 3-goal winning margin in the last group game would have guaranteed Italy a place in the next stage.
In conclusion, I think the old ranking rules are better because they are both fairer and easier to understand than the new – less chance of teams being eliminated by either ‘lots’ or simply a high scoring draw between two other teams in their final group game. The old rules were familiar to those following the domestic league tables in the English Premiership and Football League (ranked by points, then overall goal difference, then overall goals scored). On the other hand, the new rules are much more complicated to the ordinary fan. When three teams finish level on points – a scenario not uncommon in football – one has to draw up a new league table (excluding the team with the different number of points). Though the old system used head-to-head results only as a last resort short of ‘lots’, these will not even be used in the event of all four teams finishing level on points – a lottery draw is much more likely in this scenario, even if it decides the positions of three teams rather than two.
Thankfully, FIFA has now reinstated the old ranking rules for the 2006 World Cup so that the previous system of separating teams at the end of the first round group stage applies – that is, teams level on points in each group will be ranked according to the following criteria:
a) Goal difference in all group matches.
b) Goals scored in all group matches.
c) Points obtained in matches between the deadlocked teams in question.
d) Goal difference in matches between the teams in question.
e) Goals scored in matches between the teams in question.
f) Drawing of lots.
Author of page: Chris Bird
Date completed: 27 May 2006