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 next World Cup, in Germany (2006), head-to-head results take precedence over results in all group matches (as in the European Championship). Teams level on points in each first round group will 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 will 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 will 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 will feature in the revised ranking rules for the group stage of the next World Cup.

But, believe it or not, I have even written a fairly complicated computer program myself that makes thousands of simulations of the 32-team, 8-group, post-draw 1998 World Cup and tallies the number of times a 2-way, 3-way or even 4-way lottery draw is required in any of the 8 groups (if there is a 3-way 'lots' in one group and a 2-way 'lots' in another, only the higher tie, in this case the 3-way, is counted, so the 'Total' row is for any kind of tie). After thoroughly checking for errors as far as I could and correcting them, I ran the program for 100,000 World Cups using both the old ranking rules and the new, and found the following results:

Lottery         Old             New           Percentage
draw*          rules            rules           increase

2-way          11,731           12,649            7.8
3-way              89              131           47.2
4-way              32               32            0.0

Total          11,852           12,812            8.1

* in at least one group.

The above results mean that under the new rules, a drawing of lots (in at least one group) would be required once in every 7.81 World Cups (on average) instead of once in every 8.44 under the old rules - an 8% greater likelihood. However, a three-way lottery draw (in any group) would be around 50% more common using the new rules - once in every 750 World Cups as against once in every 1,100 - 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!!!).

[How the computer program works: Each of the 32 teams in the 1998 World Cup has been given a 'strength factor' estimated by the use of 'spread-betting' prediction data (e.g. based on 1st in group=25 pts, 2nd=10, 3rd=5, 4th=0) and trial and error in related computer programs. For example, in England's Group G, the strength factors were as follows, England 826, Romania 681, Colombia 578 and Tunisia 463. In the England-Romania game, the probability that England will score a goal in a given tenth of the game (period of 9 minutes) is 0.1215*826/681 and likewise for Romania 0.1215*681/826, since my estimated average number of goals per game in that World Cup was 0.1215*20 (= 2.43) in matches where the two teams involved have similar strength (the asterisk denotes the 'times' sign). By making thousands of simulations for each group (and, for example, awarding 25, 10, 5 and 0 pts respectively to teams finishing top, 2nd, 3rd and 4th in their group and calculating average scores), these strength factors are designed (with the aid of a suitable mathematical formula) to produce the best fit between these average scores and the relevant data from 'spread-betting' bookmakers (in England's 1998 Group G, the predicted group scores were England 16, Romania 13, Colombia 7.5 and Tunisia 2.5)]

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.

About this document

Prepared and maintained by Christopher Bird for the Rec.Sport.Soccer Statistics Foundation

Author: Christopher Bird (
Last updated: 21 Aug 2004

(C) Copyright Christopher Bird and RSSSF 2004
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