When Yerry Mina nodded Colombia ahead in the 74th minute of their match against Senegal, an unprecedented situation was on the cards. Japan and Senegal were tied for 2nd place in Group H with 4 points. Both teams had scored 3 goals and conceded 3 goals. Furthermore, when the two teams met on Match Day 2, they tied 1-1. Never before had a team been sent home at a World Cup after tying with another team on Points, Goal Difference, Goals Scored and Head to Head. Since Senegal had two more yellow cards than Japan (a tiebreaker that was only introduced at this World Cup), they were eliminated and Japan advanced to face Belgium in the Round of 16 on Monday. Only once before had a tie been broken after these conventional tiebreakers; in 1990 the Republic of Ireland and the Netherlands drew lots to determine which team would advance in second place, and which team would advance in third place.
It seemed odd to me that this occurrence was so infrequent. After all, the World Cup group stage is only 3 matches so the possibility of two teams tying with the same number of points is quite high. Soccer is a very low scoring game, so the chances of two teams finishing with the same number of goals scored and against also should not be that low. In addition, approximately 25% of soccer matches end in ties, so the head to head tiebreaker will rarely separate teams that have already tied on points (the only recent example of this tiebreaker being applied was in Euro 2012 when Greece advanced by virtue of beating Russia). So why is it that this was the first time in 28 years that we have resorted to unconventional methods? How often should we have expected this to happen? Was this super unexpected, or were we waiting on borrowed time before this happened? I wanted to try to answer these questions.
To go about answering this, I decided to model the results of every World Cup group since 1998 to calculate a probability for each of the 48 groups to end up with a tie in a relevant position (1st vs 2nd, or 2nd vs 3rd). 1998 was chosen as the starting point for this analysis because it was the first year to feature the standard format of 32 teams with exactly 2 teams from each group advancing to the knockout stage. To simulate individual match results, I borrowed the model fitted by Harvard Data Science fellow Laurie Shaw on his EightyFivePoints blog that uses ELO ratings to predict a Poisson distribution of the number of goals each team will score in a given match. After simulating each match in a group, I tested to see if there was an absolute tie (Points, Goal Difference, Goals Scored, Head to Head) between two teams. I repeated this analysis one million times for each group to calculate the probability for each group to end in a tie. The results of this were interesting. There was a sizable amount of variance between the 48 different World Cup Groups. The lowest probability of a tie was .4%, while the highest 1.4%, with an average of 1.03% and a standard deviation of .26%. The four groups with the highest probability of needing an unconventional tiebreaker occurred in the 2002 World Cup, while two of the four lowest were from 2010. The top 5 and bottom 5 groups are detailed in the graphic below:
It is also interesting to see the probabilities of specific groups at this World Cup ending in a draw:
We find that Group H was only the 4th most likely to require a tiebreaker at this World Cup.
Then, using these probabilities we simulated each set of these 48 groups 100,000 times to back out the distribution of how often we should have expected to see this occurrence in the last 6 World Cups. In our 100,000 simulations, we found that on average we needed to settle .49 ties. In 60.7% of our Simulations, we found that none of the 48 groups ended with a tie. In 30.5%, we found one group requiring a tie while in 7.49% we needed 2. Astoundingly, we only need 3 or more tiebreakers in around 3% of our simulations.
These results are very surprising. Given the low number of games in a World Cup, I would have expected teams to tie with the same goal difference and number of goals more often (it is not that unfeasible for two teams to tie with 4 or 7 points after drawing with each other and achieving the same result against the other two teams in the group). Based on these results, it seems as though one tie for a relevant finishing position every 12 World Cups seems about right, so in a way you could say that the tie between Japan and Senegal came earlier than expected.
What are your thoughts on this? Do these numbers seem about right? Let us know in the comments below or on our Twitter page @harvard_sports.
If you have any questions or comments for Andrew, please feel free to reach out to him on Twitter @andrew_puopolo or by email at firstname.lastname@example.org