The evolution of seeding systems and the impact of imbalanced groups in FIFA Men's World Cup tournaments 1954-2022

Abstract

The FIFA Men's World Cup tournament is the most popular sporting event in the world. Scholars have identified several flaws in the organization of the World Cup causing competitive imbalance. We empirically assess competitive imbalance between groups for the World Cup tournaments from 1954 through 2022. We average the Elo ratings of a team's opponents in the group stage to calculate their group opponents rating. In every World Cup, the range in group opponents rating exceeds 118 Elo rating points-the difference between an average participant and an average semifinalist. Using logistic regression, we find that for an average participant in a 32-team World Cup, an increase in group opponents rating of only 88 Elo rating points can reduce the probability of reaching the quarterfinal from 0.174 to 0.081, which is a decrease of more than 50%. None of the five seeding systems used by FIFA during 1954-2022 lessened the negative impact of group opponents rating on the probability of reaching the quarterfinal. We close with seven policy recommendations to restore competitive balance at the World Cup.

Full text

J. Quant. Anal. Sports 2023; 19(4): 317 –332
Research Article
Michael A. Lapré* and Elizabeth M. Palazzolo
The evolution of seeding systems and the impact
of imbalanced groups in FIFA Men’s World Cup
tournaments 1954–2022
https://doi.org/10.1515/jqas-2022-0087
Received October 16, 2022; accepted June 2, 2023;
published online June 19, 2023
Abstract:The FIFA Men’s World Cup tournament is the most
popular sporting event in the world. Scholars have iden-
tified several flaws in the organization of the World Cup
causing competitive imbalance. We empirically assess com-
petitive imbalance between groups for the World Cup tour-
naments from 1954 through 2022. We average the Elo ratings
of a team’s opponents in the group stage to calculate their
group opponents rating. In every World Cup, the range in
group opponents rating exceeds 118 Elo rating points – the
dierence between an average participant and an average
semifinalist. Using logistic regression, we find that for an
average participant in a 32-team World Cup, an increase
in group opponents rating of only 88 Elo rating points can
reduce the probability of reaching the quarterfinal from
0.174 to 0.081, which is a decrease of more than 50 %. None
of the five seeding systems used by FIFA during 1954–2022
lessened the negative impact of group opponents rating on
the probability of reaching the quarterfinal. We close with
seven policy recommendations to restore competitive bal-
ance at the World Cup.
Keywords: balance; FIFA Men’s World Cup; logistic regres-
sion; rating sports teams; seeding systems
1 Introduction
Soccer is the most popular sport in the world, and the World
Cup – the flagship soccer competition – is the most popular
sporting event in the world. A record high of 3.572 billion
people – almost half of the global population – watched the
*Corresponding author: Michael A. Lapré, Owen Graduate School of
Management, Vanderbilt University, Nashville, TN, USA,
E-mail: m.lapre@vanderbilt.edu.https://orcid.org/0000-0003-2259-8739
Elizabeth M. Palazzolo, Lazard, New York, NY, USA
2018 World Cup (FIFA 2018). Soccer’s world governing body,
Féderation Internationale de Football Association (FIFA),
organizes the Men’s World Cup every four years and has
more members than the United Nations (Haan, Koning, and
van Witteloostuijn 2007). Qualification for the World Cup
has significant economic benefits as each qualifying coun-
try receives an appearance fee of approximately 8 million
dollars (Stone and Rod 2016). Cognizant of the economic and
social benefits derived from the global mass viewership and
growing popularity of the World Cup, FIFA has undertaken
eorts to increase the attractiveness of all games played
during the World Cup (Chater et al. 2021).
The World Cup consists of a qualification phase and
a tournament phase. Prior to each World Cup, FIFA deter-
mines the number of qualifying slots for each of the six con-
tinental confederations: North and Central America (CON-
CACAF), South America (CONMEBOL), Europe (UEFA), Africa
(CAF), Asia (AFC), and Oceania (OFC). In the qualification
phase, teams compete in qualifying competitions to advance
to the tournament phase. Table 1 shows the evolution of
the tournament phase. Since 1954, the tournament phase
typically consists of a group stage and a knockout stage.
In the group stage, teams are allocated to groups of four
teams. Each group participates in a round-robin tourna-
ment, with the best teams advancing to the knockout stage.
Earlier World Cups were either knockout-stage only (1934
and 1938) or had some groups with fewer than four teams
(1930 and 1950). Therefore, in our analysis of group strength,
we focus on the 18 tournaments held between 1954 and
2022.
For soccer leagues, creating competitive excitement
is of paramount importance (Haan, Koning, and
van Witteloostuijn 2007). Uncertainty about the outcome of
a soccer game generates competitive excitement, which in
turn attracts fans (Koning 2000;Scarf and Yusof 2011). When
teams are more evenly matched, uncertainty about the
outcome is higher (Koning 2000). In the group stage of the
World Cup, groups should be balanced, i.e., groups should
be roughly at the same competitive level (Guyon 2015). With
imbalance across groups, it will be much harder for a team
Open Access. ©2023 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License.

318 —M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments
Table 1: Format of the FIFA World Cup tournament.
Years Number of Group stage Group stage Number of teams in
teams 1st round 2nd round knockout stage
1930 13 4 groups of 3 or 4 n/a 4
1934 16 n/a n/a 16
1938 15an/a n/a 15a
1950 13a4 groups of 2, 3 or 4 1 group of 4 n/a
1954– 1970 16 4 groups of 4 n/a 8
1974– 1978 16 4 groups of 4 2 groups of 4 2
1982 24 6 groups of 4 4 groups of 3 4
1986– 1994 24 6 groups of 4 n/a 16
1998– 2022 32 8 groups of 4 n/a 16
n/a: not applicable. aLess than 16 because not all teams showed up.
to advance to the knockout stage from a tough group with
several strong teams compared to a team playing in an
easier group. Such a scenario is considered unfair (Laliena
and López 2019). Instead, teams of similar strength should
have the same likelihood of advancing in the tournament.
Competitive balance across groups enhances fairness
(Guyon 2015).
To create groups, FIFA places participating teams in
four pots. Pot 1 typically consists of the host country and the
best teams – so called “seeded teams” – at the World Cup.
Allocation mechanisms for the remaining teams to pots 2,
3, and 4 have evolved over time, to some extent accounting
for geographic separation or team strength. For example, in
2010 and 2014, pots 2, 3, and 4 were based on geographic
criteria, whereas in 2018 and 2022, pots 2, 3, and 4 were
based on FIFA rankings. In a draw procedure, each group
is constructed by drawing one team from each pot. Seeding
protects the best teams as they cannot play each other in
the group stage. Table 2 describes the evolution of seeding
systems for the World Cup.
FIFA has acknowledged the importance of competitive
balance. FIFA’s Technical Study Group (TSG) publishes tech-
nical reports following each World Cup to track progress in
improving competitive balance across all matches. The TSG
contends in their technical report for the 2014 World Cup
that “this World Cup was an extremely balanced aair. Eight
of the 16 matches in the second stage went to extra time,
and four all the way to a penalty shoot-out ... [underlining]
how close the teams [were] together as well as the good
development work being done by the member associations”
(FIFA 2014a, p. 44). Contrary to TSG’s claims suggesting an
improvement in competitive balance over time, the groups
in this World Cup had very dierent strengths (Guyon 2015;
Laliena and López 2019). For example, group D was a tough
group consisting of teams with Elo rankings at the time of
the draw of 6, 9, 11, and 29 (England, Uruguay, Italy, and Costa
Rica), whereas group H was a weak group made up of teams
ranked 15, 18, 44, and 61 (Russia, Belgium, South Korea, and
Algeria).
Several papers have studied FIFA’s draw procedures for
the World Cup. Jones (1990) finds that the draw for the 1990
World Cup was mathematically unfair, and Rathgeber and
Rathgeber (2007) show that despite both teams being seeded
in the 2006 World Cup, Germany was more likely to play in
a tough group while Italy was not. Guyon (2015) identifies
three flaws in FIFA’s draw procedure for 32-team tourna-
ments: lack of balance, lack of fairness, and an uneven
distribution. First, the lack of balance results in groups of
unequal competitive strength. Second, the unfairness of the
draw increases the chance that certain teams have a greater
chance of being allocated to a stronger group. Lastly, the
draw has an uneven distribution, meaning that all possible
Table 2: Evolution of seeding systems.
Years Description
1930– 1974 Decision made in closed session
1978– 1986 In public session, seeding and draw considered geographical position of the countries represented
1990– 1994 Use ranking of the last two (1990) or three (1994) World Cups
1998– 2006 Use both performance in last three (1998– 2002) or two (2006) World Cups and FIFA ranking over the past three years
2010– 2022 Use FIFA ranking from eight months before the World Cup

M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments —319
outcomes of the draw are not equally likely. Guyon (2015),
Laliena and López (2019),andCea et al. (2020) propose better
draw procedures to create competitive balance. However,
these papers do not empirically assess imbalance at the
World Cup.
For the 1982–2006 World Cups, Monks and Husch (2009)
empirically investigate the impact of seeding, home conti-
nent, and hosting on the probability of reaching the quar-
terfinal. The authors find that being seeded and playing in
the home continent increases the probability of reaching
the quarterfinal. Yet, host teams do not enjoy any advan-
tages beyond the benefits of seeding and the home conti-
nent eect. In this paper, we empirically assess imbalance
between groups for the FIFA World Cup tournaments from
1954 through 2022. We find that the strength of the oppo-
nents in the group (“group opponents rating”) reduces the
probability of reaching the quarterfinal. Moreover, once
we include group opponents rating, seeding and home
continent no longer aect the probability of reaching the
quarterfinal. So, the findings by Monks and Husch (2009)
are likely biased due to the omission of group opponents
rating.
Lapré and Palazzolo (2022) empirically document com-
petitive imbalance for the FIFA Women’s World Cup from
1991 through 2019. The authors find that higher group oppo-
nents rating significantly decreases the probability of reach-
ing the quarterfinal. In this paper, unlike the study of the
Women’s World Cup, the longer history of the Men’s World
Cup allows us to investigate the impact of group opponents
rating on both the quarterfinal and the semifinal. Unlike
the FIFA Women’s ranking system, FIFA’s Men’s ranking
systems through 2018 have been heavily criticized. While
Lapré and Palazzolo (2022) use FIFA Women’s Ranking, in
this paper we use Elo ratings. In contrast to the Women’s
World Cup, FIFA has used dierent seeding systems in the
longer history of the Men’s World Cup. In this paper, we
study whether the dierent seedings systems aect compet-
itive imbalance at the Men’s World Cup.
The remainder of the paper is organized as follows.
In Section 2, we review related literature. In Section 3,we
use Elo ratings at the time of the draw to empirically assess
competitive imbalance between groups for the 1954 through
2022 World Cups. For each team, we average the ratings
across the opponents in the group to calculate group oppo-
nents rating. In Section 4, we quantify the impact of imbal-
ance on the probability of success at the World Cup. Using
logistic regression, we find that a small increase (relative
to the observed variation) in group opponents rating can
decrease a team’s probability of reaching the quarterfinal
by 9 to 21 percentage points depending on the number of
teams in the World Cup. In Section 5,wediscusstheevo-
lution of FIFA’s seeding systems. In Section 6, we assess
whether increases in competitive imbalance coincide with
a reduction in the predictability of the composition of the
late stages in the tournament. Lastly, we oer concluding
remarks and policy recommendations in Section 7.
2 Related research
Scholars have identified several factors contributing to com-
petitive imbalance at the World Cup including FIFA’s rank-
ing methods, allocation of confederation slots, lack of win
incentive, draw procedures, and seeding systems.
FIFA began ranking men’s national teams in 1993 and
has since updated their ranking method in 1999, 2006, and
after the World Cup in 2018. McHale and Davies (2007) note
that FIFA’s ranking methods prior to 2006 have several
subjective elements and lack justification. Weightings for
regional strength and past results are not based on objec-
tive elements. No quantitative basis is provided to justify
bonus points for away teams and points awarded for a win,
draw, or loss. No empirical justification is provided for the
decreasing weights applied to results from the past. McHale
and Davies (2007) use statistical analysis to show that the
FIFA ranking method between 1998 and 2006 does not use
information from past results eciently and does not react
quickly enough to recent changes in team performance.
Lasek et al. (2016) show that teams can exploit opportunities
to climb in the FIFA rankings by scheduling friendly matches
taking into account factors such as choosing the number of
games, risk tolerance, and forming a coalition with other
teams. Criticisms of FIFA’s ranking method between 2006
and 2018 include point-depreciation favoring certain con-
federations, disincentive to play in friendly matches, ignor-
ing home advantage, a built-in incentive to play average
teams rather than top teams, and underrating the World
Cup host team (Cea et al. 2020;Csató 2021;Kaminski 2022).
Lasek, Szlávik, and Bhulai (2013) assess the predictive power
of several ranking methods. The authors find that rela-
tively simple algorithms outperform the FIFA Men’s World
Ranking procedure. Notably, Elo rating systems based on an
update formula are competitive rating methods. Curiously,
FIFA has used an Elo rating system for the FIFA Women’s
World Ranking since they started ranking women’s national
teams in 2003 (Lasek, Szlávik, and Bhulai 2013). Yet, the
Men’s World Ranking did not switch to an Elo rating system
until as late as 2018. For the FIFA ranking method used
since 2018, Szczecinski and Roatis (2022) find that the pre-
dictive capacity of FIFA’s Elo algorithm can be improved by
incorporating home advantage, explicitly modelling draws

320 —M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments
in the game, and introducing weighting of the results with
goal dierential. Other papers have analyzed rating meth-
ods that reflect teams’ current strength (Ley, Van de Wiele,
and Van Eetvelde 2019) and find the all-time greatest teams
(Baker and McHale 2018). Koning (2017),Van Eetvelde and
Ley (2019),andGroll, Schauberger, and Van Eetvelde (2020)
provide recent reviews of rating methods.
Stone and Rod (2016) show that the system of allocat-
ing the number of teams that can participate from each
confederation does not ensure that the best teams qualify
for the World Cup, nor does it fairly allocate qualification
spots to confederations. Stone and Rod (2016) and Csató
(2023e) advocate for a more transparent allocation process.
Krumer and Moreno-Ternero (2023) study the allocation of
additional slots for the 2026 World Cup.
The World Cup’s group stage and knockout stage struc-
tures can lead to tanking – that is, a team already qualified
for the knockout stage might deliberately lose a game to face
a more desirable opponent in the knockout stage (Stronka
2020). Chater et al. (2021) study how the last round of the
group stage can lead to collusive games and stake-less games
giving rise to match-fixing opportunities. The authors then
propose changes to avoid match fixing. Guyon (2018b) and
Csató (2021) discuss the design of the 1986–1994 World Cups
featuring a single-group stage with 24 teams, which creates
several fairness issues such as group advantage, lack of
win incentive, and arbitrary choices. Csató (2023c) proposes
a framework to quantify the threat of tanking in the last
roundofthegroupstageandidentifiesascheduleforthe
2022 World Cup that minimizes the risk of tanking. Guyon
(2020) proposes alternative methods to reduce the risk of
collusion in the 2026 World Cup if FIFA were to use groups of
only three teams. Csató (2022a) identifies an incentive com-
patibility problem in the qualification phase of the World
Cup. The author shows with an example that a team with
a better result in qualification might be punished by being
placed in a weaker pot, and thus face stronger opponents in
the tournament phase.
FIFA imposes geographic constraints on the draw. For
example, since 1998, teams from the same confederation
cannot be drawn into the same group, except for UEFA. In 32-
team World Cups, FIFA constrains each group to have one or
two UEFA teams. Traditionally, FIFA has built pots 2, 3, and 4
based on confederation while completely disregarding team
strength causing many of the flaws (i.e., lack of balance, lack
of fairness, and uneven distribution) of the draw procedure
(Guyon 2015). Guyon (2015) proposes an improved draw
procedure that mitigates these flaws while satisfying the
geographic constraints. Inspired by Guyon (2015), since 2018,
FIFA has moved from continent-based pots to ranking-based
pots (Guyon 2018a). Building on Guyon (2015),Laliena and
López (2019) propose two evenly distributed draw systems
that produce groups with similar or equal competitive levels
while accounting for the geographic constraints. Using an
optimization method, Cea et al. (2020) propose a draw proce-
dure that minimizes the dierence between the maximum
and minimum ranking sums of each group’s members. Csató
(2023d) shows that the order in which pots are emptied dur-
ing the draw can aect the probability of advancing in the
tournament. The author proposes finding the optimal order
prior to the draw. For the 2022 World Cup, FIFA performed
the draw when three play-o winners were still unknown.
FIFA placed the play-o winners in pot 4. However, Csató
(2023a) shows that assigning the placeholders according to
the highest-ranked potential winner improves competitive
balance across groups.
Lastly, Scarf and Yusof (2011) use simulation to show
that seeding increases the probability that the best teams
advance beyond the group stage. In contrast, Engist, Merkus,
and Schafmeister (2021) find that seeding did not influence
tournament performance of marginally seeded teams in the
UEFA Champions League (CL) and Europa League – the
most prestigious tournaments for European clubs. Schol-
ars have also used simulation to analyze seeding systems
in the CL which has a qualification–group stage–knockout
stage sequence similar to the World Cup. Csató (2022c) stud-
ies the reform in the Champions Path of CL qualification.
Dagaev and Rudyak (2019) investigate the seeding system
reform of the group stage in the CL. The authors find only
marginal changes in tournament success measures when
UEFA changed the seeded teams in pot 1 from the high-
est ranked teams to the national champions of the Top-7
associations. Corona et al. (2019) find that this CL seeding
reform increased the uncertainty over progression to the
knockout phase, but had little impact on the composition of
the final. In this paper, the evolution of FIFA seeding systems
in Table 2 covers a much longer time frame with dierent
reforms such as (i) moving from closed to public session,
(ii) changing from continental to performance criteria, and
(iii) changing performance criteria from outcomes of prior
World Cups to recent FIFA rankings.
3 Imbalance in groups
3.1 Group strength
To assess team strength at the time of the draw, we use
World Football Elo Ratings (eloratings.net). Gásquez and
Royuela (2016) note that the Elo rating uses a low volatility
index (i.e., it has more memory present) and is particularly

M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments —321
well suited for empirical analysis over long periods of time
such as our analysis. Elo ratings are updated after every
match and have been used extensively in the literature
(Cea et al. 2020;Csató 2022b, 2023a, 2023b;Gásquez and
Royuela 2016;Lasek, Szlávik, and Bhulai 2013;Lasek et al.
2016). Let r′
iand ribe the updated rating after a match and
the old (pre-match) rating for team irespectively. Kis a
weight constant ranging from 20 for friendly matches to
60 for World Cup matches. The update formula adjusts the
rating for team iby comparing the actual match outcome
against team jwith the expected outcome:
r′
i=ri+KW−Wij,
where Wis the actual match outcome from team i’s perspec-
tive (1 for a win, 0.5 for a draw, and 0 for a loss) and the win
expectancy on a neutral field is:
Wij =1
1+10−(ri−rj)∕400 .
Win expectancy is modified if one team is playing at
home by adding 100 points to the rating for the home team.1
For each of the 18 World Cup tournaments in our study,
we obtained Elo ratings for all participating teams at the
time of the draw from international-football.net. Let rit be
the Elo rating for team ionthedateofthedrawforWorld
Cup t. For the host team, we increase the rating by 100 to
reflect home advantage (Csató 2023a). Next, we use the team
ratings to calculate group strength. For each group Gtin
1For a full description of the methodology of World Football Elo Rat-
ings see http://eloratings.net/about. Note that World Football Elo Rat-
ings take home advantage and goal dierential into account, whereas
the current FIFA ranking does not account for these factors.
World Cup t, we calculate group strength gsGtas the average
of the team ratings: gsGt=1
4
i∈Gt
rit.Guyon (2015) and Laliena
and López (2019) argue that a group can be tough when
three teams are strong even if the fourth team is much
weaker. This logic is especially applicable when only two
teams advance out of the group as is the case for the 16-
team World Cups (1954–1978) and the 32-team World Cups
(1998–2022) in our dataset. Therefore, we also calculate an
alternative measure for group strength as the average of the
team ratings of the three strongest teams in a group: gs′
Gt=
1
3(
i∈Gt
rit −min
i∈Gt
rit). Figure 1A and Bshows gsGtand gs′
Gtfor
all groups. Figure 2 shows the evolution of the range in both
measures of group strength. More dispersion in gsGtmeans
a higher competitive imbalance across groups. Conversely,
gsGt=0 for all groups would imply perfect balance across
groups. To interpret Elo ratings for World Cup teams we
calculate several averages. The average Elo rating across all
teams in all World Cups is 1,842. The average Elo rating for
all quarterfinalists is 1,930, and the average Elo rating for all
semifinalists is 1,960. So, the dierence between an average
World Cup participant and an average quarterfinalist is 88
Elo rating points, and the dierence between an average
World Cup team and an average semifinalist is 118 Elo rating
points. The range in group strength varies from 24 points
in 1966 to 200 points in 1970 and 2014. The ranges in group
strength are noticeably large. From 1994 through 2018, the
range in group strength is more than 100, exceeding the 88-
point dierence between an average team and an average
quarterfinalist. Clearly, there are many strong groups and
many weak groups. The extent of competitive imbalance
has grown since the expansion to 32 teams in 1998. The
2010–2018 levels of competitive imbalance returned to the
Figure 1A: Group strength calculated as the average Elo rating of all four teams in the group. Number of groups in 1954– 1978: 4, 1982–1994: 6,
1998– 2022: 8.

322 —M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments
Figure 1B: Group strength calculated as the average Elo rating of the best three teams in the group. Number of groups in 1954– 1978: 4, 1982–1994: 6,
1998– 2022: 8.
Figure 2: Range in group strength. Number of groups in 1954– 1978: 4, 1982–1994: 6, 1998–2022: 8.
levels observed as far back as 1962 and 1970. These dif-
ferences in group strength imply substantial competitive
imbalance. Furthermore, when we consider gs′
Gtinstead of
gsGt, the range in groups strength exceeds 88 points from
1994 through 2022.
3.2 Group opponents rating
Following Lapré and Palazzolo (2022), we calculate group
opponents rating for team iin World Cup tas gopprit =
1
3
j∈Git
rjt,whereGit is the set of three opponents for team
iin the (first) group stage of World Cup t.Wealsocal-
culate an alternative measure for group opponents rating
by averaging the ratings of the two strongest opponents:
goppr′
it =1
2(
j∈Git
rjt −min
j∈Git
rjt). Figure 3 shows the range in
both measures of group opponents rating for each World
Cup. For both measures, the range in group opponents rat-
ing is large – it exceeds the 118-point dierence between an
average team and an average semifinalist in every World
Cup.
4 Impact of imbalanced groups
We investigate the impact of group opponents rating on
two measures of success at the World Cup. The World Cups
in 1954–1970 consisted of a single group stage followed by
a knockout stage starting with quarterfinals. Similarly, the
World Cups in 1986–2022 consisted of a single group stage

M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments —323
Figure 3: Range in group opponents rating. Number of groups in 1954– 1978: 4, 1982–1994: 6, 1998–2022: 8.
followed by a knockout stage starting with 16 teams. For
World Cups with a single group stage followed by a knock-
out stage, reaching the quarterfinal or the semifinal are
logical measures of success. However, in 1974 and 1978 the
first group stage with four groups of four teams yielded 8
teams advancing to a second group stage with two groups
of four teams each. Since these World Cups consisted of two
group stages, we make slight adjustments to account for
these two years. Although there were no quarterfinals or
semifinals in 1974 and 1978, the winners of the second-stage
groups played the final, and the second-placed teams played
a match to determine third and fourth place. Therefore,
we can instead identify the top 8 and the top 4 in these
tournaments as proxy measures for success. In 1982, the first
group stage with six groups of four teams yielded 12 teams
advancing to the second group stage with four groups of
three teams each. The winners of the second-stage groups
then advanced to the semifinals. In a similar fashion, we
can instead identify the top 12 in the 1982 tournament as a
proxy measure of success. So, our first measure of success is
reaching the quarterfinal (or top 8 in 1974–1978 and top 12
in 1982), and our second measure of success is reaching the
semifinal (or top 4 in 1974–1978).
4.1 Impact of group opponents rating
on reaching the quarterfinal
Our first dependent variable is QFit =1ifteamireached
the quarterfinal in World Cup t, top 8 in 1974–1978, or top
12 in 1982, and 0 otherwise. Our results are robust when
we omit the 1982 World Cup. We control for several factors
which can aect reaching the quarterfinal. First, we control
for the number of teams, Nt, in World Cup t. Second, teams
playing in their home continent can benefit from climatic
conditions, cultural circumstances, and shorter travel dis-
tances for their fans (Groll, Schauberger, and Tutz 2015;
Monks and Husch 2009). We control for a home continent
advantage with HCit =1 if World Cup twas held in the
home continent of team i, and 0 otherwise. Third, in theory,
seeded teams are the stronger teams. Seeded teams avoid
playing each other in the (first) group stage. We control
for the potential benefit of being seeded (Monks and Husch
2009)withSit =1ifteamiwas a seeded team from pot 1
in World Cup t. Fourth, we control for the strength of team
iin World Cup twith rit. As described in Section 3,home
advantage for the host is included in the host rating. For
our key independent variable of interest, group opponents
rating for team iin World Cup t, we use both gopprit and
goppr′
it. Additionally, we test whether changes in the seeding
systems used in the five eras listed in Table 2 have lessened
the impact of group opponents rating. Let Dj=1ifaWorld
Cup was held during era j, and 0 otherwise. Lastly, we intro-
duce an interaction variable gopprit ×Djto test if the slope
parameter for group opponents rating changes during era
j. We use logistic regression to estimate the probability of
reaching the quarterfinal as follows:
ln Pr(QFit =1)
1−Pr(QFit =1) =𝛽0+𝛽1Nt+𝛽2HCit +𝛽3Sit +𝛽4rit
+𝛽5gopprit +
5

j=2
𝛽5jgopprit ×Dj+eit
We do not include dummy variables for the dierent
eras because the main eect of eras is captured by the
number of teams, Nt. A negative value for 𝛽1means that
a team playing in a World Cup with more teams has a
lower probability of reaching the quarterfinal. A positive

324 —M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments
Table 3: Logistic regression models: top 8 in 1954– 1978 and 1986–2022 or top 12 in 1982.
(1) (2) (3)
Constant, 𝛽5.034 1.631 5.455
(5.425) (4.988) (6.383)
Number of teams, 𝛽−0.099∗∗∗ −0.093∗∗∗ −0.096
(0.020) (0.020) (0.091)
Home continent, 𝛽0.349 0.398 0.376
(0.252) (0.251) (0.258)
Seed, 𝛽0.566 0.509 0.569
(0.309) (0.313) (0.310)
Team rating, 𝛽0.0068∗∗∗ 0.0071∗∗∗ 0.0067∗∗∗
(0.0012) (0.0012) (0.0012)
Group opponents rating (all 3), 𝛽−0.0088∗∗∗ −0.0090∗∗∗
(0.0024) (0.0026)
Group opponents rating (best 2), 𝛽−0.0070∗∗∗
(0.0021)
Group opponents rating (all 3) ×D– ,𝛽 0.0001
(0.0004)
Group opponents rating (all 3) ×D– ,𝛽 −0.0001
(0.0004)
Group opponents rating (all 3) ×D– ,𝛽 −0.0000
(0.0008)
Group opponents rating (all 3) ×D– ,𝛽 0.0000
(0.0008)
LR χ2150.49∗∗∗ 147.94∗∗∗ 151.56∗∗∗
Pseudo R20.271 0.266 0.273
Number of observations 432 432 432
Dependent variable: Reach the Quarterfinal (or top 8 in 1974– 1978, or top 12 in 1982). Standard errors in parentheses. ∗Significant at 0.05, ∗∗ at 0.01,
and ∗∗∗ at 0.001.
value for 𝛽2means that a team playing in its home conti-
nent has a higher probability of reaching the quarterfinal.
A positive value for 𝛽3means that a seeded team has a
higher probability of reaching the quarterfinal. A positive
value for 𝛽4means that a higher quality team has a higher
probability of reaching the quarterfinal. A negative value
for 𝛽5implies that a team playing against higher quality
opponents in the group stage has a lower probability of
reaching the quarterfinal. A positive value for 𝛽5jmeans
that in era jthe seeding system reduced the negative impact
of group opponents rating on the probability of reaching the
quarterfinal.
When conducting logistic regression, Hosmer,
Lemeshow, and Sturdivant (2013) recommend at least 10
observed events per independent variable to avoid
overfitting. For the 17 World Cups in years 1954–1978
and 1986–2022, we have 17 ×8=136 top-8 observations.
Combined with the top 12 teams in 1982, we have a total
of 148 success observations. So, applying the rule of ten
events per variable, we can include at most 14 independent
variables. Since we include only 9 independent variables in
the full model, we are not at risk of overfitting.
Table 3 shows the results of the logistic regression for
reaching the quarterfinal. In Model (1), the positive and
statistically significant estimate for 𝛽4indicates that higher
quality teams have a higher probability of reaching the
quarterfinal. The negative and statistically significant esti-
mate for 𝛽5supports the notion that playing against tougher
opponents in the group reduces the probability of reaching
the quarterfinal.2Model (2) shows that the impact of group
opponents rating is robust if we measure group opponents
ratings by averaging the ratings of the two strongest oppo-
nents in the group.
For each model, the LR χ2rejects the null hypothesis
that all coecients are zero. The pseudo R2in Table 3 is the
McFadden pseudo R2.Hemmert et al. (2018) derive sample-
sensitive benchmark values for McFadden pseudo R2. All
models in Table 3 have 432 observations and the percent-
age of success (top 8 in 1954–1978 and 1986–2022 or top 12
in 1982) is 34 %. For models with more than 200 observa-
tions and percentage of success under 38 % or above 62 %,
2We discuss the significance of the control variables in Appendix A.1.

M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments —325
McFadden R2values between 0.11 and 0.20 indicate good
model fit, and values above 0.20 indicate excellent fit (Hem-
mert et al. 2018). All models in Table 3 have a pseudo R2
above 0.20 indicating excellent model fit.
Next, we illustrate the impact of group opponents
rating on the probability of reaching the quarterfinal. In
Appendix A.1, we re-estimate Model (1) without the statisti-
cally insignificant variables. Let 
𝛽ibe the estimate for 𝛽ifor
variable ifrom Model (5) in Table 5. We use the estimated
logistic regression model to determine the estimated proba-
bility of reaching the quarterfinal, Pr(
QFit =1):
ln Pr(
QFit =1)
1−Pr(
QFit =1) =
𝛽0+
𝛽1Nt+
𝛽4rit +
𝛽5gopprit
⇔Pr
QFit =1=e
𝛽0+
𝛽1Nt+
𝛽4rit+
𝛽5gopprit
1+e
𝛽0+
𝛽1Nt+
𝛽4rit+
𝛽5gopprit
In Figure 4A,weplotPr(

QFit =1) for an average team play-
ing in 16-, 24-, and 32-team World Cup tournaments. Recall
that an average team has an Elo rating of 1,842 and the dif-
ference between an average team and an average quarterfi-
nalist is 88 points. Note that 88 points is much less than the
observed ranges in Figure 4A. Next, we compare an average
team facing average opponents versus average quarterfi-
nalists in the group, i.e., an increase in group opponents
rating of 88 points. A change in group opponents rating
from 1,842 to 1,930 drastically decreases the probability of
reaching the quarterfinal. In a 16-team World Cup, we find
that an increase in group opponents rating from 1,842 to
1,930 decreases Pr(
QFit =1) from 0.51 to 0.30. In a 24-team
World Cup, an increase in group opponents rating from
1,842 to 1,930 decreases Pr(
QFit =1) from 0.32 to 0.16. In a
32-team World Cup, an increase in group opponents rating
Figure 4A: Impact of group opponents rating (all 3 opponents) on
reaching the quarterfinal (or top 8 in 1974– 1978, or top 12 in 1982).
Estimated probability of reaching the quarterfinal in 16-, 24-, and 32-team
World Cups for an average team. The observed ranges in group
opponents rating (all 3) for 16-, 24-, and 32-team World Cups were 1,699
to 2,022, 1,727 to 1,978, and 1,651 to 2,007 respectively.
Figure 4B: Impact of group opponents rating (strongest 2 opponents)
on reaching the quarterfinal (or top 8 in 1974– 1978, or top 12 in 1982).
Estimated probability of reaching the quarterfinal in 16-, 24-, and 32-team
World Cups for an average team. The observed ranges in group
opponents rating (strongest 2) for 16-, 24-, and 32-team World Cups were
1,766 to 2,061, 1,755 to 2,045, and 1,713 to 2,054 respectively.
from 1,842 to 1,930 decreases Pr(
QFit =1) from 0.174 to 0.081.
Thus, an increase of group opponents rating by only 88
points decreases the probability of reaching the quarterfinal
by 21, 16, and 9 percentage points depending on the number
of teams in the World Cup.
Similarly, in Figure 4B,weusetheestimatesfromModel
(6) in Table 5 to plot Pr(
QFit =1) as a function of group
opponents rating taking only the strongest two opponents
into account. The average group opponents rating for the
strongest two opponents is 1,906 points. Increasing goppr′
it
by 88 points from 1,906 to 1,994, decreases Pr(
QFit =1) in a
16-team World Cup from 0.50 to 0.33; in a 24-team World Cup
from 0.32 to 0.19; and in a 32-team World Cup from 0.181
to 0.098. Hence, an increase of goppr′
it by only 88 points
decreases the probability of reaching the quarterfinal by 17,
13, and 8 percentage points depending on the number of
teams.
Model (3) in Table 3 shows that none of the estimates for
𝛽5jare statistically significant. Hence, none of the seeding
systems reduced the negative impact of group opponents
rating on the probability of reaching the quarterfinal esti-
mated for 1954–1974. We find the same if we use group
opponents rating for only the strongest two opponents. We
discuss these findings in Section 5.
4.2 Impact of group opponents rating
on reaching the semifinal
Our second dependent variable is SFit =1ifteamireached
the semifinal in World Cup tor top 4 in 1974–1978, and 0
otherwise. Table 4 shows the logistic regression results. For
the 18 World Cups from 1954 through 2022, we have 18 ×4
=72 top-4 observations. Applying the rule of ten events per

326 —M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments
Table 4: Logistic regression models: top 4 in 1954– 2022.
(1) (2)
Constant, 𝛽−6.928 −4.623
(6.543) (6.092)
Number of teams, 𝛽−0.062∗∗ −0.066∗∗
(0.023) (0.023)
Home continent, 𝛽0.538 0.549
(0.294) (0.294)
Seed, 𝛽0.763∗0.686
(0.348) (0.353)
Team rating, 𝛽0.0068∗∗∗ 0.0067∗∗∗
(0.0015) (0.0015)
Group opponents rating (all 3), 𝛽−0.0035
(0.0028)
Group opponents rating (best 2), 𝛽−0.0045
(0.0025)
LR χ286.73∗∗∗ 88.40∗∗∗
Pseudo R20.223 0.227
Number of observations 432 432
Dependent variable: Reach the Semifinal (or top 4 in 1974– 1978).
Standard errors in parentheses. ∗Significant at 0.05, ∗∗ at 0.01, and
∗∗∗ at 0.001.
variable, we can include at most 7 independent variables.
Since we include 5 independent variables, we are not at risk
of overfitting. In Model (1), the estimate for 𝛽5is not signif-
icant. So, in contrast to our quarterfinal analysis, a higher
group opponents rating does not reduce the probability of
reaching the semifinal. This finding is robust in Model (2)
when we use only the two strongest opponents in the group
to calculate group opponents rating. For each model, the LR
χ2rejects the null hypothesis that all coecients are zero.
The pseudo R2values are above 0.20 indicating excellent
model fit.
4.3 Impact on group winners
Following Lapré and Palazzolo (2022), we explore an
alternative explanation for the substantial variation in
Pr(
QFit =1). Could it be that each group has some high-
performing teams of similar ability and some poorly per-
forming teams of similar ability? The team that finishes
first in the group standings after round-robin play is the
group winner. Figure 5 shows the range in group opponents
rating for all the group winners. In every World Cup, there
is substantial variation in group opponents rating for the
group winners. This means that group winners faced dif-
ferent levels of competition in the group stage. In 2014 and
2018, the range in group opponents rating (strongest 2) for
group winners grew back to the all-time high observed back
in 1970.
5 Longitudinal assessment of FIFA’s
seeding systems
To create balance across groups, FIFA identifies the stronger
teams as seeds and places seeds in dierent groups. Table 2
shows the evolution of the seeding systems used by FIFA.
In Section 4.1, we found that none of the seeding systems
lessened the negative impact of group opponents rating on
the probability of reaching the quarterfinal observed for the
earlier years 1954–1974.
1954– 1974. Prior to 1978, the FIFA Organising Commit-
tee decided on seeds in a closed session (FIFA 2014b). In 1954,
there were 8 seeds (half of the participating teams). There
were no seeds in 1958 and 1970. In each of the other years
(i.e., 1962, 1966, 1974), two of the four seeds did not survive
the group stage. These years illustrate how FIFA’s early
Figure 5: Range in group opponents rating for the group winners. Number of groups in 1954– 1978: 4, 1982–1994: 6, 1998–2022: 8.

M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments —327
decisions in closed sessions boiled down to a 50/50
proposition for seeds to advance to the quarterfinal. Conse-
quently, these seeding decisions contributed to a marginal
extent to create competitive balance.
1978– 1986. “The division of teams into groups was
made by the Organising Committee in a public session by
means of seeding and a draw having regard inter alia
to the geographical position of the countries represented”
(FIFA 2014b, p. 3). Drawing teams from pots that are based
on geography can lead to groups with unequal strengths
(Guyon 2015;Lapré and Palazzolo 2022). So, it is not sur-
prising that the coecient for group opponents rating for
1978–1986 in Table 3 did not significantly change from the
previous era.
1990– 1994. After each World Cup, FIFA creates a World
Cup ranking as follows. The outcomes of the final and the
match for third place determine the rankings for the first
four teams. The losing quarterfinalists are ranked 5 through
8 based on all matches played (3 points for a win, 1 point
for a draw, and 0 points for a loss). The teams eliminated
in the round of 16 are ranked 9 through 16 based on all
matches played, and teams eliminated in the group stage are
ranked 17 through 24 based on the three matches played in
the group stage. FIFA’s World Cup rankings do not control
for the strength of the opponents which is a serious draw-
back. To determine seeds for 1990, “[t]he ranking obtained
at the last two FIFA World Cups was decisive, with the rank
gained in Mexico 1986 counting double” (FIFA 2014b,p.3).
For 1994, FIFA used the World Cup rankings in the last three
World Cups. In 1990 and 1994, all seeded teams survived
the group stage. In 1990, 4 of the 6 seeds advanced to the
quarterfinal, whereas in 1994, 3 out of 6 seeds advanced
to the quarterfinal. As Table 3 shows, this seeding system
did not lessen the impact of group opponents rating on
the probability of reaching the quarterfinal. Even though
this era was a step in the right direction with an attempt
to take team strength into account, ample opportunity for
improvement remained. First, World Cup rankings failed to
consider the strength of opponents. Second, performance
going back 8–12 years is not very informative as teams have
a lot of turnover among their players.
1998– 2006. For 1998 and 2002, “[t]he seeded teams
were determined upon the finalists’ performance in the past
three FIFA World Cup finals (ratio 3:2:1), and their position
over the past three years in the monthly FIFA/Coca-Cola
Ranking (equal ratio)” FIFA (2014b,p.2).For2006,thissys-
tem was modified by only using the past two FIFA World
Cup rankings and the FIFA Men’s World rankings. As Table 3
shows, in terms of mitigating the impact of group oppo-
nents rating on the probability of reaching the quarterfinal,
this system did not significantly improve over the earlier
years 1954–1974. First, World Cup rankings are problematic
and going back 12 (or 8) years results in using outdated
information. Second, as discussed in Section 2,FIFAMen’s
World rankings in this era are problematic (Cea et al. 2020;
Lasek et al. 2016;Lasek, Szlávik, and Bhulai 2013).
2010– 2022. In this era, FIFA uses the Men’s World rank-
ing from eight months before the World Cup. Since 2018,
FIFA has created all four pots based on the Men’s World
ranking. Again, this system did nothing to lessen the impact
of group opponents rating on the probability of reaching
the quarterfinal estimated for the earlier years 1954–1974
(Table 3). While eliminating past FIFA World Cup rankings
and focusing on recent performance are steps in the right
direction, for 2010–2018 recent performance was measured
using the flawed FIFA Men’s World rankings.
6 Composition of the late stages
of the tournament
Figures 2 and 3illustrate the evolution of competitive imbal-
ance with the ranges in group strength and group oppo-
nents rating, respectively. If the imbalance in the group
stage increases, that should result in a reduction in the
predictability of the tournament outcomes. Next, we assess
the composition of the late stages of the tournament to find
out if the highest ranked teams advance. For each World
Cup t, we rank the participating teams based on their Elo
rating at the time of the draw from 1 to Nt. If a tournament
has high predictability, the average rank of the quarterfinal-
ists would be close to 4.5 which is the average rank of the
teams ranked 1 through 8. Similarly, a highly predictable
tournament would have an average rank for the semifi-
nalists close to 2.5 which is the average rank of the teams
ranked 1 through 4. Figure 6 shows the average rank among
participants (at the time of the draw) for the quarterfinalists
(QF), the semifinalists (SF), and the losing quarterfinalists
(LQF).
In Figure 2, we note an increase in the range in group
strength with the expansion to 24-team World Cups in 1982.
This increase mirrors the increase in the average rank of
quarterfinalists and semifinalists during the 24-team World
Cups in 1982 through 1994 in Figure 6. However, the reduc-
tion in predictability could be due to the increased num-
ber of participants as well as the design of a single-group
stage with 24 teams. More interesting is the comparison of
the seven 32-team World Cups. If we look at the range in
groups strength measured by the three strongest teams in
the group, Figure 2 shows this range to be larger in 2002,

328 —M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments
Figure 6: Average rank among participants (at the time of the draw) of top 8 in 1954– 2022 or top 12 in 1982 (QF), top 4 (SF), and top 8 (or 12 in 1982)
that do not reach the top 4 (LQF). Number of groups in 1954– 1978: 4, 1982– 1994: 6, 1998–2022: 8.
2010, 2014, and 2018. These four World Cups also have a
higher average rank for the quarterfinalists in Figure 6.
Conversely, the three years with a lower range in group
strength (again strongest three teams) in Figure 2, 1998,
2006, and 2022, are also the three years with a lower average
rank for the quarterfinalists in Figure 6, indicating higher
predictability. However, predictability increases in the semi-
finals as shown by the lower average rank for the semifinal-
ists.3The average rank discrepancy in evolution for quar-
terfinalists and semifinalists dovetails with the significance
findings for group opponents rating in Tables 3 and 4,where
we find that group opponents rating reduces the probabil-
ity of reaching the quarterfinal, but not the semifinal. So,
it seems that competitive imbalance has a bigger impact
on the quarterfinal composition than on the semifinal
composition.
7 Discussion and conclusion
Competitive balance is essential for an exciting tournament.
However, groups at the World Cup show substantial compet-
itive imbalance. For all World Cups from 1954 to 2022, the
range in group opponents rating has exceeded 118 Elo rating
3The 2022 World Cup is an exception with two unusual upsets in the
quarterfinals. Morocco, with an Elo rank of 34 at the time of the draw,
beat 8th ranked Portugal. Croatia, ranked 16, beat 1st ranked Brazil. The
semifinals produced results according to expectation. Third-ranked
Argentina beat 16th ranked Croatia and 2nd ranked France beat 34th
ranked Morocco.
points – the dierence between an average World Cup par-
ticipant and an average semifinalist. Moreover, in five of the
32-team tournaments from 1998 to 2022, the range in group
opponents rating has exceeded 236 Elo rating points – twice
the dierence between an average participant and an aver-
age semifinalist. For an average participant in a 32-team
World Cup, an increase in group opponents rating of only
88 Elo rating points –the dierence between an average
participant and an average quarterfinalist– can reduce the
probability of reaching the quarterfinal from 0.174 to 0.081,
which is a decrease of more than 50 %.
Historically, FIFA has struggled with assessing the
strength of teams. From 1990 through 2006, FIFA used past
World Cup rankings which failed to take opponent strength
into account. From 1998 through 2018, FIFA used Men’s
World rankings. Several scholars have identified numerous
flaws in FIFA ranking methods through 2018.
The implementation of seeding systems has not been
eective. For example, in 2018, group A consisted of teams
with Elo rankings – at the time of the draw – 13 (Uruguay),
44 (seed and host Russia), 50 (Egypt), and 66 (Saudi Arabia)
whereas group C contained teams with Elo rankings 5 (seed
France), 12 (Peru), 18 (Denmark), and 35 (Australia). Seeding
a low-ranked host country inherently contributes to compet-
itive imbalance.
Assigning teams in the draw procedure to pots 2, 3, and
4 based on continents has further contributed to compet-
itive imbalance. Adopting one of Guyon’s (2015) proposals
for 2018, FIFA moved from continent-based pots to ranking-
based pots (Guyon 2018a). While this move is a step in the
right direction, the allocation of confederation slots still

M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments —329
does not match the actual distribution of the best teams
in the world (Csató 2023e). As mentioned above, group A
in 2018 contained teams ranked 50 and 66 in a 32-team
World Cup. The more the allocation of confederation slots
matches the distribution of the best teams in the world,
the more competitive imbalance can be reduced. One of
FIFA’s objectives is to grow the game globally. So, some of
the slots allocated to non-UEFA and non-CONMEBOL con-
federations foster global development. In Appendix A.2,we
explain that our measures for group strength based on the
three strongest teams and group opponents rating based
on the two strongest opponents can be adequately used to
assess competitive imbalance while still allowing for global
development.
To avoid substantial competitive imbalance, we recom-
mend simultaneous adoption of the following conditions:
1. Use recent performance to assess team strength
2. Use a rating method such as an Elo rating system to
steer clear of the flaws inherent to FIFA’s earlier rank-
ing methods
3. Build pots based on team strength instead of continents
4. Adopt a draw procedure developed to create balance
(e.g., Guyon 2015;Laliena and López 2019,orCea et al.
2020)
5. Do not make the host a seed by default
6. Allocate confederation slots more closely aligned with
the distribution of the best teams in the world
Since 1930, FIFA has made some progress. By 2018, they
adopted three of these six conditions: recent performance
to assess team strength, pots based on team strength, and
a draw procedure proposed by Guyon (2015). For 2022, they
adopted a fourth condition: an Elo rating system. However,
FIFA could still improve the predictive capacity of their Elo
algorithm by taking home advantage and goal dierential
into account (Szczecinski and Roatis 2022). Moreover, the
last two conditions have been neglected. By making a low-
ranked host (such as Qatar ranked 51 in 2022) a seed and
by having an allocation of confederation slots that does not
reflect the distribution of the best teams, the World Cup will
remain imbalanced.
In fact, in the draw for the 2022 World Cup, FIFA has
added yet another source for potential competitive imbal-
ance. The draw was held when only 29 out of 32 teams
were known and eight teams still had yet to compete in
play-os to determine the final 3 teams. One of these slots
was a European play-o slot for which Wales (ranked 18 at
the time of the draw) was still a possible candidate. This
European play-o team was drawn into group B with teams
ranked 5 (England), 15 (United States), and 21 (Iran). If Wales
were to qualify, all four teams in group B would be ranked
higher than the worst two teams in each of the other groups.
Wales did indeed qualify. In hindsight, Csató’s (2023a) solu-
tion would have prevented the occurrence of this group. We
recommend a seventh condition:
7. Do not perform the draw until all participating teams
are known
The good news is that FIFA has adopted some of the advice
from scholarly research in attempts to make the World
Cup more balanced. The not so good news is that several
obstacles remain. Lastly, if FIFA were to use 16 groups of
three teams in 2026, then that decision could indeed ruin
the World Cup due to the increased risk of collusion (Guyon
2020).
Acknowledgments: The authors gratefully acknowledge
Julia Amato and Anna Lapré for research assistance
with data collection, cross-checking, and calculations. The
authors thank the Associate Editor and two anonymous
reviewers for the thoughtful and constructive feedback dur-
ing the review process. The authors also thank participants
at the INFORMS 2022 Annual Meeting, as well as seminar
participants at Vanderbilt University for helpful comments.
Author contribution: All the authors have accepted respon-
sibility for the entire content of this submitted manuscript
and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no con-
flicts of interest regarding this article.
Appendix
A.1 Control variables
Model (1) in Table 5 is the base model for reaching the quar-
terfinal with only the control variables. The negative and
statistically significant estimate for 𝛽1indicates that more
participating teams at a World Cup reduce the probability
of reaching the quarterfinal. The positive and statistically
significant estimate for 𝛽2indicates that teams playing in
their home continent have a higher probability of reaching
the quarterfinal. The positive and statistically significant
estimate for 𝛽3indicates that seeded teams have a higher
probability of reaching the quarterfinal. In Model (2), the
positive and statistically significant estimate for 𝛽4indicates
that higher quality teams have a higher probability of reach-
ing the quarterfinal. In Model (3), the negative and statis-
tically significant estimate for 𝛽5supports the notion that
playing against tougher opponents in the group reduces the

330 —M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments
Table 5: Logistic regression models: top 8 in 1954–1978 and 1986 –2022 or top 12 in 1982.
(1) (2) (3) (4) (5) (6)
Constant, 𝛽0.707 −13.552∗∗∗ 5.034 1.631 5.573 2.213
(0.447) (2.258) (5.425) (4.988) (5.371) (4.955)
Number of teams, 𝛽−0.080∗∗∗ −0.071∗∗∗ −0.099∗∗∗ −0.093∗∗∗ −0.100∗∗∗ −0.095∗∗∗
(0.017) (0.018) (0.020) (0.020) (0.020) (0.020)
Home continent, 𝛽0.522∗0.408 0.349 0.398
(0.233) (0.246) (0.252) (0.251)
Seed, 𝛽1.814∗∗∗ 0.825∗∗ 0.566 0.509
(0.259) (0.297) (0.309) (0.313)
Team rating, 𝛽0.0077∗∗∗ 0.0068∗∗∗ 0.0071∗∗∗ 0.0078∗∗∗ 0.0080∗∗∗
(0.0012) (0.0012) (0.0012) (0.0011) (0.0011)
Group opponents rating (all 3), 𝛽−0.0088∗∗∗ −0.0100∗∗∗
(0.0024) (0.0023)
Group opponents rating (best 2), 𝛽−0.0070∗∗ −0.0081∗∗∗
(0.0021) (0.0020)
LR χ285.36∗∗∗ 136.17∗∗∗ 150.49∗∗∗ 147.94∗∗∗ 145.10∗∗∗ 142.58∗∗∗
Pseudo R20.154 0.245 0.271 0.266 0.261 0.257
Number of observations 432 432 432 432 432 432
Dependent variable: Reach the Quarterfinal (or top 8 in 1974–1978, or top 12 in 1982). Standard errors in parentheses. ∗Significant at 0.05, ∗∗ at 0.01,
and ∗∗∗ at 0.001.
probability of reaching the quarterfinal. Model (4) shows the
same if we measure group opponents ratings by averaging
only the two strongest opponents in the group. Note that
the estimates for 𝛽1and 𝛽4are consistent across all models.
However, the estimates for 𝛽2and 𝛽3are not statistically
significant in Models (3) and (4).
Dropping HCit and Sit in Models (5) and (6) yields the
same insights as Models (3) and (4). The insignificance of
home continent is not surprising as the stronger teams from
UEFA (e.g., Germany and Italy) and CONMEBOL (e.g., Brazil
and Argentina) tend to outperform the other teams regard-
less of the continent where the World Cup is played. In fact,
all world champions and runners-up are from UEFA or CON-
MEBOL. The insignificance of the seed variable means that
group opponents rating better captures the performance
dynamics at the World Cup. Without group opponents rating
in Model (2), seed picks up some of the variation in the
data relating to seeds playing weaker opponents. However,
in Models (3) and (4), group opponents rating picks up the
variation in opponent strength for all teams – not just the
seeded teams. Models (3) and (4) show that there is no addi-
tional eect for seed beyond the eect for group opponents
rating.
A.2 Global development and imbalance
The biggest changes in allocation of confederation slots
occurred whenever FIFA expanded the number of teams at
the World Cup. The strongest confederations are UEFA and
CONMEBOL. The combined percentage of teams from UEFA
and CONMEBOL participating at the 16-, 24-, and 32-team
World Cups has averaged 86 %, 74 %, and 58 % respectively.
With each expansion at the World Cup, FIFA has allocated
more slots to the other confederations (CONCACAF, CAF,
AFC, and OFC) to help grow the game globally, i.e., global
development.
Next, we show that our measures of group strength for
the strongest three teams and group opponents rating for
the strongest two opponents can be used to assess competi-
tive imbalance while still allowing for global development.
First, for each World Cup, we identify the participating
teams by their Elo rank at the time of the draw. Second, for
all 16-team World Cups, we calculate the average Elo rank
of the strongest teams, the second strongest teams, down
to the sixteenth strongest teams. Third, in Figure 7,weplot
these average Elo ranks as curve ‘16’. Fourth, we repeat this
process for 24- and 32-team World Cups. For each curve,
the marker represents the strongest team in the bottom
25 % of teams. So, for the 16 curve, the marker represents
the thirteenth strongest team. A significant shift upwards
means that those teams have much worse Elo ranks indica-
tive of much lower ranked teams from non-UEFA and non-
CONMEBOL confederations. For the 16 curve, the “upward
break” happens for the sixteenth ranked team whereas for
the 32 curve, the upward break happens for the 28th team.
These breaks happen in the bottom 25 % of the teams. Note
that group strength for the strongest three teams and group
opponents rating for the strongest two opponents ignore the

M. A. Lapré and E. M. Palazzolo: Imbalanced groups in FIFA Men’s World Cup tournaments —331
Figure 7: Average Elo rank (at the time of the draw) of the ith ranked team among participants at the World Cup for the 16-, 24-, and 32-team
tournaments. Point markers indicate the highest ranked team from the bottom 25% of the teams at the World Cup.
bottom 25 %. As long as FIFA places the bottom 25 % in pot
4, as they have started to do since 2018, our measures can be
adequately used to assess competitive imbalance while still
allowing for global development with significantly lower
ranked teams in the bottom 25 %.
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