page 1 marek m. kaminski host paradox · page 4 marek m. kaminski host paradox 2) average score for...

MAREK M. KAMINSKI Host Paradox

How Strong are Soccer Teams? ‘Host Paradox’ in FIFA’s ranking.*

Marek M. Kaminski

University of California, Irvine

Abstract: FIFA's ranking of national soccer teams is littered with paradoxes (or non-

intuitive properties). The most surprising phenomenon is that it underrating the teams of

the main championship tournament hosts. This “Host Effect” follows from the absence of

hosts in preliminaries and the resulting restriction of hosts’ pre-tournament matches to

friendlies (friendly matches) that enter the FIFA system with low weights. Various models

built with the FIFA data allow estimating the magnitude of the effect at 16.5-35.4

positions.

Keywords: football, soccer, FIFA ranking, social choice paradoxes, Euro 2012.

Department of Political Science i Institute for Mathematical Behavioral Science,

University of California, 3151 Social Science Plaza, Irvine, CA 92697-5100, U.S.A.;

email: [email protected]; tel. 9498242744.

* Barbara Kataneksza, Grzegorz Lissowski and Marcin Malawski provided helpful

comments. Center for the Study of Democracy provided financial support.


1. Introduction: FIFA ranking

FIFA (Fédération Internationale de Football Association) is the international governing

body of national soccer associations. It organizes the World Cup and coordinates the

activities of six regional federations that supervise local championships and friendlies

(friendly matches) of their members. Based in Zurich, FIFA is managed by 25-member

strong Executive Committee headed by the President. One of FIFA’s high profile

activities is the monthly announcement of the ranking of the best national soccer teams.

The positions are noted by the media and affect sponsors’ generosity. In addition, the

position in FIFA’s ranking affects the team’s chances in drawing opponents in

preliminaries and main tournaments of various Cups. Higher positions in the ranking are

associated with lower expected quality of opponents.

FIFA’s ranking evolved over time. The most recent 2006 version takes into

account the results of the official matches the national team played in the past four years,

the opponent’s position in the ranking, the strength of opponent’s federation and the

match’s importance.1 For every game the team receives corresponding points. Then, the

average score is calculated for the past 12 months, previous 12 months, etc; the average is

lowered for teams that played fewer than five matches. The position in ranking is the

function of weighted average score for the past 48 months. A detailed description of the

procedure and its components is as follows:

1) Score for a match: For every match the team receives the number of points equal to

the product:

P = M × I × T × C

1 Procedures, scores and ranking positions are quoted from FIFA’s website (2012a).


where the factors are calculated according to the following rules:

• M (points for the match’s result): 3 for victory, 1 for tie and 0 for defeat; when

penalty shots where used, the winner receives 2 points and the loser 1 point. If

preliminaries include a two-match game, and the results are symmetric, the result of

the second match is disregarded and the points are assigned as if penalty shots were

applied;

• I (importance) depends on the match’s category and is equal to:

1 – a friendly or a minor tournament

2.5 – preliminaries to World Cup or a federation’s cup

3 – main tournament of a federation’s cup

4 – main tournament in World Cup;

• T (opponent’s strength) depends on the most recent position of the opponent in

FIFA ranking and is equal to (200–opponent’s position in the ranking).

Exceptions: the ranking’s leader has the strength of 200 and the teams ranked from

position 150 downwards have the strength of 50;

• C (correction for federation’s strength) is equal to the average strength of the team

and its opponents’ federations. The strength of every federation is calculated from

its members results in the three most recent World Cups. At the end of 2011, the

value of C was equal to:

1 for UEFA (Europe) and CONMEBOL (South America)

0,88 for CONCACAF (North America, Central America and the Caribbean)

0,86 for AFC (Asia and Australia) and CAF (Africa)

0,85 for OFC (Oceania)

MAREK M. KAMINSKI Host Paradox 2) Average score for the past year (beginning at a certain point and ending exactly 12

months later) is calculated as an arithmetic mean from all matches if the team played at

least five times. With a smaller number of matches, the average is multiplied by

0,2×number of matches played.

3) Position in ranking r at a given moment represents the total weighted sum of points

over the past four years according to the formula:

R = P-1 × 0.5 P-2 × 0.3 P-3 × 0.2 P-4

where every component P-i is a weighted score for matches played over the period:

P-1 – last 12 months;

P-2 – from 12 to 24 months back;



2. Paradoxes

The formula of FIFA’s ranking is vulnerable to „paradoxes.” Here, the term „paradox,”

made popular in voting theory and social choice theory by books by Brams (1975) and

Ordeshook (1986), denotes a situation when the ranking behaves contrary to our basic

intuition. In other words, the function that assigns to the relevant soccer statistics a

ranking doesn’t satisfy certain properties that are interpreted as “obvious,” “desired” or

“fair.” Social choice theory socialized us to a situation when certain desired properties

MAREK M. KAMINSKI Host Paradox cannot be satisfied at the same time (Arrow 1951). Whether one can find an equivalent of

Arrow’s Theorem for ranking teams remains an open question. Below, I start by providing

several examples that illustrate a few striking paradoxes. The analysis of the main paradox

follows.

It is easy to point out certain components of the FIFA formula that would generate

surprise or protest with most fans. For instance, the number of points doesn’t depend on

whether a team plays at home or not. Thus, in a match of a similar rank, a team receives

more points for defeating Qatar (the controversial organizer of 2022 World Cup and #93 in

the ranking at the end of 2011) than for a tie with Brazil (#6) played on the famously

intimidating Estádio do Maracanã in Rio. The ranking’s quirks make certain teams reach

very high position against common sentiment placing them lower. For instance, in

September 1993 and July and August 1995, Norway was second while in 2006 USA was

fourth. Sometimes paradoxical results happen systematically.

2.1. Violation of Goal Monotonicity: losing a goal increases the score

An apparently obvious property is that the score used by FIFA should increase or stay

constant with every goal won by a team. Under certain conditions, this property of “Goal

Monotonicity” is violated.

Team A plays with Team B in two-match competition for advancing to the next

round. A defeats B at home 2:0, and then loses 0:2.2

Let’s analyze the consequences for A of losing the second goal: By losing 0:1 A

would advance to the next round receiving zero points for the lost match. When A loses

the second goal, the score becomes symmetric (2:0 and 0:2), and the result of the second

match is decided by penalty shots. But this increases A’s score for this match (versus

2 Example from football-rankings (2012).

MAREK M. KAMINSKI Host Paradox receiving zero points for defeat 0:1) since under two possible outcomes A wins some

points. If A loses, it receives the relevant number of points with a multiplier 1; if A wins,

the multiplier is 2. In both cases the number is positive. As an effect, losing the second

goal by A automatically increases A’s FIFA score for the match and possibly its position in

the ranking!

A mirror problem appears for Team B that receives more points for a match won

1:0 than for winning a second goal, regardless of the result of penalty shots.

The “Goal Monotonicity” paradox took place in Jordan-Kyrgyzstan preliminaries.

On October 19, 2007, Jordan lost 0:2 and ten days later beat Kyrgyzstan at home 2:0. For

winning 2:0 and then winning penalty shots Jordan received 284.75 points while for

winning only 1:0 it would receive substantially more, i.e., 427.125 points.3 A similar

problem was noted when Australia beat Uruguay when competing for advancement to the

2006 World Cup. In general, similar problems appear always when the result of a two-

match competition is settled with penalty shots.

It is not easy to eliminate the above paradox. The core problem is that penalty

shots are an additional “mini-match” that takes place after two games that ended with

symmetric results. If penalty shots affect the score, then we get problems similar to those

described above. If penalty shots do not affect the score, then the fact that one team

overall beat the second one is disregarded.

The number of problems is greater. In all examples offered below, we assume that

all teams played at least five matches in every twelve-month period used for calculating the

means and exactly five matches in the last period; that previously played matches will not

be re-classified to a different period after the ranking is modified and that no other matches

were played in the period between the announcement of old and new rankings. The

Federation weight is always 1 and the points are rounded in the usual way.

3 Ibidem.


2.2. Unlucky Leaders: The ranking leaders automatically lose their positions after a

match

Team A is the ranking’s leader and Team B is second. Team C is third. A and B play a

friendly. Regardless of the score, after the match C becomes the new ranking leader.

Table 1: Initial data for the paradox of Unlucky Leaders

Position in

ranking

P-1

(five matches)

P-2 = P-3 = P-4 R

(total score)

Team A 1 700 500 1200

Team B 2 700 490 1190

Team C 3 645 540 1185

Note: P-i denotes mean score for year i back.

The table shows the scores before A and B play the match. After the match the score

changes depending on the result. The maximum number of points that A can receive for

defeating B is P = M×I×T×C = 3×1×198×1 = 594. As an effect, the average score for the

last 12 months for A is 682 (after rounding), and the total score for the ranking is 1182.

Similarly, the best case scenario for B is defeating A. In such a case, B’s score is equal to

1173. Both numbers are smaller than the total score of C which remains unchanged. Thus

C becomes the new ranking leader.

MAREK M. KAMINSKI Host Paradox In the above example the problem appears due to low score for the friendly. Even

glorious defeat of a high-ranked opponent may lower the total score and the position in the

ranking.

2.3. Tie Reversing the Ranking

Team A is higher ranked than Team B. In a friendly, A ties with B. As an effect, the

ranking of A versus B is reversed.

Table 2: Initial data for the Paradox of Tie Reversing the Ranking

Position in

ranking

P-1

(five matches)

P-2 = P-3 = P-4 R

(total score)

Team A 20 780 500 1280

Team B 30 600 650 1250

For a tie in a match with B Team A receives P = M×I×T×C = 1×1×170×1 = 170 points

while B receives P = M×I×T×C = 1×1×180×1 = 180 points. After including the result of

the tie in the mean for the last twelve months, the total score of Team A in the ranking is

1178 (after rounding) while B’s score is 1180. As an effect, B is now higher in the ranking

than A.

The problem appears due to the fact that A is ranked higher thanks to a relatively

better previous year. As an effect, the tie lowers A’s score by more points than the B’s

score.


What is interesting is that the paradox may appear even if the higher ranked A beats

B (as shown below)! However, in order to obtain this stronger version of the paradox,

much greater differences between the scores of both teams in different years are needed.

This makes the occurrence of such a paradox less likely.

2.4. Victory Reversing the Ranking

Team A ranks higher than Team B. In a friendly, A beats B and, as an effect, B is now

ranked higher than A.

Table 3: Initial data for the Paradox of Victory Reversing the Ranking

Position in

ranking

P-1

(five games)

P-2 = P-3 = P-4 R

(total score)

Team A 20 1100 200 1300

Team B 30 200 1050 1250

Team A receives for the won match 3×1×170×1 = 510 points while B receives 0. As an

effect, A has after the match 1202 points while B has 1217. B is now higher ranked than

A.

The source problem for all the examples above is the low score assigned for

friendlies and the fact that the means for four years are computed independently. If a

team’s place in the ranking depends mostly on the fantastic previous year then even a

victory in a low-value friendly may ruin its position. On the other hand, for a team with a

weak previous year, even a defeat may have low effect on the team’s position. The

MAREK M. KAMINSKI Host Paradox Reader, equipped with all this knowledge, should be able to construct the following

paradox:

1. Teams A, B and C are in one group of a round-robin tournament in World Cup;

2. Ranking before the tournament: A, B, C;

3. Results of the tournament: A, B, C;

4. Ranking after the tournament: C, B, A.

The next paradox has a different structure and appears on a regular basis. Section 3

introduces this paradox.

3. The Paradox of Tournament Host

The hosts of the official FIFA tournaments are treated very poorly by the ranking.

Similarly to the examples described above, the source of problems is a low weight

assigned to friendlies versus preliminaries to World Cup or regional Federation Cups (the

multiplier of 1 versus 2.5). Since the hosts advance to the main tournaments automatically,

they do not take part in the preliminaries that often start about two years before the

tournament. Thus, for almost two years before the tournament the host has much lower

chance to play highly-scoring matches than other teams. Even when the host scores very

well, its position in the ranking may go down!4

4 This disadvantage of tournament hosts was acknowledged by FIFA (2012b), that vaguely says that the host has “less opportunity for getting more points.”

MAREK M. KAMINSKI Host Paradox Table 4: How the FIFA ranking disadvantages tournament hosts (a simple numerical

example)

P-1

(five matches)

P-2 = P-3 = P-4 R

(total score)

Team A 600 600 1200

Team B 550 550 1100

Team A is the host of Euro (the European Championship). In all four years, A received

better scores than B. A and B each play one match with C (position in the ranking 50) that

is counted in the last year’s score. Both teams beat C whose position doesn’t change

between the matches. B wins its match in the preliminaries to the Euro Championship

while A wins a friendly. As a result, A receives 450 points (total score 1175) while B

receives 1125 points (total score 1196). B is now ranked higher than A.

Let’s consider an example from Euro 2012. In 2011 Poland, as a co-host of Euro 2012,

played only friendlies. Out of 13 matches, Poland won 7, tied 3 and lost 3. They beat such

strong opponents as Argentina (#10 at the end of 2011) or Bosnia and Herzegovina (#20),

losing in close games to Italy (#9) and France (#15), and ending in a tie matches with

Greece (#14), Germany (#2) and Mexico (#21). Overall, 2011 was a very good year for

the Polish team, and it was much better than the previous two years (In 2010, victories-

ties-defeats were 2-6-3; 2009: 3-2-2). Despite such a good year, Poland ended 2011

ranked 66 with 492 points, only slightly better than the terrible 2010 (#73) and lower than

in 2009 (58). The FIFA ranking was even less generous for Ukraine, the second co-host of

Euro 2012. At the end of 2009 Ukraine was ranked 22, at the end of 2010 it was ranked

34, and at the end of 2011 it went down to position 55.


If Poland played all its 2011 matches in the Euro 2012 preliminaries with identical

results then it would receive at the end of 2011 approximately 1381 points instead of just

492. With such score, it would have been ranked second, behind Spain (1564) and ahead

of the Netherlands (1365)! The difference in weights for friendlies and preliminaries is

substantial and suggests a strong effect.

The estimation of the Host Effect presents substantial methodological challenges.

Below, four alternative methods will be discussed that use different data and make

different assumptions.5

3.1: Average loss of the position in the ranking.

I will start with a hypothesis that can be tested with the FIFA data. Team A is a

tournament host in Year N+3. As the host, A doesn’t participate in the preliminaries, some

of which take place in Year N+1 and some take place in Year N+2.6 The first negative

effects of the Host Effect may appear in Year N+1 and the effect ends in Year N+2. Let’s

denote the A’s position in the ranking at the end of Year i by ri. The most interesting

comparison is between the position of A at the end of Year N (just before the

preliminaries) and at the end of Year N+2 (after the end of preliminaries), i.e., rN and rN+2;

two more comparisons are also worth analyzing. Table 5 shows the calculations for two

regional Federation Cups and the World Cup.

5 A typical situation when methodological difficulties lead to simultaneous consideration of various estimation methods is the valuation of public companies. Two most important methods include comparative analysis of similar companies and estimation of discounted future earnings. 6 The assumption that preliminaries take place in Years N+1 and N+2 is satisfied for the vast majority of championships and teams. In some cases, the preliminaries took place exclusively in Year N+2. In rare cases, teams finished their preliminaries in Year N+1 (e.g., Kuwait before 2010 World Cup) or host teams took part in preliminaries anyway since they were also preliminaries for a regional Federation Cup (e.g., Republic of South Africa before 2010 World Cup).


Hypothesis: The team of the Host of the tournament taking place in Year N+3 has a lower

position in the ranking at the end of year N+2 than at the end of Year N, i.e., rN − rN+2 < 0.

Table 5. The average changes in positions in the FIFA ranking for the hosts of the World

Cup, Euro (UEFA) and the Asia Cup (AFC).7

Tournaments Number of

hosts

rN − rN+1 rN − rN+2 rN+2 − rN+3

Euro + World + Asia

Euro

World Cup

Asia Cup

19

7

5

7

-16,6

-11,7

1,4

-43,1

-18,8

-11,0

4,4

-32,3

14,1*

9,2*

16,4

15,9

Note: * With no Poland and Ukraine of 2012 [PLEASE NOTE: THESE DATA

POINTS WILL BE INCLUDED LATER]; p-value for one-sided binomial test (rN

7 Certain regional tournaments were omitted: CAF and CONCACAF Cups take place bi-annually, and the preliminaries take place in the same year as the main tournaments. Since for earlier years FIFA offers only annual rankings, the isolation of the Host Effect for such data is not possible. CONMEBOL has small number of members and has no preliminaries while OFC is a small amateurish federation with 11 official members and the best team ranked at 119 (New Zealand). After the change in the ranking methodology in 2006, the rankings were re-calculated since 1995 which made possible including tournaments taking place from 1998 onwards.

The analyzed data involve a few methodological dilemmas. Most notably, the data do not constitute a “representative sample” but are generated by three processes, i.e., non-random selection of the host, another non-random selection of the host and other teams’ competitors and the random process with an unknown distribution, i.e., the results of matches. The author believes that the first process could affect the analysis in a noticeable way only for the World Cup while the second process doesn’t introduce any systematic bias.


− ½(rN+1 + rN+2) < 0) is equal about 0,002. Due to small numbers of cases p-values

for particular tournaments were not calculated. The Appendix includes Table 8

with the data for all 19 hosts.

The average loss of a position in ranking between the end of year immediately preceding

the beginning of preliminaries and the year ending the preliminaries (two years later) is

equal to 18.8. Due to various sources of noise in the data that were impossible to eliminate

and that lowered the estimates, this number should be considered conservative. It is also

interesting to note another effect, i.e., that the host gains on average 14.1 positions after the

tournament. This jump is due to playing at home in a high-weight tournament. However,

the second number underestimates the Host Effect due to the fact that the two years with

no preliminaries are also included in the calculations of position at the end of the

tournament year.

The Host Effect estimates for specific tournament types have to be treated with

caution. It is interesting that the effect didn’t appear in the World Cup (the change of

+4.4). One can speculate that this is due to the fact that all recent World Cup host teams

are very strong in their regions. Two years before the World Cup, all five teams took part

in the main regional cups, where it was relatively easy to qualify. Three host teams also

took part in the previous World Cup. Thus, the Host Effect is partially offset by the non-

random process of selecting the hosts, i.e., the higher probability of offering the World

Cup organization to strong teams, who have more opportunity to play in high-weight

matches than weak teams, and who lose less due to not playing in preliminaries. (I will

return in a moment to the hypothesis that the strength of the Host Effect is related to the

position of a team in the ranking.) Moreover, World Cup is an incredibly prestigious event

that is comparable only with the Summer Olympics. One can speculate that the host’s

MAREK M. KAMINSKI Host Paradox spending on the national team increases greatly in the years before the Cup, and that, in

turn, increases the host’s position in the ranking.

There are more teams that play in the Regional Cups than in the World Cup. Thus,

non-participation in the World Cup preliminaries is offset to a greater degree by

participation in the Regional Cups than vice versa. One would expect a stronger effect for

the hosts of regional preliminaries than for the hosts of the World Cup. The data confirm

this hypothesis.

One can notice a very strong Host Effect for the Asian Federation AFC (–32,3).

One can speculate that the effect is relatively less polluted by the participation in other

main tournaments since the teams of the organizers of AFC Cup are relatively weaker than

the organizers of the World Cup or Euro. While every host of the World Cup took part in

the earlier Regional Cups, no host of AFC Cup except for China participated in the earlier

World Cup. China didn’t gain anything from this participation since they scored no points

and not a single goal. Thus, the hosts of AFC Cup earned their ranking points only in

Federation preliminaries and main tournaments as well as in friendlies. The only non-

systematic effect influencing the results was non-participation in the regional

championship.

In the case of Euro organized by UEFA, the Host Effect of –11 is solid but

somewhat reduced by the fact that four out of seven hosts participated in the earlier World

Cup in Year N+1. Similarly to World Cup, the hosts of Euro have much stronger teams

than the hosts of AFC Cup. Those teams have more chances of playing in high-weight

matches than the hosts of AFC Cup.

3.2: OLS with the explanatory variable „host position two years before the championships”

MAREK M. KAMINSKI Host Paradox The second question, implicitly present in the earlier discussion, deals with the

strength of the Host Effect for different subsets of teams. A strong team has more chances

to play in high-weight tournaments than a weak team due to a higher probability of

advancing to regional Cups and the World Cup. One can speculate that the strength of the

Host Effect decreases for stronger hosts. An assessment of this relationship allows for a

more precise estimation of the losses due to the Host Effect by teams from different

positions in the ranking.

The low p-value p<0.001 for OLS with the explanatory variable rN (position in the

ranking three years before the tournament) and the response variable rN − rN+2 (the change

in ranking over the period of preliminaries) allows to reject the null hypothesis of no

relationship. For predicting rN − rN+2, I used the regression forcing the intercept to be equal

to zero, i.e., preserving the corresponding positions in the ranking at positive values (see

Table 6). The estimated parameters for both regressions differ insignificantly. The

advantage of the second regression is that it doesn’t take the estimations beyond the range

for the response variable while the OLS would implicitly predict for high values of rN

small negative values of rN+2.

Table 6: Regression for variables rN and rN − rN+2: rN − rN+2 = β × rN

Variable β SE(β) t p 95% C.I.

rN 0,326 0,056 5,77 0,000 [0,208, 0,445]

Note: R2 = 0,6494; R2(ADJ) = 0,6300; F(1, 18) = 33,35, p<0,0001. All data used for this

model are listed in Table 8 in the Appendix.

MAREK M. KAMINSKI Host Paradox The value of the slope β=0.326 means that the host team with a certain position in the

ranking in time N can expect in two years to slide down about 1/3 of its initial position.

Thus, knowing the host’s ranking position at time N+2, rN+2, one can estimate the

“effective” position at time N+2 after eliminating the Host Effect as 1/(1+0,326) ≈ 0.75 of

the actual position, or 0.75 rN+2. For the Polish team, the estimated slide down in the

ranking is 16.5.

[[WILL BE ADDED: A SCATTER PLOT OF ACTUAL VERSUS CORRECTED

POSITIONS FOR ALL HOSTS AT TIME N+2]]

3.3: Comparative analysis of the positions in the FIFA and alternative rankings

While the FIFA ranking is the most popular, there are many alternative rankings that use

different methodologies for ordering national teams. Table 7 below shows the position of

the Polish team at the end of 2012 according to the five most popular rankings.

Table 7. The position of Polish national team in selected rankings. 8

Ranking FIFA ELO RoonBa Rankfootball CTR AQB

Position 66 38 23 31 33 28

Note: Positions in rankings at the end of 2011 and beginning of 2012.

[[NOTE: THIS TABLE WILL BE SUBSTITUTED WITH A TABLE SHOWING THE

AVERAGE DIFFERENCES BETWEEN FIFA AND OTHER RANKINGS]]

8 Alternative rankings are cited after the websites ELO (2012), RoonBa (2012), Rankfootball (2012), CTR (2012) and AQB (2012).

MAREK M. KAMINSKI Host Paradox Alternative rankings seem to be immune to Host-like effects. In addition, these alternative

rankings seem to have lower sensitivity to the time factor than the FIFA ranking. For the

Polish team, the average position in the alternative ranking is equal to 30.6. Having in

mind the impossibility of separating the Host Effect from the effects of lower weights

given to older matches, one can estimate the difference between the position of the Polish

team in the FIFA ranking and its mean position in alternative rankings at 35.4.

3.4: Substituting friendlies with preliminaries

The final estimation method was outlined at the beginning of Section 3. One can ask: what

would be the position of the Polish national team if some of the matches played in 2010

and 2011 had higher “preliminary” multiplier of 2.5 instead of the “friendly” multiplier of

1?

Let’s estimate the modified score for years 2010 and 2011, when the preliminaries

took place, under the following assumptions:

(1) The points and positions in the ranking of all other teams remain unchanged

(2) Each of the 26 matches of Poland played in 2010-11 receives the multiplier

(preliminary versus friendly) equal to (26-9.725)/26 × 1 + (9.725/26) × 2,5 = 1,56 (see

explanation below).

(3) The question of the possibility of being in the same preliminary group with the actual

friendly opponent is disregarded (Poland couldn’t be in the same group with its non-

European opponents in the friendlies such as Argentina or Mexico; in the case of friendly

opponents such as Germany, France and Italy, only one team could be in the same group

with Poland). The implicit assumption here is that specific teams are less important and

that the results are considered to be proxies for the results with potential opponents.

MAREK M. KAMINSKI Host Paradox (4) The possibly lower incentive to play in a friendly is also disregarded as well as the fact

that, according to some experts, teams such as Argentina included many reserve players in

their teams. Such an effect may make it easier for weaker teams score well against teams

that are stronger but not motivated enough or that experiment with reserve players.

(5) All matches played in 2010-11 are included. 9

In point (2) the weights were calculated on the basis of the average number of matches

played by the European teams in the preliminaries. Since 51 teams played jointly 248

matches, the average is equal to 9.725. The difference in the number of matches is due to

the fact that six groups had six teams and three groups had five teams, and that there were

additional rounds. The weight of 1.56 uniformly distributes the extra weight from 9.725

hypothetical preliminary matches to 26 actual friendly matches.

Under such assumptions, the results of the Polish national team would look as

follows:

2008: 288,74 (unchanged);

2009: 171,4 (unchanged);

2010: 347,52 (estimated);

2011: 389,1 (estimated).

The total number of points at the end of 2011 would be equal to 288,74×0,2+ 171,4×0,3+

347,52×0,5+ 389,1≈672. Such a score would have given Poland 39th position in the

9 I am grateful to Marcin Malawski for discussing problems described in (3)-(5). He suggested another alternative method of estimation that would take into consideration only those teams with whom Poland could actually be competing in the preliminaries.

MAREK M. KAMINSKI Host Paradox ranking, i.e., 27 positions higher than the actual position in the FIFA ranking from

December 2011. 10

4. Conclusion

Intuition suggests that being a host of a match or entire tournament helps to achieve a

better score and to reach higher ranking AFTER the tournament. However, it is not easy to

eliminate the impact of all factors that help the hosts, such as better familiarity with the

local conditions, having cheering fans, familiar cuisine or shorter trip. We have to accept

such advantage. Intuition suggests as well that the fact of being a host should be irrelevant

for the team’s position in the ranking BEFORE the tournament. Surprisingly, this is not

the case with the FIFA ranking. The host’s position suffers over the period of two years

preceding the tournament due to the host team’s absence from the highly weighted

preliminaries. Various methods allow estimating this Host Effect at the end of year that

precedes the tournament year at between 16.5 and 35.4, i.e., the position of the host team

should be higher by this number if it were corrected by the Host Effect.

The Host Effect has obvious implications. It leads to substantial

fluctuations in the host team’s position before and after the tournament. It contradicts the

FIFA intention that the ranking provides a universal and objective tool for evaluating

teams’ strengths.11 The low ranking of the team translates as well into lower chances in

the next preliminaries since the lower-ranked teams are bundled in the lower “baskets” for

drawing, and expect facing stronger opponents. 12

10 The scores of all teams were recorded as of February 17, 2012, when Poland’s position in the FIFA ranking was 70. 11 FIFA (2012c). 12 In the preliminaries for the 2010 World Cup CONCACAF, CAF and UEFA used FIFA rankings from various months preceding the drawing for separating teams from various „baskets;” for 2010 World Cup the


Perhaps the most salient effect is the lowering the interest in the tournament among

the fans and sponsors! When the author traveled to Poland during Euro 2012, his casual

conversation with a cabbie about the chances of the Polish team started with a resigned

statement: “Sir, they are so low in the ranking that nothing will help them.” Later, the

author’s father repeated this gloomy prognosis using the same FIFA ranking. Thus, the

low position in the ranking leads to the underestimation of the host’s chances by its own

fans and lowers their interest in the tournament. It may cause dismissing comments from

the observers13 and decrease the stream of money flowing from the sponsors.

While pretending to be a “neutral” tool that promotes some objective standards in

evaluating national teams, the FIFA ranking actually disheartens host fans and discourages

the sponsors. The flaws in the ranking are not impossible to eliminate or restrict. An

obvious solution suggested by Method #4 would be an introduction of higher weights for

friendlies played by the hosts. While the details of such weighting could be worked out in

a few different ways and introduce certain obvious dilemmas, any sensible solution of this

sort would greatly curb the negative effects of the present formula used by FIFA.

REFERENCES

AQB. Soccer ratings 2012. Access: http://www.image.co.nz/aqb/soccer_ratings.html.

Date of access: 1/10/2012.

Arrow, Kenneth J. 1951, 2nd ed. 1963. Social Choice and Individual Values. New York:

Wiley.

October 2009 ranking was used; for the preliminaries to the 2012 Olympics CAF used the ranking of March, 2011 (Wikipedia 2012). 13 For instance Peter Schmeichel, former Danish goalkeeper and the coach of Manchester United, maliciously opined in an interview for a leading Polish newspaper: „There will be 15 best European teams playing in Euro and 28th in the ranking [in Europe – MMK] Poland.” (Gazeta 2012).

MAREK M. KAMINSKI Host Paradox Brams, Steven. 1975. Game Theory and Politics: New York: Free Press.

CTR. CTR ranking 2012. Access: http://ctr-fussball-

analysen.npage.de/ratings_37612669.html. Date of access: 1/9/2012.

ELO. ELO ratings. 2012. Access: http://www.eloratings.net/system.html. Date of access:

1/10/2012.

FIFA. Official website of FIFA (Fédération Internationale de Football Association).

2012a. Access: www.fifa.com/index.html. Date of access: 1/12/2012.

FIFA. Frequently asked questions about the FIFA/Coca-Cola World Ranking. 2012b.

Access: http://www.fifa.com/mm/document/fifafacts/r&a-wr/52/00/95/fs-

590_05e_wr-qa.pdf. Date of access: 1/12/2012.

FIFA. FIFA/Coca-Cola World Ranking Procedure. 2012c. Access:

http://www.fifa.com/worldfootball/ranking/procedure/men.html. Date of access:

1/12/2012.

football-rankings. FIFA Ranking: Flaw in the calculation 2012. Access:

http://www.football-rankings.info/2009/09/fifa-ranking-flaw-in-calculation.html.


Gazeta Wyborcza. Peter Schmeichel dla Sport.pl: Bossowi nie stawia się żądań. (Peter

Schmeichel for Sport.pl: You don’t tell boss what to do) 5.03.2012. Access:

http://www.sport.pl/euro2012/1,109071,11283110,Peter_Schmeichel_dla_Sport_pl

__Bossowi_nie_stawia.html. Date of access: 3/8/2012.

Ordeshook, Peter C. 1986. Game theory and political theory. Cambridge: Cambridge

University Press.

rankfootball. ranking 2012. Access: http://www.rankfootball.com/. Date of access:

1/1/2012.

RoonBa. RoonBa ranking. 2012. Access: http://roonba.com/football/rank/world.html.


MAREK M. KAMINSKI Host Paradox Wikipedia. FIFA World Rankings 2012. Access:

http://en.wikipedia.org/wiki/FIFA_World_Rankings#Uses_of_the_rankings. Date

of access: 1/12/2012.


APPENDIX

Table 8: The hosts of World Cup, Euro (UEFA) and Asia Cup (AFC) from 1998 and their

positions in the FIFA ranking

Championship Host rN rN+1 rN+2 rN+3

2010 World Cup

2006 World Cup

2002 World Cup

2002 World Cup

1998 World Cup

2011 Asia (AFC)

2007 Asia (AFC)

2007 Asia (AFC)

2007 Asia (AFC)

2007 Asia (AFC)

2004 Asia (AFC)

2000 Asia (AFC)

2012 Europe (UEFA)

2012 Europe (UEFA)

2008 Europe (UEFA)

2008 Europe (UEFA)

2004 Europe (UEFA)

2000 Europe (UEFA)

2000 Europe (UEFA)

South Africa

Germany

South Korea

Japan

France

Qatar

Indonesia

Malaysia

Thailand

Vietnam

China

Lebanon

Poland

Ukraine

Austria

Switzerland

Portugal

Belgium

Netherlands

77

12

51

57

8

84

91

120

79

103

54

90

58

22

69

35

4

41

22

76

19

40

38

3

86

109

123

111

120

63

85

73

34

65

17

11

35

11

85

16

42

34

6

112

153

152

137

172

86

111

66

55

94

44

17

33

19

51

6

20

22

2

93

133

159

121

142

54

110

TBD

TBD

92

24

9

27

8


Note: Data from Table 8 were used for calculating the averages in Table 5 and running the

regression in Table 6. Some championships had two and more hosts. Four last columns

show the host’s position in the December ranking (the last in the year) at the end of the

following years:

rN – two years before the beginning of the tournament year;

rN+1 – one year before the beginning of the tournament year;

rN+2 –the beginning of the tournament year;

rN+3 – the end of the tournament year (i.e., the first December following the tournament).

page 1 marek m. kaminski host paradox · page 4 marek m. kaminski host paradox 2) average score for...

Documents