Page 1 MAREK M. KAMINSKI Host Paradox

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

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.

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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). Page 3 MAREK M. KAMINSKI Host Paradox

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)

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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;

P-3 – from 24 to 36 months back;

P-4 – from 36 to 48 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 Page 5 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 (#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- (2012). Page 6 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 -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. Page 7 MAREK M. KAMINSKI Host Paradox

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 P-1 P-2 = P-3 = P-4 R ranking (five matches) (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. Page 8 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 P-1 P-2 = P-3 = P-4 R ranking (five matches) (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. Page 9 MAREK M. KAMINSKI Host Paradox

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 P-1 P-2 = P-3 = P-4 R ranking (five games) (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 Page 10 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.” Page 11 MAREK M. KAMINSKI Host Paradox

Table 4: How the FIFA ranking disadvantages tournament hosts (a simple numerical example)

P-1 P-2 = P-3 = P-4 R (five matches) (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. Page 12 MAREK M. KAMINSKI Host Paradox

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., before 2010 World Cup) or host teams took part in preliminaries anyway since they were also preliminaries for a regional (e.g., Republic of South Africa before 2010 World Cup). Page 13 MAREK M. KAMINSKI Host Paradox

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 rN − rN+1 rN − rN+2 rN+2 − rN+3 hosts Euro + World + Asia 19 -16,6 -18,8 14,1* Euro 7 -11,7 -11,0 9,2* World Cup 5 1,4 4,4 16,4 Asia Cup 7 -43,1 -32,3 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.

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− 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 Page 15 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”

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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.

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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). Page 18 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. Page 19 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. Page 20 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 Page 21 MAREK M. KAMINSKI Host Paradox

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). Page 22 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..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. Date of access: 1/3/2012. 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. Date of access: 1/9/2012. Page 23 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.

Page 24 MAREK M. KAMINSKI Host Paradox

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 South Africa 77 76 85 51 2006 World Cup Germany 12 19 16 6 2002 World Cup South Korea 51 40 42 20 2002 World Cup Japan 57 38 34 22 1998 World Cup France 8 3 6 2 2011 Asia (AFC) Qatar 84 86 112 93 2007 Asia (AFC) Indonesia 91 109 153 133 2007 Asia (AFC) 120 123 152 159 2007 Asia (AFC) Thailand 79 111 137 121 2007 Asia (AFC) Vietnam 103 120 172 142 2004 Asia (AFC) China 54 63 86 54 2000 Asia (AFC) 90 85 111 110 2012 Europe (UEFA) Poland 58 73 66 TBD 2012 Europe (UEFA) Ukraine 22 34 55 TBD 2008 Europe (UEFA) Austria 69 65 94 92 2008 Europe (UEFA) Switzerland 35 17 44 24 2004 Europe (UEFA) Portugal 4 11 17 9 2000 Europe (UEFA) 41 35 33 27 2000 Europe (UEFA) Netherlands 22 11 19 8 Page 25 MAREK M. KAMINSKI Host Paradox

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).