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S TATISTICS IN PROFESSIONAL SOCCER A comparison of styles among the top professional soccer teams in the world

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INTRODUCING THE DATA Statistical revolution in other sports Why not in soccer? Statistics kept during soccer games Individual vs. Team Statistics Goals for and goals against for winners of EPL, La Liga, MLS, and Serie A for past 6 seasons 24 data points Nonparametric vs. Parametric methods

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T HE DATA CountryYearProportion GFProportion GAGFPGGAPG Spain200666/3840/381.736841.05263 Italy200680/3834/382.105260.89474 USA200652/3238/321.625001.18750 England200683/3827/382.184210.71053 Spain200784/3836/382.210530.94737 Italy200769/3826/381.815790.68421 USA200756/3034/301.866671.13333 England200780/3822/382.105260.57895 Spain2008105/3835/382.763160.92105 Italy200870/3832/381.842110.84211 USA200850/3036/301.666671.20000 England200868/3824/381.789470.63158 Spain200998/3824/382.578950.63158 Italy200975/3834/381.973680.89474 USA200941/3031/301.366671.03333 England2009103/3832/382.710530.84211 Spain201095/3821/382.500000.55263 Italy201065/3824/381.710530.63158 USA201044/3026/301.466670.86667 England201078/3837/382.052630.97368 Spain2011121/3832/283.184211.14286 Italy201168/3820/381.789470.52632 USA201148/3428/341.411760.82353 England201193/3829/382.447370.76316

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E XPLANATION OF S TYLES Italy Catenaccio Spain Tiki-Taka USA Not developed their own style England International mix of styles

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T ESTING FOR GENERAL DIFFERENCES BETWEEN LEAGUES (K RUSKAL -W ALLIS ) Model Y ij = Ɵ +τ j + ij, i=1..6, j=1..4 H o : τ 1 =τ 2 =τ 3 =τ 4 H a : Not all τ j ’s are equal. H = 14.38 DF = 3 P = 0.002 Conclusion

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A SSUMPTIONS

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P ARAMETRIC E QUIVALENT : O NE -W AY A NOVA Model Y ij =m+a i +e ij i=1..6,j=1..4 H 0 : µ 1 = µ 2 = µ 3 = µ 4 H a : Not all µ are equal. P-value 0.000 F=9.75, df=3,20

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T ESTING FOR N ORMALITY

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A NOTHER W AY OF T ESTING V ARIANCES Descriptive Statistics: GFPG Variable Country StDev GFPG England 0.322 Italy 0.1426 Spain 0.492 USA 0.1884

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J ONCKHEERE -T ERPSTRA T EST F OR O RDERED A LTERNATIVES H o : τ 1 =τ 2 =τ 3 =τ 4 H a : τ 4 ≤ τ 3 ≤ τ 2 ≤ τ 1 Why did I choose this alternative? J = 189, p-value = 1.549e-05 There is significant evidence of differences in goals for per game across countries Which countries differ?

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M ULTIPLE C OMPARISONS Decide τ u ≠τ v if abs(W * uv )≥3.633, which is based on q α, a large sample approximation For Spain vs. USA, I got the following answer: (56-39)/4.415=3.90 England vs. USA: (56-39)/4.415=3.90 These were the only two significant differences

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T UKEY ’ S M ETHOD Grouping Information Using Tukey Method Country N Mean Grouping Spain 6 2.4956 A England 6 2.2149 A B Italy 6 1.8728 B C USA 6 1.5672 C

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C OMPARING GOALS FOR AND G OALS A GAINST : H OW DO THE T OP T EAMS W IN ?

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N ONPARAMETRIC C ORRELATION T ECHNIQUES Kendall's rank correlation tau data: Goalsf and Goalsa z = -0.5221, p-value = 0.6016 Sample estimates: tau -0.07706539

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A CCOUNTING FOR R ECENT T RENDS (G ENERAL L INEAR M ODEL ) Model Y i =β 0 + β 1 X i1 + β 2 X i2 +E i Estimate Std. Error t value Pr(>|t|) (Intercept) -78.53435 72.16573 -1.088 0.289 Countries -0.31272 0.05488 -5.698 1.18e-05 *** Year 0.04050 0.03593 1.127 0.272 No predictive linear relationship between Year and GFPG

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LSRL AND LOWESS M ODELS Pearson R-sq=.7%

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