Uncertainty, Competitive Balance and Professional Team Sports

Uncertainty, Competitive Balance and Professional Team Sports Part A: The Concept and Quantification of Competitive Balance Ιωάνννης Ντζούφρας, Τμήμα Στατιστικής, Οικονομικό Πανεπιστήμιο Αθηνών 2

The Concept of Competitive Balance The nature of the industry (of baseball) is such that competitors must be of approximate equal size if any are to be successful (Rottenberg, 956). Competitive Balance is literally the balance between the sporting capabilities of teams (Michie & Oughton, 2004). 3

Why Competitive Balance? Competitive Balance is an important concept for professional team sports Creates an uncertainty of outcome nstigates the interest of sport fans ncreased demand for sport events (El-Hodiri & Quirk, 97; Rottenberg,, 956). 4

Quantification of Competitive Balance Quantification of Competitive Balance is a complicating issue (Downward, Dawson, & Dejonghe, 2009; Zimbalist, 2003). Multidimensional concept A variety of different indices exist Econometric studies testing the relative significance of the indices is an area of research relatively undeveloped (Borland & MacDonald, 2003). 5

Why Competitive Balance in European Football? the heartland of football, the only truly global team sport (Gerrard, 2004). Competitive Balance is an important issue for the viability of European football (Michie & Oughton, 2004). Any optimal index may differ from sport to sport (Zimbalist, 2003). European football leagues are complex in structure. 6

Dimensions of Competitive Balance Match Measures the strength difference in match level. Seasonal Measures the relative performance of teams within a season. Between-seasons Captures the relative performance of teams across seasons. 7

Dimensions of Competitive Balance Units of Measurement Match level. % of Points difference of the two teams 2. % of Wins difference 3. Betting odds (taken from bookies) difference 4. Probability odds or difference calculated by a well-fitted prediction model Not found significant, max-attendance when home team has 0.6 win probability. Seasonal Dispersion (or concentration) of points or win percentage (%) of all teams at the end of the season (we use the final league table). Between-seasons Correlation or variance of the difference of ranking or point or win percentage (%) across seasons. 8

Quantification of Seasonal Dimension Existing Seasonal ndices: Ratio of Standard Deviation (RSD) (Noll, 988; Scully, 989). National Measure of Seasonal mbalance (NAMS) (Goossens, 2006). Stadard deviation of win Herfindahl-Hirschman ndex (HH*) (Owen, percentages Ryan, & divided Weatherston, by Standard 2007). the deviation deal Standard of win percentages Deviation divided (SD). Gini Coefficient (Gini) (Utt & Fort, by 2002). the Complete SD=0,5/ 2N ) Relative Entropy (Horowitz, 977). mbalance (WSD) to account for different N. Concentration Ratio. / 2 N WSD= 2 N The area of industrial organization theory offers a wide range of indices measuring the relative industry competitiveness. f we consider a professional football league as industrial sector, the industrial output can be measured by the win percantage, winning share or total points. They have not been developed in the context of complex structure in Europe. They refer to the North American unitary structure with a single prize. 9

ssues Measuring Competitive Balance in European National Leagues Standardization from zero to one => to make comparable leagues with differ number of teams (across different countries and/or seasons/years). Promotion-relegation rule => a large number of between-seasons indices should be excluded or modified. Multiple levels of Competition => Teams are competing not only for the first place but also for other positions leading to European competitions 0

Σύνθετη ομή Τριών Σταδίων (Manasis, Avgerinou, Ntzoufras, & Reade, 20b) ο Στάδιο: Τίτλος του πρωταθλητή NCR Ο Normalized Concentration Ratio for the Champion (NCR ) ερμηνεύει τον βαθμό επικράτησης του πρωταθλητή 2ο Στάδιο: Ευρωπαϊκές διοργανώσεις ΑCR Κ Ο Adjusted Concentration Ratio (ACR ) ερμηνεύει τον βαθμό επικράτησης των πρώτων Κ ομάδων αλλά και το επίπεδο ανταγωνισμού μεταξύ των ομάδων αυτών 3ο Στάδιο: Υποβιβασμός NCR Ι Ο Normalized Concentration Ratio for relegated teams (NCR ) ερμηνεύει τον βαθμό υστέρησης των Ι υποβιβασθεισών ομάδων SCR Ο Special Concentration Ratio (SCR ) ο οποίος είναι περιεκτικός δείκτης, αναφέρεται δηλαδή και στα τρία στάδια με ανάλογη ερμηνεία

Development of Specially Designed ndices The design of the new indices is inspired by the necessity: Quantify the level of competition in each level. Weight ranking positions according to their significance for fans. For the development it is employed the NCR, which can be easily adapted to capture any of the three levels. 2

Normalised Concentration Ratio (NCR ) NCR is the normalization of the widely used CR index. t rangesr from 0-0 and is relatively robust to variation in N and/or. t captures the level of domination by the top teams. P 2 i N i NCR, N /2 2 ( N ) Here we use two points for every win but the index can be easily adjusted for the 3-point 3 system. 3

Why NCR? i P i Captures the number of points for the top- teams Under perfect imbalance CR i P 2 (2N ) Under perfect imbalance NCR NCR i i max min i i P min i P 2 N 2 ( N ) Every team in i-th position wins the following N-i i teams. This is multiplied by 2 times playing to each other and 2 (or 3) the number of points for each win max 22 ( N i) 4N i All teams gain the same number of Points Total Number of points = 2N(N-) Each team wins 2(N-) points Top -teams win 2(N-) min 2 ( N ) ( ) 2 4

5 Normalised Concentration Ratio for the Champion (NCR ) Captures first stage nterpretation: The degree of Champion s domination 2 2 ) ( 2 2 N N P NCR N N P NCR i i

First & Second Stage Team Ranking 2 3 4 5 6 7 8 9 0 0 0 NCR 0.667 NCR 2 0.75 0.75 Average (NCR, NCR 2 ) League A: 36 24 20 8 6 6 4 4 2 0.875 League B: 30 30 20 8 6 6 4 4 2 0.708 6

Adjusted Concentration Ratio (ACR ) Average of NCR for top- teams Captures first & second stage nterpretation: The level of domination by the top teams The level of competition among the top teams ACR NCR w P C i i i i i, w i 2( in i) C ( N ) i N i 7

Relative Significances in ACR for =8 0.3 Relative Significance 0.2 0. 0.0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 Ranking 8

Concentration Ratio for Relegated Teams (NCR ) Captures third stage nterpretation: The degree of weakness of the relegated teams NCR 2 N 2 N N in Pi, N / 2 9

20 Special Concentration Ratio i N N i i i i i i w w w N w N C C P w w P NCR NCR SCR for 3 2, 2, SCR Captures all three stages nterpretation: The level of domination by the top teams The level of competition among the top teams The degree of weakness of the relegated teams

Top teams Bottom teams 2

Moving Averages of lag five for NCR (Champion) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 46 46 43 43 43 44 53 54 ncreased competiveness for champion from 982-992 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season Points adjusted for 6 teams and 2--0 system: 5, 52, 5, 55, 53 22

Moving Averages of lag five for ACR (Top Teams) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 0 Greece England Germany 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season 23

Moving Averages of lag five for NCR (Relegation) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season Μικρότερες τιμές εν σχέση με τους άλλους δείκτες, άρα μεγαλύτερος ανταγωνισμός για τον υποβιβασμό. 24

Moving Averages of lag five for SCR (All Levels) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 0 Greece England Germany 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season Βρέθηκε ότι η τάση είναι σημαντική: Α) Για την Ελλάδα, δευτέρου βαθμού με χαμηλότερο σημείο το 986. Β) Για την Αγγλία, γραμμική αυξητική τάση που φτάνει το 36%. 25

Quantification of Between-seasons Dimension Teams identity matters Two units of measurement: Ranking mobility or change Change in winning percentages or shares Scarcity of applicable indices to European football (Buzzacchi et al., 2003). Due to the promotion relegation rule (open leagues) 26

ndices not applicable to European football ndices of ranking mobility over long periods Relative HH (Hirfindahl-Hirchman index; Eckard, 998) Adjusted HH (Gerrard, 2004) Gini coefficient (Fizel, 997; Quirk & Fort, 997) Markov-based approach (Hadley, Cieka, & rautman, 2005) Hope statistic (aplan, Nadeau, and O Reilly, 20) ndices of winning percentage change across seasons Correlation coefficient (Balfour & Porter, 99) ANOVA-based measure (Eckard, 998) Competitive Balance Ratio (Humphreys, 2002) Linearised Turnover Gain Function (Lenten, 2009) 27

ndices that can be applied in European football G index (Buzzacchi et al., 2003) The modified Adjusted G ndex (ag) is developed with range from 0 to. * ndex of Dynamics DN t (Haan, oning, & van Witteloostuijn, 2002) endall s tau coefficient (τ) (Groot, 2008) Spearman s rho (r s ) (Daly & Moore, 98) 28

Development of specially designed indices A similar process for the seasonal dimension is followed For the development it is employed the Dynamic ndex (DN ) which is a modification of the widely used * index (Haan, oning, & van Witteloostuijn, 2002). DN t DN i r i, t r i, t, N N 2 r: ranking position t captures the ranking mobility of the top teams in two adjacent seasons. t can be correctly adapted to capture any of the levels. 29

Extension for multi-prized league First level (champion) DN r, t ( N r, t ) First & second level Third level (relegation) ADN DN i N in DN r N i r it, it, All three levels => Special concentration index SDN i DN i DN 30

Moving Averages of lag five for DN (Champion) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season 3

Eric Cantona from Leeds United for.2 million UND Wins the title Moving Averages of lag five for DN (Champion) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season Η ManU κέρδισε τα 3 από τα τελευταία Υπάρχουν 22 πρωταθλήματα δύο περιπτώσεις ενώστην δεν Αγγλία 6 November όπου ομάδα 986 που ανέβηκε έπεσε από ποτέ τηνκάτω 2 η κατηγορία, από την τρίτη κέρδισε θέση! το πρωτάθλημα. (Ferguson Hired) Η pswich το 96 και η Nottingham το 997 32

Moving Averages of lag five for DN (Champion) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season Υπάρχει και μια περίπτωση στην Γερμανία όπου ομάδα που ανέβηκε από την 2 η κατηγορία, κέρδισε το πρωτάθλημα, η aiserslauten το 998. 33

Moving Averages of lag five for ADN (Top Teams) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season 34

Moving Averages of lag five for DN (Relegation) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season 35

Moving Averages of lag five for SDN (All Levels) from 959-2008 Value of Compatitive Balance 0,8 0,6 0,4 0,2 Greece England Germany 0 960 964 968 972 976 980 984 988 992 996 2000 2004 2008 Season Βρέθηκε ότι η τάση είναι σημαντική: Α) Για την Ελλάδα, τάση δευτέρου βαθμού με χαμηλότερο σημείο το 987. Β) Για την Αγγλία, γραμμική αυξητική τάση που φτάνει το 30%. Γ) Για την Γερμανία, τάση τρίτου βαθμού με μεγάλη βελτίωση του δέικτη στο τέλος της δεκαετίας του 90. 36

Average competitive balance across Europe 0,8 0,750 959-998 Value of Competitive Balance 0,7 0,6 999-2008 0,575 0,56 0,555 0,558 0,597 0,546 0,568 0,570 0,694 0,579 0,660 0,64 0,702 0,657 0,698 0,5 Sweden Norway Germany France England taly Belgium Greece 37

38