The Market Reaction to the Sporting Performance
of European Football Clubs.
Dion Thomas
10437975
University of Amsterdam, FEB, BsC Finance and Organization June 25, 2015
Abstract: This paper is about the influence of specified match outcomes on the stock returns of seven listed European football clubs. Previous literature shows that wins lead to positive abnormal returns where losses and draws are punished with negative abnormal returns. The analysis is done by using an even study. In this research the findings with respect to negative match outcome, i.e. loss or draw, are in line with the existing literature. The findings concerning the matches won are in contrast with those documented in existing literature.
Outline
1. Introduction………. 3
2. Literature Review……….4
3. Hypotheses……….. 6
4. Data and methodology………..7
4.1. Methodology………... 7
4.1.1. Type of research………... 7
4.1.2. Determining the abnormal return……….. 8
4.1.3. Statistical significance test……….. 9
4.2. Data……….. 9
5. Results………... 10
6. Conclusion………... 13
References………. 15
1. Introduction
On 12th October 1983, Tottenham Hotspurs was the first European football club who went public. In the subsequent years a lot of clubs followed Tottenham Hotspurs. Clubs such as Manchester United, AS Roma, Borussia Dortmund, AFC Ajax, Olympique Lyonnais and many others went public. Not all of them are still public anymore. In the current football business the wealthiest clubs dominates the European top. An IPO was seen as an easy way to obtain capital, which could be invested in for instance attracting players. Those players may strengthen the team and on the long-term this must lead to successful performance and to the related higher revenues. The value created by the organization of a football clubs differs from a normal business organization but Renneboog and Vanbrabant (2002) stated that even football organizations are engaged in commercial activities. However, the main factor determining the organization value is still the on pitch performance. If a club performs well during the season, the popularity will increase. As a result the sales of merchandise and tickets will rise. Not only this kind of revenues will be influenced by the performance of the club. The increased popularity as described above will contribute to the attractiveness of the club for several sponsorship deals. In this paper the effect of this on-pitch performance on the value of the organization is analyzed. The analysis examined if a win lead to a positive abnormal return and if a loss or a draw lead to a negative abnormal return. Besides taking the effect of the specific match outcome into account, this paper researched if the match type has an effect on the value of the abnormal return.
All those questions are answered by using an event study. After collecting all the required data both the expected and the realized returns were calculated. The abnormal returns, which were used to answer our hypotheses, were determined by the difference between the expected and the realized return.
After the introduction the paper starts with a literature review in section two. In the third section the hypotheses are appointed. In section four the data and methodology are presented. The results of the analysis are retrievable in section five. The sixth section of this paper concludes and discuss.
2. Literature Review
This paper analyzes the effect of the on-pitch performance of European football clubs on their share prices. The match played by a club is seen as an event. The match has a positive or a negative outcome in case of respectively a win or a loss/draw. As known most of the supporter-investors have several expectations about the match outcome (Edmans et al., 2007). So the event will have an expected or an unexpected outcome. Chuvakhin (1999) did research to the reaction of the market to several events. Besides the distinction between favourable, unfavourable and expected, unexpected events Chuvakin (1999) makes the distinction between efficient and inefficient markets. The following graphical illustrations explain the market reaction according to a favourable event.
In case of an expected event the efficient market adjust the prices gradually and it will stabilize on the event date. The price in case of an inefficient market will rise even after the event date.
Figure 1. Market reactions to an expected event1
On the other hand, the efficient market will adjust the price to new information directly. The adjustment process takes longer and goes progressively in the inefficient market.
Dobson and Goddard (2004) stated that applying this theory to the football industry in practice is hard due to several characteristics. The football match itself is of course an expected event; it is publicly known when and where the match is going to take place. But it is not clear if the outcome of the event i.e. match is favourable or unfavourable for the club and its underlying stock price. Consequently the effect of an event on the stock price could be misled if the event outcome was not expected. An event, which occurs as expected, should not have any effect on the stock prices, if the market is efficient. Only the unexpected event outcomes should have an effect (Dobson and Goddard, 2004).
The four main studies specified on the market reaction to football games are those from Ashton, Gerrard and Hudson (2003), Benkraiem, Louhichi and Marques (2009), Renneboog and Vanbrabant (2000), Scholtens and Peenstra (2010). The studies of Renneboog and Vanbrabant (2000) and from Asthon et al. (2003) primarily focus on Great Britain. Renneboog and Vanbrabant (2000) used a time frame of three years and focuses on seventeen English clubs. Ashton et al. (2003) focused on the British national soccer team with a time frame of eighteen years. Benkraiem et al. (2009) and Scholtens and Peenstra (2010) put in more diversity by taking a sample of clubs from several European Leagues they used a time frame of respectively one and four years.
Ashton et al. (2003) stated that the sporting performance of England’s national team had a significant effect on the returns of the London Stock exchange for two reasons. First national sporting success creates a so-called ‘feel good factor’ which provide confidence about the future. Second, the commercial importance of international matches and in particular finals is increasing. An efficient stock market will revise some expectations of the potential economic benefits that can be derived from a successful performance of a national sport team. The expectation is that a stock market reaction to qualifying and final matches will be greater than for friendly matches. Dobson (2011) support the findings of Ashton et al. (2003) by quoting that the importance of regular European participation has been enhanced by the rapid growth in the financial rewards available from for instance increasingly lucrative television contracts. The reason for the different impact on stock prices is the difference in the revenues across different type of matches. An international match for example is as mentioned-above associated with much higher revenues than a league match (Renneboog and Vanbrabant, 2000).
Both Renneboog (2000) and Scholtens (2010) find in their analysis a positive abnormal return in case of a win and negative abnormal returns in case of a loss or a draw. The value of the negative abnormal return of a loss exceeds the one from a draw. The abnormal returns depending on the match outcome are asymmetric i.e. the influence of a loss is significant greater than the influence of a win. Those findings from Renneboog (2000) and Scholtens (2010) are confirmed by Bernile and Lyandres (2011).
Analysis National matches International Matches Win Renneboog Scholtens
Benkraiem 1,00%* 0,38%* 0,33% 1,00%** 0,22% - Loss Renneboog Scholtens
Benkraiem -1,40%* -1,14%* 1,90%*** -1,80%* -2,14%* -
Table 1: Abnormal returns on next post-match trading day (*,**,***=significant at respectively 1%, 5% and 10% level)
In contrast to Renneboog (2000) and Scholtens (2010) the findings relating to wins in the analyses of Benkraiem et al. (2009) and Bernile (2011) are not significant. This insignificance is explained by the allegiance bias, founded by Edmans et al. (2007). Supporter investors, who often hold a significant proportion of the listed teams’ capital, consider as a reference that their team will win. In other words, the win constitutes the norm. The expectation is a victory one day before the match and does not reward it the day after. Conversely, this is probably why the market punishes the loss or draw one day after the match
3. Hypotheses
The matches are divided into two subpopulations, the international and national matches. Both type of games have three possible outcomes namely a win, loss or a draw.
Based on the literature review the expectation is that there is a significant influence of the sporting performance on the stock prices of the European listed football clubs. Based on previous findings about the influence of matches won, the first hypothesis is as follows.
H1: A win leads to a positive abnormal return on the first post-match trading day.
The positive abnormal return due to a win arises from the expectations from the fans. The supporter investors, who often hold a significant proportion of the listed teams’ capital, expect a win of their team. If those expectations are not met, the market will punish the organization behind the team with a negative abnormal return. So vice versa the first hypothesis the second hypothesis is as follows. H2: A loss or draw leads to a negative abnormal return on the first
The sample of clubs played in their season a lot of matches. This analyse makes the distinction between two types of matches: the national and the international matches. As seen in the literature review the financial reward of a win in an international match exceeds those of a national match. Therefore the expectation is that the influence on the stock prices in an international match exceeds the influence of national match.
H3: The influence of international matches on stock prices exceeds the influence of national matches.
4. Methodology and Data
4.1. Methodology 4.1.1. Type of research
The analysis is done with the aid of an event study. An event study is a methodology to analyse the influence of a specific event on underlying stock prices. In this case a football match and its outcome are seen as the event. This outcome is simply a win, loss or a draw. The analysis consists of two event studies, namely one for the national matches and one for the international matches.
According to Benkraiem et al. (2009) an event study consist out of three main steps: 1) An estimation needs to be established to see what the return would have
been if the event would not have occurred.
2) The estimated value needs to be compared to the actual observed value in order to calculate the abnormal return.
3) Describing the statistical analysis and the establishment of the significance of the results to find out if the abnormal effect is significant.
About the length of the event period Scholtens and Peenstra (2010) stated that it is useful to use a short event period. They stated that given the large number of matches and using a short event period, it is not possible to arrive at an estimation period that does not include event-related returns of the football teams. Therefore in this analysis an event period of one single day is used. This is the period between the trading day preceding match-day and the first day post match-day. Where the trading day preceding match-day is seen as t=0 and the trading day post match-day is seen as t=1. Using this extremely short event period is not uncommon. Scholtens and Peenstra (2010) used this short event period to avoid overlapping periods, which could result in misinterpretations of the analysis outcome. Dyckman et al. (1984) also advise to look for a short period to be able to focus on a direct result of an event.
4.1.2. Determining the abnormal return
To determine the abnormal return, first the expected and the realized return of the share need to be determined. The realized return is calculated as follows:
Rj,t = (Pt+1 – Pt) / Pt (1)
where;
- Pt+1 is the stock prices post match-day
- Pt is the stock prices pre match-day
The Capital Asset Pricing Model is used to compute the expected return, E[Ri,t] . The
CAPM is described as:
E[Ri,t] = E[Rf,t] + βi ( E[Rm,t] - E[Rf,t] ) (2)
where;
- E[Rf,t] is the risk-free rate
- (E[Rm,t] - E[Rf,t]) is the market risk premium
- βi is the firm specific risk i.e. beta
The CAPM-model consists of the above-mentioned variables. Those variables are derived as follows:
-‐ The risk-free rate is a benchmark rate given by a sovereign bond. In the US those are Treasury Bonds. While the whole sample in this analysis consists of European clubs the risk-free rate is derived from the rate of interest of a German bond with a maturity of 30 years.
-‐ The market return is derived from the Euro Stoxx-100, for the same reason as mentioned above the European variant of the American S&P 500 is used.
-‐ Beta is computed by de covariance between the market return and the return of the asset divided by the variance of the market. Those betas are valued on daily return base over the period in which the events occur and determined by a simple OLS-regression.
If both the realized return and the expected return are determined by using respectively formula (1) and (2) the abnormal return can be computed as follows:
4.1.3. Statistical significance tests
To test whether the abnormal returns differ significant from zero Renneboog and Vanbrabant (2000) used the t-test with a Student T-distribution for the data. The formulas used are displayed below.
(4)
where; -‐
-‐
-‐
To test whether the difference between the national and international abnormal return is significant, the paired t-test is used.
According to Brown and Warner (1980) daily returns deviate more from the normal distribution than monthly returns. They stated that the Central Limit Theorem shows that the distribution of abnormal returns converges towards a normal distribution when the number of shares increased if the abnormal returns are independent and identically distributed samples from a distribution with finite variance. They also quoted that an eventually non-normality of the daily returns does not have a significant impact on the methodology of an event study.
4.2. Data
In this analysis there are used two types of data. The football match related data and the stock market related data. The data concerning the football matches comes from the European Football Database. This website writes up the statistics (scores, transfers, dates etc.) of all the national football associations. From the European Football Database are extracted the data of seven different European listed football clubs for both the national as international matches in the 2010-2011 season. This gives 308 matches of which 68 were international and 240 national matches. Over this sample the teams won 166 matches, lost 78 and 64 matches ended in a draw. Those matches were spread over several match days. A match day could exist out of several dates, not all the matches in a particular match day were played at one day. The national matches mostly were played in the weekend when the stock market is closed. The observations with respect to the returns are determined the trading days
pre and post match day. So the trading days for a match played in the weekend are Friday and Monday. For midweek played matches on for instance Wednesday the trading days used are Wednesday and Thursday.
The stock market data, which are used to calculate the returns, are obtained from Yahoo Finance. Below you will find the sample of clubs, their stock symbol and the exchange on which the clubs are listed.
Club Country Symbol Exchange
AFC AJAX The Netherlands AJAX.AS Amsterdam
Benfica SL Portugal SLBEN.LS Lisbon
Borussia Dortmund Germany BVB.DE Xetra
FC Copenhagen Denmark PARKEN.CO Copenhagen
Olympique Lyonnais France OLG.PA Paris
AS Roma Italy ASR.MI Milan
Galatasaray SK Turkey GSRAY.IS Istanbul
Table 2. Sample of the European listed clubs
5. Results
In section three of this paper there were made three several hypotheses about the influence of a match outcome on the stock prices at the post match trading day of seven European listed football clubs. Those outcomes were specified into three, namely a win, a loss or a draw. The matches were split up into two parts, the international and national matches. Based on the literature review the expectation stated in the hypothesis is, that a win leads to a positive abnormal return and vice versa a loss or a draw leads to a negative abnormal return. In table 3 and 4 the results of the event study are displayed.
National Matches Abnormal Return t-statistic*
Win -2,94%*** 3,10
Loss -5,89%** 2,43
Draw -4,80%*** 3,40
Table 3. Abnormal returns on post national matches trading days. *The t-statistic values are absolute. (*,**,***=significant at respectively 10%, 5% and 1% level)
The first hypothesis in this analysis stated the following:
H1: A win leads to a positive abnormal return on the first post-match trading day.
The results displayed in table 3 shows that the first hypothesis is rejected. A win lead to a negative abnormal return of 2,94%. This result could be seen as curiously, but
can be explained by a combination of two facts. First is the ‘allegiance bias’ founded by Edmans et al. (2010). Supporter investors, who often hold a significant proportion of the listed teams’ capital, consider as a reference that their team will win. In other words, the win constitutes the norm. Conversely, it expects a victory one day before the match and does not reward it the day after. If a win is not rewarded the day after the realized return is close to zero.
Second the abnormal return is expressed as the difference between the realized return and the expected return. As described in the methodology part of this research the expected return was based on the CAPM-model. The average of the expected returns of the listed clubs is 4,12%. So a win leads on average to a positive realized return but this return is smaller than the expected return and therefore the abnormal return is negative. Chuvakhin (1999) confirms this by quoting that an expected event will not have a positive effect on the stock prices. A win is seen as an expected event according to Edmans et al. (2007).
The second hypothesis stated the following:
H2: A loss or draw leads to a negative abnormal return on the first post-match trading day
The results displayed in table 3 show that the second hypothesis is accepted. A loss or a draw gives respectively a negative abnormal return of 5,89% and 4,80%. Both values are significant at respectively a five and one percent level with t-values of respectively 2,43 and 3,40.
International Matches Abnormal Return t-statistic*
Win -3,80%* 1,85
Loss -6,19%* 1,72
Draw -4,31% 0,18
Table 4. Abnormal returns on post international matches trading days. *The t-statistic values are absolute. (*,**,***=significant at respectively 10%, 5% and 1% level).
The third hypothesis in this research stated the following:
H3: The influence of international matches on stock prices exceeds the influence of national matches.
Comparing table 3 and table 4, between the national and international matches gives for a win, loss or a draw respectively a difference of 0,86%, 0,30% and -0,49%. The significance values are displayed in table 5.
Differences Abnormal Return t-statistic*
Win 0,86%** 2,14
Loss 0,30%*** 2,90
Draw -0,49% 0,08
Table 5. Differences in abnormal returns on post trading days between international and national matches. *The t-statistic values are absolute. (*,**,***=significant at respectively 10%, 5% and 1% level).
For a loss the hypothesis is accepted. As expected, the negative abnormal return as results of a loss in an international match exceeds the negative abnormal return of a national match.
In case of a win again the results are curious. The absolute value of the abnormal return in case of an international match exceeds as expected the absolute value of the abnormal return in case of a national match. However, the positive realized return of an international match is smaller than the realized return of a national match. As described above the international leagues goes along with higher revenues. The expectations therefore were that a win in an international match would lead to a larger positive abnormal return compared to national matches. However, the abnormal return is negative and is larger for the international matches compared to the national matches. Consequently, the realized return of the international win is smaller than the national win. This cannot be explained by the literature review. An explanation based on economic intuition could be that a win in the national league brings the organization closer to replacing itself to the international league in the next season. Participation in the international competitions goes along with higher revenues due to the existence of starting premiums. The revenues of replacing for another international season are higher than the revenues concerning reaching the next round could be a reason for the higher abnormal return with respect to the national matches.
For a draw the findings are not significant so further explanations or statements are not relevant.
6. Conclusion
This research analyzed the influence of a match outcome on the stock prices of seven listed European football clubs. A match has three possible outcomes, a win, a loss or a draw. Using an event study the influence of a specified match outcome was determined for both national and international matches. Besides analysing the effect of a specified outcome this paper examined if there was a difference in the effects between national and international matches.
In case of a win in a national match the findings are not in line with the reviewed literature from Bekraiem et al. (2009), Scholtens (2010) and Renneboog (2000) but may be explained by the theories from Dobson (2004), Chuvakhin (1999) and Edmans et al. (2007). They stated that an expected match outcome would not have any effect on the share price. As Edmans et al. (2007) described in their paper, the supporter investors often hold a significant proportion of the listed teams’ capital, consider as a reference that their team will win. In other words, the win constitutes the norm. So if a team wins their match, it is seen as normal and there will be a return that is not larger than the expected return.
The findings about a loss or a draw in national matches are in line with the findings Benkraiem et al. (2009), Scholtens (2010) and Renneboog (2000). All of these researches find a negative abnormal return as a result of a loss. However, the abnormal returns in this analysis are larger than the values founded in the reviewed literature. A different time window or a different way of determining the expected returns, which are used, could explain this.
In the last part of this paper the effects of the international and national matches are compared. Based on studies of Ashton et al. (2010) the expectation was that the effect of international matches is larger than the effect of national matches.
For the matches with a loss as outcome the effect is indeed larger after an international match. This could be explained by the findings of Asthon et al. (2010) and Renneboog (2000). They both stated that the revenues in the international leagues are much higher than the revenues in the national leagues. A loss in an international match lead to the larger loss of revenues and the market will punish the organization harder than in national matches.
The results concerning the difference in case of a win are not in line with the expectations. The negative abnormal return of international matches is larger than the negative abnormal return from national matches. With respect to the theory of Ashton et al. (2010) the expectation was the reverse of the findings. The findings are explained by an economic intuition; the revenue of replacing to another European tournament, obtained by good performance in the national league, are higher than the revenue of continuing the European season, obtained by good performance in the international leagues.
About the international matches with draw as outcome there is no conclusion possible. The results are insignificant. An explanation for the insignificance could be the small number of matches ended in a draw.
Most of the findings in this research are in line with the existing literature. The analysis confirmed some expectations but also raise questions and ambiguities. Those questions and ambiguities can be solved by extended research. For instance a research with a wider time window with more matches played or adding more listed clubs to the sample can solve the ambiguities.
References
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Appendix.
Calculations with respect to the abnormal return and its standard deviation. Legenda:
-‐ SOM: total AR during 1 match day -‐ AVERAGE: AR per match
-‐ T: number of match day
-‐ CUM AVERAGE AR: is the cumulative of the average AR
-‐ D.AVERAGE AR2: is the double average calculated with (sub) formula (4.3)
National matches
Matches won:
SOM AVERAGE AR 1/T CUM AVERAGE AR D.AVERAGE AR2 (AR-AR2)^2
-0,0595 -0,0595 1,0000 -0,0595 -0,0595 0,0000 -0,1041 -0,0347 0,5000 -0,0942 -0,0471 0,0002 -0,1106 -0,0221 0,3333 -0,1163 -0,0388 0,0003 -0,0764 -0,0191 0,2500 -0,1354 -0,0339 0,0002 -0,0213 -0,0036 0,2000 -0,1390 -0,0278 0,0006 -0,1524 -0,0305 0,1667 -0,1695 -0,0282 0,0000 0,0230 0,0058 0,1429 -0,1637 -0,0234 0,0008 -0,0799 -0,0266 0,1250 -0,1903 -0,0238 0,0000 -0,1222 -0,0244 0,1111 -0,2148 -0,0239 0,0000 -0,0633 -0,0158 0,1000 -0,2306 -0,0231 0,0001 -0,1605 -0,0267 0,0909 -0,2573 -0,0234 0,0000 0,0951 0,0238 0,0833 -0,2336 -0,0195 0,0019 -0,2199 -0,0440 0,0769 -0,2776 -0,0214 0,0005 -0,2250 -0,0563 0,0714 -0,3338 -0,0238 0,0011 -0,0648 -0,0162 0,0667 -0,3500 -0,0233 0,0001 -0,1642 -0,0328 0,0625 -0,3829 -0,0239 0,0001 -0,2067 -0,0413 0,0588 -0,4242 -0,0250 0,0003 -0,1242 -0,0207 0,0556 -0,4449 -0,0247 0,0000 -0,0376 -0,0125 0,0526 -0,4574 -0,0241 0,0001 -0,1244 -0,0249 0,0500 -0,4823 -0,0241 0,0000 -0,1204 -0,0301 0,0476 -0,5124 -0,0244 0,0000 -0,1234 -0,0411 0,0455 -0,5535 -0,0252 0,0003 -0,1043 -0,0522 0,0435 -0,5462 -0,0237 0,0008 -0,1294 -0,0259 0,0417 -0,6316 -0,0263 0,0000 -0,1285 -0,0643 0,0400 -0,6959 -0,0278 0,0013 -0,1794 -0,0449 0,0385 -0,7407 -0,0285 0,0003 -0,2321 -0,0580 0,0370 -0,7987 -0,0296 0,0008 -0,0836 -0,0279 0,0357 -0,8266 -0,0295 0,0000 -0,1084 -0,0271 0,0345 -0,8537 -0,0294 0,0000 -0,1183 -0,0394 0,0333 -0,8932 -0,0298 0,0001 -0,0409 -0,0204 0,0323 -0,9136 -0,0295 0,0001 -0,2879 -0,0576 0,0313 -0,9712 -0,0303 0,0007 -0,2149 -0,0716 0,0303 -1,0428 -0,0316 0,0016 -0,1079 -0,0216 0,0294 -1,0644 -0,0313 0,0001 -0,0480 -0,0480 0,0286 -1,1124 -0,0318 0,0003 0,0000 - 0,0278 -1,1124 -0,0309 - 0,0000 - 0,0270 -1,1124 -0,0301 - -0,0618 -0,0309 0,0263 -1,1433 -0,0301 0,0000 -4,0882 -1,1433 0,0125
Matches lost:
SOM AVERAGE 1/T
CUM AVERAGE
AR D.AVERAGE AR2 (AR-AR2)^2
-0,2347 -0,0782 1,0000 -0,0782 -0,0782 0,0000 -0,1624 -0,0406 0,5000 -0,1188 -0,0594 0,0004 0,0000 0,3333 -0,1188 -0,0396 -0,1563 -0,0391 0,2500 -0,1579 -0,0395 0,0000 0,0000 0,2000 -0,1579 -0,0316 -0,1279 -0,0426 0,1667 -0,2005 -0,0334 0,0001 -0,0825 -0,0412 0,1429 -0,2418 -0,0345 0,0000 -0,1102 -0,0551 0,1250 -0,2968 -0,0371 0,0003 0,0000 0,1111 -0,2968 -0,0330 0,0395 0,0395 0,1000 -0,2573 -0,0257 0,0043 -0,0541 -0,0541 0,0909 -0,3114 -0,0283 0,0007 -0,0573 -0,0573 0,0833 -0,3687 -0,0307 0,0007 -0,0430 -0,0430 0,0769 -0,4118 -0,0317 0,0001 -0,1762 -0,0587 0,0714 -0,4705 -0,0336 0,0006 0,0000 0,0667 -0,4705 -0,0314 -0,0750 -0,0750 0,0625 -0,5455 -0,0341 0,0017 -0,1301 -0,1301 0,0588 -0,6756 -0,0397 0,0082 0,0000 0,0556 -0,6756 -0,0375 -0,1207 -0,0604 0,0526 -0,7360 -0,0387 0,0005 -0,0934 -0,0467 0,0500 -0,7827 -0,0391 0,0001 -0,1160 -0,0580 0,0476 -0,8406 -0,0400 0,0003 -0,0358 -0,0358 0,0455 -0,8764 -0,0398 0,0000 -0,1095 -0,0548 0,0435 -0,8529 -0,0371 0,0003 -0,0480 -0,0480 0,0417 -0,9791 -0,0408 0,0001 -0,1546 -0,0515 0,0400 -1,0307 -0,0412 0,0001 -0,2299 -0,0575 0,0385 -1,0881 -0,0419 0,0002 -0,0246 -0,0246 0,0370 -1,1127 -0,0412 0,0003 -0,0982 -0,0491 0,0357 -1,1618 -0,0415 0,0001 0,0000 0,0345 -1,1618 -0,0401 0,0000 0,0333 -1,1618 -0,0387 -0,1762 -0,0441 0,0323 -1,2059 -0,0389 0,0000 -0,0437 -0,0437 0,0313 -1,2496 -0,0390 0,0000 -0,4236 -0,1412 0,0303 -1,3908 -0,0421 0,0098 0,0000 0,0294 -1,3908 -0,0409 -0,0455 -0,0455 0,0286 -1,4363 -0,0410 0,0000 0,0000 0,0278 -1,4363 -0,0399 -0,0956 -0,0956 0,0270 -1,5319 -0,0414 0,0029 0,0000 0,0263 -1,5319 -0,0403 -3,1854 -1,5319 0,0318
Matches draw: SOM AVERAGE 1/T CUM AVERAGE
AR D. AVERAGE AR2 (AR-AR2)^2
-0,1444 -0,0481 1,0000 -0,0481 -0,0481 0,0000 0,0000 0,0000 0,5000 -0,0481 -0,0241 -0,0953 -0,0477 0,3333 -0,0958 -0,0319 0,0002 0,0000 0,0000 0,2500 -0,0958 -0,0239 -0,0347 -0,0347 0,2000 -0,1305 -0,0261 0,0001 0,0000 0,0000 0,1667 -0,1305 -0,0217 -0,0303 -0,0303 0,1429 -0,1608 -0,0230 0,0001 -0,0809 -0,0405 0,1250 -0,2013 -0,0252 0,0002 -0,0695 -0,0347 0,1111 -0,2360 -0,0262 0,0001 -0,1032 -0,0516 0,1000 -0,2876 -0,0288 0,0005 0,0000 0,0000 0,0909 -0,2876 -0,0261 -0,0736 -0,0368 0,0833 -0,3244 -0,0270 0,0001 0,0000 0,0000 0,0769 -0,3244 -0,0250 0,0000 0,0000 0,0714 -0,3244 -0,0232 -0,1367 -0,0456 0,0667 -0,3700 -0,0247 0,0004 -0,0448 -0,0448 0,0625 -0,4148 -0,0259 0,0004 -0,0351 -0,0351 0,0588 -0,4499 -0,0265 0,0001 -0,0389 -0,0389 0,0556 -0,4888 -0,0272 0,0001 -0,1381 -0,0691 0,0526 -0,5579 -0,0294 0,0016 0,0000 0,0000 0,0500 -0,5579 -0,0279 -0,0528 -0,0528 0,0476 -0,6107 -0,0291 0,0006 -0,1521 -0,0507 0,0455 -0,6614 -0,0301 0,0004 -0,1544 -0,0515 0,0435 -0,6647 -0,0289 0,0005 -0,0601 -0,0601 0,0417 -0,7730 -0,0322 0,0008 -0,0828 -0,0414 0,0400 -0,8144 -0,0326 0,0001 0,0000 0,0000 0,0385 -0,8144 -0,0313 -0,1215 -0,0607 0,0370 -0,8751 -0,0324 0,0008 -0,1007 -0,0503 0,0357 -0,9255 -0,0331 0,0003 -0,1702 -0,0567 0,0345 -0,9822 -0,0339 0,0005 -0,2093 -0,0698 0,0333 -1,0520 -0,0351 0,0012 0,0000 0,0000 0,0323 -1,0520 -0,0339 0,0000 0,0000 0,0313 -1,0520 -0,0329 0,0000 0,0000 0,0303 -1,0520 -0,0319 0,0000 0,0000 0,0294 -1,0520 -0,0309 0,0000 0,0000 0,0286 -1,0520 -0,0301 -0,0798 -0,0399 0,0278 -1,0919 -0,0303 0,0001 -0,0451 -0,0451 0,0270 -1,1370 -0,0307 0,0002 0,0000 0,0000 0,0263 -1,1370 -0,0299 -2,2545 -1,1370 0,0094
International matches
Matches won:
Matches lost:
SOM AVERAGE AR 1/T CUM AVERAGE AR D.AVERAGE AR2 (AR-AR2)^2
0,0000 0,0000 1,0000 0,0000 0,0000 0,0000 0,0000 0,5000 0,0000 0,0000 -0,0704 -0,0704 0,3333 -0,0704 -0,0235 0,0022 0,0000 0,0000 0,2500 -0,0704 -0,0176 -0,1199 -0,0599 0,2000 -0,1303 -0,0261 0,0011 -0,0898 -0,0449 0,1667 -0,1752 -0,0292 0,0002 -0,1502 -0,0376 0,1429 -0,2128 -0,0304 0,0001 -0,0813 -0,0406 0,1250 -0,2534 -0,0317 0,0001 -0,2122 -0,0531 0,1111 -0,3064 -0,0340 0,0004 -0,2155 -0,1078 0,1000 -0,4142 -0,0414 0,0044 -0,1756 -0,0878 0,0909 -0,5020 -0,0456 0,0018 -0,0816 -0,0408 0,0833 -0,5428 -0,0452 0,0000 -0,0494 -0,0494 0,0769 -0,5922 -0,0456 0,0000 -0,0366 -0,0366 0,0714 -0,6288 -0,0449 0,0001 0,0000 0,0000 0,0667 -0,6288 -0,0419 0,0000 0,0000 0,0625 -0,6288 -0,0393 0,0000 0,0000 0,0588 -0,6288 -0,0370 -0,1876 -0,2024 0,0556 -0,8312 -0,0462 0,0244 -1,4701 -0,8312 0,0348 SOM AVERAGE AR 1/T CUM AVERAGE
AR D.AVERAGE AR2 (AR-AR2)^2
0,0000 0,0000 1,0000 0,0000 0,0000 0,0000 -0,0873 -0,0436 0,5000 -0,0436 -0,0218 0,0005 -0,0429 -0,0429 0,3333 -0,0865 -0,0288 0,0002 -0,0828 -0,0276 0,2500 -0,1142 -0,0285 0,0000 -0,1414 -0,0354 0,2000 -0,1495 -0,0299 0,0000 -0,1212 -0,0404 0,1667 -0,1899 -0,0317 0,0001 -0,0320 -0,0320 0,1429 -0,0320 -0,0046 0,0008 -0,0837 -0,0419 0,1250 -0,2637 -0,0330 0,0001 -0,1382 -0,0691 0,1111 -0,3329 -0,0370 0,0010 0,0113 0,0113 0,1000 -0,3216 -0,0322 0,0019 -0,0559 -0,0280 0,0909 -0,3495 -0,0318 0,0000 -0,1921 -0,0640 0,0833 -0,0920 -0,0077 0,0032 -0,0358 -0,0358 0,0769 -0,4493 -0,0346 0,0000 0,0000 0,0000 0,0714 -0,4493 -0,0321 0,0267 0,0267 0,0667 -0,4226 -0,0282 0,0030 0,0000 0,0000 0,0625 -0,4226 -0,0264 -0,0511 -0,0511 0,0588 -0,4737 -0,0279 0,0005 0,0000 0,0000 0,0556 -0,4737 -0,0263 -1,0264 -0,4737 0,0113
Matches draw:
SOM AVERAGE AR 1/T CUM AVERAGE AR D.AVERAGE AR2 (AR-AR2)^2
-0,1635 -0,0545 1,0000 -0,0545 -0,0545 0,0000 -0,0351 -0,0351 0,5000 -0,0896 -0,0448 0,0030 -0,0441 -0,0220 0,3333 -0,1117 -0,0372 0,0080 -0,0324 -0,0324 0,2500 -0,1440 -0,0360 0,0125 0,0000 0,0000 0,2000 -0,1440 -0,0288 -0,0305 -0,0305 0,1667 -0,1745 -0,0291 0,0207 -0,0901 -0,0901 0,1429 -0,2646 -0,0378 0,0305 -0,0984 -0,0492 0,1250 -0,3138 -0,0392 0,0700 0,0000 0,0000 0,1111 -0,3138 -0,0349 -0,1096 -0,0548 0,1000 -0,3686 -0,0369 0,0985 -0,0352 -0,0352 0,0909 -0,4037 -0,0367 0,1358 -0,0297 -0,0297 0,0833 -0,4334 -0,0361 0,1630 0,0000 0,0000 0,0769 -0,4334 -0,0333 -0,0151 -0,0151 0,0714 -0,4485 -0,0320 0,1878 0,0000 0,0000 0,0667 -0,4485 -0,0299 -0,0495 -0,0495 0,0625 -0,4980 -0,0311 0,2011 0,0000 0,0000 0,0588 -0,4980 -0,0293 0,0000 0,0000 0,0556 -0,4980 -0,0277 -0,7330 -0,4980 0,9309
Significance test: differences between national and international matches:
International match AR S(AR) Var(AR)
Win -0,0380 0,0204 0,0004 Loss -0,0619 0,0381 0,0014 Draw -0,0431 0,2340 0,0548 National Match Win -0,0294 0,0095 0,0001 Loss -0,0590 0,0276 0,0008 Draw -0,0480 0,0208 0,0004 Combined S(AR) Win 0,0040 Loss 0,0010 Draw 0,0568 Difference t-value Win -0,0086 -2,1427 Loss -0,0029 -2,9098 Draw 0,0048 0,0853
