Home advantage in speed skating: Evidence from

Journal of Sports Sciences, April 2005; 23(4): 417 – 427

Home advantage in speed skating: Evidence from individual data

RUUD H. KONING

Downloaded by [University of Groningen] at 01:23 09 January 2012

Department of Econometrics, University of Groningen, Groningen, The Netherlands

Abstract Home advantage is a well-documented phenomenon in many sports. Home advantage has been shown to exist for team sports (soccer, hockey, football, baseball, basketball) and for countries organizing sports tournaments like the Olympics and World Cup Soccer. There is also some evidence for home advantage in some individual sports, but there is a much more limited literature. This paper addresses the issue of home advantage in speed skating. From a methodological point of view, it is difficult to identify home advantage, because skaters vary in their abilities and the conditions of tournaments vary. There is a small but significant home advantage using a generalized linear mixed model, with random effects for skaters and fixed effects for skating rinks and seasons. Even though the home advantage effect exists, it is very small when compared to variation in skating times due to differences of rinks and individual abilities.

Keywords: Home advantage, linear mixed model, random effects, speed skating

Introduction Home advantage is a well-documented phenomenon in many sports. A significant volume of research has been published documenting its existence, and quantifying its effect on the outcome of sports contests. Home advantage has been shown to exist for individual sports (alpine skiing), team sports (soccer, hockey, football, baseball, basketball) and for countries organizing sports tournaments like the Olympics and World Cup Soccer. Literature on home advantage in sports is reviewed in Nevill and Holder (1999). Home advantage is usually attributed to four factors: crowd support, familiarity with local conditions, reduced travel time for home athletes and, finally, the rule factor (Nevill & Holder, 1999). These factors are of different relevance for different sports, and are examined later in detail. The main aim of this paper is to test for the existence of home advantage in speed skating. A comparison is also made of the magnitude of home advantage, if any, to other sources of variation in skating times. The case of speed skating is interesting for several reasons. First, it is an individual sport. Most research on home advantage has concentrated on team sports; Bray and Carron (1993), Holder and Nevill (1997) and Balmer, Nevill and Williams (2003) are notable exceptions. Bray and Carron (1993) reported the existence of home advantage in

alpine skiing, and Holder and Nevill (1997) found sparse evidence in tennis and golf. Balmer et al. (2003) found highly significant home advantage in boxing and gymnastics, sports that are subjectively judged. Invariably, individual results are not obtained from a balanced competition schedule, which complicates estimation of the home advantage effect. In a balanced competition schedule, all opponents are played in a home and away contest, and home advantage can be estimated by comparing performance in home and away games. On the other hand, individual results are typically obtained through tournaments, contests that are held in a fixed location. During another tournament, in a different location, a different set of players may meet. Are Dutch tennis players successful in a tournament in Holland because of home advantage, or because no foreign world-class players compete in that particular tournament? Second, skating performances are rated with an absolute measure of performance – the time skated – so performances are rated on a ratio scale and not on some ordinal scale as is often the case in judged sports. Third, there is a unique data set with multiple measurements per skater within and between seasons, with skaters skating different distances. This allows us to identify home advantage without imposing very strong parametric assumptions on the statistical model, while at the same time allowing for different abilities of skaters.

Correspondence: R. H. Koning, Department of Econometrics, University of Groningen, Post Box 800, 9700 AV Groningen, The Netherlands. Email: [email protected]. ISSN 0264-0414 print/ISSN 1466-447X online # 2005 Taylor & Francis Group Ltd DOI: 10.1080/02640410400021625

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The framework of this paper is as follows. I first discuss speed skating and the possible role of home advantage. A statistical model of speed skating results. Identification and estimation of a home advantage effect is then proposed.


Speed skating and home advantage Skating is a winter sport with a long history. In fact, the International Skating Union was founded in 1893 and is the oldest governing international winter sport federation. Continuous progress has improved the results of skaters. The first world record over 1500 m was skated on a frozen lake near Groningen, The Netherlands, by a skater wearing woolen clothes. The last world record at this distance was skated in the high-tech skating rink of Salt Lake City, which is at a high altitude and has a covered roof. The special quality of the Salt Lake City skating rink is examined in detail by Reese (2003). Moreover, modern skating suits are aerodynamic, having been developed in wind tunnels; the quality of skates has improved immensely as well. A concise history of skating, and especially a discussion of the role of technological progress, can be found in Kuper and Sterken (2003b). Modern speed skating usually takes place on refrigerated ovals. Currently, only a few nonrefrigerated ovals are used for international competitions. Skaters start at the firing of a starting gun (which starts the electronic timer) and skate 400 m laps in one direction. Each lap they change from the inside lane to the outside lane, or vice versa. The time skated is measured when they pass the finish line, crossing a laser beam (this equipment is also used to measure the time for intermediate laps). Skaters compete against each other during tournaments or events. Some of these events are national events (the Dutch or Norwegian championship), and because within a country only a few skating rinks exist, it is not reasonable to search for home advantage for a particular skater within a country. Variation of performances will be due to variation in the quality of the skaters and the different rinks in a country, not to any perceived home advantage. However, skaters also meet at international competitions. The most important international competi-tions are the World Cup (a series of meetings in different venues, culminating in the World Cup Final), the World Championship Distances, the World Championship Sprint, the all-round European and World Championships, and the Olympic Winter Games. These international meetings are held in different locations

throughout the world and therefore provide a suitable basis for examining the existence of national home advantage. This paper does not use data for any all-round tournaments, where skaters have to skate four distances in 2 – 3 days. These tournaments are very different from contests where a skater can focus on one or two distances. Therefore, only data for World Cup meetings, World Championship Distances and Olympic Winter Games are used. Distances skated by men are 500 m, 1000 m, 1500 m, 5000 m and 10,000 m. Women skate 500 m, 1000 m, 1500 m, 3000 m and 5000 m. Both for men and women, the longest distance is highly specialized, with only a few skaters competing for the top positions. Since World Cup meetings, the World Championship Distances and the Olympic Winter Games are held in different countries, there may be some identifiable home advantage for skaters of the country hosting the event. Nevill and Holder (1999) discuss the factors contributing to home advantage in detail. They distinguish between four factors: crowd support, familiarity with local conditions, reduced travel time for home athletes and, finally, the rule factor. To what extent are these factors applicable to speed skating? Crowd support can help an athlete to perform better than anticipated. In skating, crowds tend to cheer for most skaters, although it is likely that crowds will support local favourites the most. Antagonism between crowds and skaters is rare. Crowd support could, in theory, influence decisions by referees. Referees in skating have to make two sorts of decisions: whether or not the skater moved before the firing of the starting gun, and whether or not the skater from the inner lane gave way to the skater coming from the outer lane during the changeover of lanes. Both types of decision are usually uncontroversial and no skaters are disqualified. The most frequent cause of a skater not finishing is a fall during the race. Familiarity with local conditions is potentially a more important factor in determining home advantage. This was stressed in a personal conversation with a Dutch Olympic gold medallist: ‘‘it takes 3 days to get used to the ice and skating rink at high altitude. Canadians and Americans have a great advantage in that respect’’. Skating rinks are located at different altitudes, and some are covered while others are not. There is also a difference in curvature of different rinks. Some ovals have tighter bends than others. These effects will be represented by rink-specific effects in the empirical analysis. A skater who is used to training frequently at a high-speed skating rink (for


Home advantage in speed skating example, the Olympic Oval in Calgary, Canada) may develop skills that other skaters lack from training at lower-speed rinks. In particular, skating bends at high speed is difficult and requires a lot of practice. Such techniques are best learnt at highspeed skating rinks, which provides an advantage to skaters who can train on such rinks regularly. For this reason, skaters from countries at low altitude have training sessions at such high-speed rinks in the summer or early in the season. According to skating folklore, ‘‘power skaters’’ perform well at covered and uncovered low-altitude skating rinks, while ‘‘flyers’’ are the best performers under the controlled conditions of high-altitude covered rinks. Reduced travel time for home athletes is unlikely to be important for the home advantage. During the season, most skaters participate in the same events and hence they are subject to the same time differences. Skating events take place at the weekend, so the rest of the week can be used for travel and overcoming travel fatigue. Finally, it is unlikely that the rules benefit home skaters. Rules can be manipulated to benefit a skater in two ways. First, the ice is cleaned at regular intervals, and there is a small advantage to skating on a clean rink. However, the decision when to clean the ice is made by the referee(s) and a representative of the International Skating Union. This decision is communicated to the coaches before the order of pairs of skaters is known. During the event, it may be decided that more frequent treatments of the rink are necessary, and this decision could benefit some skaters and harm others. The second important issue is the order of skating. Most skaters prefer to skate last, so that they know the times of their competitors. The order of skating is determined as follows. Skaters are allocated to groups based on their times in previous events, or on their performance at other distances during the same event. The order and pairing is then determined by a draw. This leaves little room for manipulation to benefit a home skater. In summary, there are two possible sources of home advantage in skating: crowd support and familiarity with the track and skating at that particular altitude. Whether these sources of home advantage are statistically significant or empirically relevant in determining the outcome of a skating contest is, however, not clear. Balmer et al. (2003) compared home advantage for different sports at Summer Olympic Games. They found that the role, of referees and jurys are important sources of home advantage. Considering the very marginal importance of refereeing decisions in skating contests, home advantage, if any, is likely to be small.

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An empirical model of speed-skating results This section focuses on the measurement of home advantage in speed skating and tests whether it is statistically significant. The analysis is based on a database of finishing times of participants in World Cup meetings, World Championship Distances and Olympic Winter Games from 1986 – 87 to 2002 – 03. The data relate to both men and women skaters. The data are for 17 seasons, 21,963 times for men skaters and 15,905 times for women skaters. I removed observations that were outliers, which usually occurred when a skater fell during the race. All skating times were transformed to their 500 m equivalent, a common means of making different distances comparable. The average 500 m skating time was the dependent variable and was used to assess the existence and magnitude of home advantage. From now on, I omit the dimension of our measure of performance, so when I refer to ‘‘speed’’ or ‘‘time’’, I mean ‘‘time (in seconds) per 500 m’’. Most empirical studies of home advantage consider either team data or national aggregated data. Usually, evidence of home advantage is found in a win percentage that exceeds 50%, based on aggregate data (see the review by Nevill & Holder, 1999). As discussed in the Introduction, this assumes that a balanced competition schedule is played. If an unbalanced competition is played, or if home advantage is expected to vary between teams, a better approach is to separate home advantage and team quality, for example along the lines of Clarke and Norman (1995). Their model was applied to soccer results, and home advantage was measured as the expected difference in goals scored and conceded when playing a (hypothetical) opponent of the same quality as the home team. They found that home advantage differs markedly between teams. The data used here are unbalanced in the sense that there is not a home advantage for every skater, because skating tournaments take place in a few countries only. Moreover, we encounter an additional complication. The performances of skaters are not comparable between different rinks and, in this respect, this study differs significantly from all other studies of home advantage. Figure 1 shows the distribution of skating speed by means of box-andwhisker plots. In these box-and-whisker plots, the left side of the box indicates the first quartile and the right side the third quartile. The dot in each box is the median. The whiskers indicate the minimum and maximum, except when these deviate more than 1.5 times the interquartile range. Observations deviating more than 1.5 times the interquartile range are depicted by dots. We plot skating times given sex of the skater, cover, and altitude of the rink. Also, we distinguish between home results and away results.

R. H. Koning


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Figure 1. Distribution of speed by sex, cover and altitude.

Each cell of Figure 1 is based on 17 seasons of data. Clearly, the median speed varies by these conditioning factors and the variation in speeds caused by these observable factors is larger than any variation due to home advantage. However, it is apparent from Figure 1 that there is some home advantage, mainly for covered skating rinks. A possible explanation for this may be that weather conditions vary during outdoor events, masking any home advantage effect. Covered skating rinks give better measurements of the quality of a skater. Another issue we need to take into account is improvement of skating speeds over time. Figure 2

shows the median speeds by season for both men and women, conditional on the distance skated. For every distance, there is a marked improvement over time. Of course, part of this improvement is due to the advent of covered skating rinks, but other factors have contributed. The most significant example of technological progress is the introduction of the klap skate in the 1996 – 97 season (see Kuper & Sterken, 2003b). Other important factors include improvements in training methods (Gemser & De Koning, 2001) and improvements in clothing (Kuper & Sterken, 2003a).

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Home advantage in speed skating

Figure 2. Development of median times by season for men (solid line) and women (dashed line).

Thus there are three important sources of variation in skating performances: whether the track is covered or not, the altitude of the track and general improvements in speed over time. Figure 1 suggests that besides these factors, home advantage may also be a determinant. Up to this point, I have not made explicit the definition of home advantage in the context of speed skating. Home advantage is usually defined as the performance advantage of an athlete,

team or country when they compete at a home ground. This definition is not very fruitful in the present study: from Figure 1 is clear that variation in skating times due to home advantage is small when compared with the variation caused by differences in altitude and whether a track is covered or uncovered. Skating conditions are not comparable between countries; high-speed, high-altitude skating rinks are found only in Canada (Calgary) and the USA


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(Salt Lake City), whereas only lowland rinks are available in The Netherlands. Because of this, I opt for a different definition of home advantage: Home advantage is the performance advantage of an athlete, team or country when they compete at a home ground compared to their performance under similar conditions at an away ground. The controlled experiment implicit in this definition is not observed. Observed skating times vary by season, distance and rink. I allow for this variation by using a statistical model for the expected skating time, given relevant covariates, one of which is home advantage. Note that I interpret performance advantage as the fact that athletes perform better, so home advantage is ex post. Home advantage does not mean that the conditions at a home skating event are better, for example because of better financial incentives. Of course, these incentives may influence the athletic performance, and hence have an indirect effect on our measure of home advantage. The data allow us to measure home advantage on the national level only. It is probably the case that a skater is most familiar with the conditions of the skating rink where he or she usually trains. However, national tournaments and training meetings of regional and national selections tend to be organized at different rinks, so a skater with some years of experience will be reasonably familiar with conditions at different rinks within his or her country. The data used here do not contain information on where a particular skater trains (or trained during his or her formative years). For this reason, I measure home advantage on a national level even though this definition may lend itself better to the crowd support hypothesis than the familiarity with local conditions hypothesis. An important issue in identification of the home advantage is that one has to allow for variation in the quality of skaters, as has been pointed out by, for example, Balmer, Nevill and Williams (2001). Suppose, for example, that US skaters are much better than all other skaters. Any good performance of these US skaters during a meeting in the USA should be attributed to their superior quality, not to home advantage. We are able to allow for variation in quality because the data set contains multiple results by the same skater, which enables us to estimate his (or her) quality. Let the average speed of skater i at distance k during event t be denoted by Tikt. Speed depends on the rink, the distance skated and the season when event t takes place. Even though the trends displayed in Figure 2 suggest a linear improvement in performance over time, I am hesitant to impose such a linear effect. A linear time trend does not allow sudden improvements in skating times due to important innovations like the klapskate. Besides

these determinants of skating speed, I also allow for the possibility that speeds skated during special events, such as the World Championship Distances or the Olympic Games, are better than expected (when compared with speeds skated at World Cup meetings). Finally, I allow for home advantage. I model skating times using a log linear mixed model. I prefer this model to a linear model because the estimated residuals are closer to a normal distribution in the log linear specification. A somewhat similar approach to modelling skating times was taken by Reese (2003), who used a hierarchical model (with more levels than one) to model skating times. The specification for the logarithmic skating times is as follows: log Tikt ¼

44 X r¼1

þ y2 WCDt þ

br Rrt þ 16 X t¼1

5 X k¼1

gk Dikt þ dHit þ y1 OGt

ft Srt þ ai þ eikt

ð1Þ

The dummy variable Rrt is 1 if event t is held at rink r, and 0 otherwise. The variables Dikt are dummy variables, with Di1t = 1 for a 1000 m event. Di2t, Di3t, Di4t, and Di5t correspond to the 1500 m, 3000 m, 5000 m and 10,000 m events, respectively. Hit is the home dummy: 1 if event t is a home event for skater i, and 0 otherwise. OGt and WCDt are dummy variables indicating whether or not event t is Olympic Games or World Championships Distance respectively. Stt is a dummy variable taking a value of 1 if event t is in season t. Finally, ai is a random effect capturing the quality of skater i (see below), and eikt is a normally distributed error term that is independent between skaters, distances and events. Because of the logarithmic specification, the parameters can be interpreted as approximate proportional effects. The parameters are interpreted as follows. The bparameters are the fixed effects, one for each skating rink. The g-parameters quantify the effect of distance: average speed decreases when the observation is from a longer distance. Note that g3 cannot be estimated for men because they don’t skate 3000 m frequently in official events. Since women do not skate 10,000 m, g5 is not estimable for them. As distance is a categorical variable, we had to choose a reference category, which is 500 m. The d-parameter measures home advantage. If home advantage exists, we expect d to be negative. The y-parameters measure tournament effects: y1 captures the effect of Olympic Games, and y2 the effect of World Championship Distances. A World Cup meeting is the reference category. jt are the fixed seasonal effects. A season dummy is included for each of the seasons 1987 – 88 to 2002 – 03. The 1986 – 87 season is the reference category.


Home advantage in speed skating The specification as discussed so far does not allow for variation in quality between skaters. This effect is captured by ai. Data are available for 665 male skaters and 453 female skaters. Clearly, it is not feasible to estimate a separate quality parameter for each of them. Instead, I model quality variation by assuming that deviations from average quality follow a normal distribution with mean 0 and variance s2a . The parameter ai is fixed for each skater between different events and seasons. Below, I discuss estimation results for separate seasons, where I estimate ai as fixed effects. The model was estimated using maximum likelihood (see Venables & Ripley, 2002). The venuespecific fixed effects br,r = 1,. . . ,44 are given in Table II in the Appendix. The fixed effects are summarized graphically in Figure 3, for given values of cover and altitude. Clearly, men skate faster than women on each type of track (the average difference is 3.7 s), and skaters are faster on covered rinks than uncovered rinks (the average difference is 0.874 s for men and 0.934 s for women). Note also that there is some variation of the fixed effects in most cells, which justifies the approach to estimate separate fixed effects for each rink. The correlation between the fitted times and observed times is 0.95 for men and 0.94 for women. Table I shows give the estimation results of model (1). Point estimates and their standard errors are provided. Of course, the large sample size ensures small standard errors, making even small effects statistically significant. For ease of interpretation, the exponentiated point estimate is also provided. For example, 1.003 (the exponentiated coefficient of the 1000 m for men) should be interpreted as follows. Keeping all other factors (including the random individual effect) constant, the 1000 m speed for men is 0.3% slower than the 500 m speed for men. Using similar reasoning, the expected speed over 1500 m is 2.6% slower than the expected speed over the 500 m distance. The estimates for both men and women are consistent with prior expectations. Average speed is a decreasing function of distance, as the coefficients of the distances show. The time skated in a 1000 m event is only marginally less than the time skated in a 500 m event (0.3% for men and 0.9% for women). This is because time is lost in the 500 m event to accelerate to high speed. Over longer distances, this loss of time is averaged over a longer distance and hence improves average speed. On the other hand, fatigue sets in over longer distances, which decreases speed. Apparently, the latter effect dominates for distances of 1500 m and more. We also see that both men and women skate significantly faster at the major tournaments: the Olympic Games and the World Distances Cham-

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pionship. The effect is of the order of 1%, both for men and for women for both types of events. The existence of this effect could be caused by national selection of skaters participating in these tournaments: only the very best at that moment qualify for such events. Suppose that we interpret ai as the average quality of skater i, but that we allow for some individual variation of quality over time (captured by eikt in model (1)). If there is some persistence in this variation, skaters who perform above their average (i.e. their ai) are selected. This selection effect is captured by the Olympic Games-and World Distances Championship-dummies. Also, these tournaments attract a lot of media coverage, which makes it important for skaters to perform as well as they can. Poor performances during these two tournaments can have dire consequences for future sponsorship deals and access to training facilities and new materials. Qualification criteria for World Cup meetings are usually less strict. General progress is significant, and has affected women skaters slightly more than men skaters. Over the 17 years of the data set, average speed has increased by 7% for women and 6.6% for men. Note the improvement of approximately 2% in the 1997 – 98 season. This corresponds to the broad acceptance of the klapskate (see Kuper & Sterken, 2003b). Now consider the estimate of home advantage. Home advantage is both positive and statistically significant. The point estimates are approximately 0.2%, both for men and for women. Even though home advantage is significant, the effect is very small compared with variation of times caused by other factors, such as general progress and variation between skating rinks. However, in a given meeting 0.2% may make the difference between a first and a second place. The average time difference between gold and silver medallists at the 2002 Winter Olympics was 0.77% for men and 0.45% for women. It may be argued that home advantage is confounded with access to new technology, if skaters from some countries have earlier access to new technology than other skaters. Two examples come to mind. First, Dutch female skaters started using the klapskate in the 1996 – 97 season, earlier than other skaters. Second, American and Dutch skaters used special suits in the 2001 – 02 season, which had a positive impact on their skating times (Kuper & Sterken, 2003a). Because not all skaters were able to use these new advances, this progress is not fully captured by the season fixed effects. For that reason, I reestimated model (1), removing those seasons from the analysis. The new point estimates for home advantage are within one standard error of those reported in Table I. It appears that our estimate of home advantage is not confounded with early access to new technologies by a select group of skaters.

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Figure 3. Distribution of rink fixed effects, by cover and altitude.

Finally, let us consider the standard deviation of the individual effects ai. The standard deviation of the individual effects is 3.1% for men and 3.4% for women. This suggests that variation in the ability of different skaters is empirically important. The 95% confidence interval for individual effects of male skaters is ( – 0.0604, 0.0604) and the corresponding interval for women is ( – 0.0657, 0.0657). A compar-

ison of these intervals to the estimated home advantage effect shows that the latter is dwarfed by variation in individual abilities. This is also confirmed by the signs and magnitudes of the estimates of the best linear predictors of the individual effects, as some examples show: Koss 0.962, Romme 0.958, Niemann-Stirnemann 0.939 and LeMay-Doan 0.956. These skaters are known to be exceptional


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Table I. Estimation results for men and women. Men


Estimate distance1000 m distance1500 m distance3000 m distance5000 m distance10000 m home result OG WCD season87/88 season88/89 season89/90 season90/91 season91/92 season92/93 season93/94 season94/95 season95/96 season96/97 season97/98 season98/99 season99/00 season00/01 season01/02 season02/03 sa se

Women

SE

Exp(est.)

0.0026 0.0258

0.0004 0.0005

1.003 1.026

0.1018 0.1326 70.0020 70.0099 70.0098 70.0047 70.0096 70.0065 70.0118 70.0119 70.0134 70.0130 70.0153 70.0220 70.0254 70.0458 70.0565 70.0616 70.0679 70.0675 70.0682 0.0308 0.0199

0.0006 0.0010 0.0005 0.0008 0.0008 0.0011 0.0011 0.0012 0.0013 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014

1.107 1.142 0.998 0.990 0.990 0.995 0.990 0.994 0.988 0.988 0.987 0.987 0.985 0.978 0.975 0.955 0.945 0.940 0.934 0.935 0.934

and an estimated individual effect smaller than 1 indicates that they skate faster than an average skater under similar circumstances. It is interesting to note that the standard deviation of the random effects is larger for women than for men. This suggests that there is more competition in men’s events than in women’s events. This observation is in accordance with Gould’s hypothesis that variation in the quality of athletes decreases over time when a sport matures (Gould, 1997; see also Reese, 2003). Men’s international speed skating (as analysed in this paper) has a longer history than that of the women, and therefore one would expect less variation in the abilities of top athletes. The estimate for home advantage in Table I may be biased if skaters perform according to a life-cycle model, where they improve their skills over time until they reach a peak. Then, as ageing sets in, their performance will deteriorate. If a skater is at his peak in a season when there are skating contests in his home country, his peak performance may be erroneously attributed to home advantage. To examine this issue, I estimated a variant of model (1) twice, for the 2001 – 2002 season (which includes the Salt Lake City Olympic Winter Games) and the 2002 – 2003 season. By focusing on a single season one can reasonably assume that the quality of the skater is constant. The season dummies were

Estimate

SE

Exp(est.)

0.0088 0.0348 0.0829 0.1140

0.0004 0.0006 0.0007 0.0010

1.009 1.035 1.086 1.121

70.0025 70.0117 70.0099 70.0052 70.0009 0.0034 0.0011 70.0048 70.0091 70.0131 70.0154 70.0196 70.0274 70.0500 70.0572 70.0617 70.0711 70.0704 70.0729 0.0335 0.0204

0.0006 0.0010 0.0008 0.0016 0.0019 0.0017 0.0018 0.0020 0.0018 0.0018 0.0019 0.0018 0.0019 0.0018 0.0019 0.0019 0.0018 0.0019 0.0019

0.997 0.988 0.990 0.995 0.999 1.003 1.001 0.995 0.991 0.987 0.985 0.981 0.973 0.951 0.944 0.940 0.931 0.932 0.930

removed, and individual effects of the skaters were incorporated as fixed effects. Based on these estimation results, 95% confidence intervals for the estimated home advantage for men are ( – 0.0088, – 0.0022) in 2001 – 2002 and ( – 0.0081, – 0.0017) in 2002 – 2003. Even though the point estimates for the home advantage effect are higher, it should be noted that the first interval almost covers the point estimate of home advantage of Table II, and the second interval includes the point estimate. For women, these intervals are ( – 0.0098, – 0.0024) and ( – 0.0041, 0.0022), which both cover the point estimate reported in Table II. A bias due to a life-cycle model of skating results is not significantly present. Earlier, I distinguished between two variables responsible for the existence of home advantage: crowd support and familiarity with local conditions. In particular, skating bends at high speed is difficult and requires practice. If this is the reason for the home advantage, it is reasonable to suppose that the magnitude of home advantage depends on the distance: speed in the bends is lower when skating 5000 m than when skating 500 m. To test this, I interacted the home advantage dummy in specification (1) with the distance skated. However, the additional regression coeffcients were not jointly significantly different from 0 (neither for men nor for women). A second approach to testing this idea is to

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see whether Americans and Canadians (who have access to the two fastest rinks in the world, Salt Lake City and Calgary; see also Figure 3) have greater home advantage than others. I interacted the home advantage dummy with a country dummy (which is 1 if the skater is from the USA or Canada) and examined whether the extra coefficients differ from 0. For men, this was not the case (P-value 0.34), but for women the extra coeffcients were significant at a 5% level but not at a 1% level (P-value 0.012). This may provides some evidence that familiarity with local conditions is a cause of home advantage for women.

Acknowledgements The data used in this paper were kindly provided by Jeroen Heijmans (http: //weasel.student.utwente.nl/ *speedskating/). The statistical analysis was performed using the R statistical software system (Ihaka & Gentleman, 1996), which can be obtained from www.r-project.org. The original paper was typeset using mikTEX, which can be obtained from www.miktex.org. I thank Gerard Kuper and three anonymous referees for detailed comments on an earlier draft of the manuscript.

Summary and Conclusions

References

This paper examined whether there is any proof of the existence of home advantage in speed skating. Performance in speed skating can be measured objectively by the time taken to cover a certain distance, and refereeing decisions do not usually affect the results. According to the existing literature, these two considerations indicate that it is unlikely that home advantage exists. However, two other causes of home advantage may apply to speed skating: support of the home crowd and familiarity with local conditions. There are problems in estimating home advantage: skaters differ in their abilities, and some skating rinks are of better quality than others. To accommodate these problems, I used a statistical model that allows for quality variation of skating rinks and for different abilities of skaters. Using this model identified a significant home advantage, that is similar for men and women: it is approximately 0.2%. In examining whether this home advantage could be attributed to local crowd support or familiarity with local conditions, I found some evidence that both apply for women. No proof was found that home advantage for men is caused by familiarity with local conditions. The magnitude of this home advantage effect is small when compared with other sources of variation, such as variation in individual abilities, variation in quality of skating rinks and improvements in performance over time. Hence, I conclude that even though a significant home advantage exists, it plays a minor role in determining the performances of skaters. In this sense, skating differs from many other sports where a well-established, non-negligible home advantage exists.

Balmer, N.J., Nevill, A. M. & Williams, A. M. (2001). Home advantage in the Winter Olympics (1908 – 1998). Journal of Sports Sciences, 19, 129 – 139. Balmer, N. J., Nevill, A. M. & Williams, A. M. (2003). Modelling home advantage in the Summer Olympic Games. Journal of Sports Sciences, 21, 469 – 478. Bray, S. R. & Carron, A. V. (1993). The home advantage in alpine skiing. Australian Journal of Science and Medicine in Sport, 25, 76 – 81. Clarke, S. R. & Norman, J. M. (1995). Home ground advantage of individual clubs in English soccer. The Statistician, 44, 509 – 521. Gemser, H. & De Koning, J. (2001). Schaatsen met de computer: Op zoek naar prestatiebepalende factoren (Skating with the computer: Searching for perfomanace enhancing factors). Communication to the symposium on ‘‘Sport and Computers’’, Amsterdam. Gould, S. J. (1997). Full house. New York: Random House. Holder, R. L. & Nevill, A. M. (1997). Modelling performance at international tennis and golf tournaments: Is there a home advantage? The Statistician, 46, 551 – 559. Ihaka, R. & Gentleman, R. (1996). R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5, 299 – 314. Kuper, G. H. & Sterken, E. (2003a). Do skin suits increase average skating speed? Unpublished manuscript, Department of Economics, University of Groningen. Kuper, G. H. & Sterken, E. (2003b). Endurance in speed skating: The development of world records. European Journal of Operational Research, 148, 293 – 301. Nevill, A. M. & Holder, R. L. (1999). Home advantage in sport: An overview of studies on the advantage of playing at home. Sports Medicine, 28, 221 – 236. Reese, C. S. (2003). Is Salt Lake City’s ice the fastest on earth? A statistical investigation. Communication to the Joint Statistical Meeting, San Fransisco, CA. Venables, W. N. & Ripley, B. D. (2002). Modern applied statistics with S (4th edn.). New York: Springer.


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Appendix Table II. Fixed rink effects estimation results for men and women.


Men

Albertville (FRA) Asama (JPN) Assen (NED) Baselga di Pine (ITA) Bergen (NOR) Berlin (GDR) Berlin (GER) Butte (USA) Calgary (CAN) Chuncheon (KOR) Collalbo (ITA) Davos (SUI) Den Haag (NED) East Berlin (GDR) Erfurt (GER) Eskilstuna (SWE) Goteborg (SWE) Groningen (NED) Hamar (NOR) Harbin (CHN) Heerenveen (NED) Helsinki (FIN) Ikaho (JPN) Innsbruck (AUT) Inzell (FRG) Inzell (GER) Jeonju (KOR) Karuizawa (JPN) Lake Placid (USA) Larvik (NOR) Medeo (KAZ) Milwaukee (USA) Nagano (JPN) Obihiro (JPN) Oslo (NOR) Ostersund (SWE) Roseville (USA) Sainte-Foy (CAN) Salt Lake City (USA) Savalen (NOR) Seoul (KOR) Skien (NOR) Warszawa (POL) West Berlin (FRG)

Women

Estimate

SE

Exp(est.)

Estimate

SE

Exp(est.)

3.6963 3.6836 3.7030 3.6910 3.7183 3.7056 3.6860 3.6814 3.6585 3.7103 3.6795 3.6865 3.6945

0.0021 0.0025 0.0024 0.0017 0.0033 0.0020 0.0017 0.0019 0.0017 0.0024 0.0020 0.0017 0.0022

40.299 39.790 40.567 40.083 41.194 40.673 39.886 39.702 38.803 40.864 39.627 39.904 40.227

3.7802 3.7669 3.8030 3.7834

0.0029 0.0033 0.0032 0.0025

43.823 43.246 44.835 43.965

3.6812 3.7174 3.7456

0.0022 0.0027 0.0025

39.695 41.159 42.336

3.7826 3.7771 3.7754 3.7465 3.7957 3.7655 3.7893 3.7820 3.7787 3.7655

0.0025 0.0023 0.0025 0.0023 0.0033 0.0027 0.0024 0.0026 0.0033 0.0028

43.928 43.688 43.615 42.374 44.509 43.185 44.224 43.906 43.760 43.184

3.6710 3.6808 3.6761 3.7176 3.6831 3.6991 3.6839 3.6890 3.7049 3.6950 3.7084

0.0017 0.0025 0.0016 0.0020 0.0024 0.0017 0.0019 0.0017 0.0024 0.0019 0.0030

39.291 39.679 39.494 41.167 39.770 40.412 39.801 40.005 40.646 40.247 40.789

3.6998 3.6689 3.6771 3.7027 3.7132 3.7070 3.7085 3.7418 3.6553 3.6961 3.6998 3.7119 3.7114 3.7066

0.0026 0.0019 0.0018 0.0021 0.0019 0.0025 0.0020 0.0030 0.0019 0.0023 0.0019 0.0038 0.0021 0.0019

40.438 39.208 39.530 40.555 40.986 40.733 40.791 42.174 38.679 40.288 40.440 40.931 40.911 40.714

3.8193 3.7590 3.7726 3.7641 3.8076 3.7760 3.7881 3.7759 3.7828 3.8031 3.7872 3.8066 3.8007 3.7924 3.7627 3.7676 3.7957 3.8262

0.0036 0.0024 0.0030 0.0023 0.0024 0.0030 0.0024 0.0024 0.0024 0.0030 0.0026 0.0028 0.0041 0.0036 0.0025 0.0024 0.0028 0.0029

45.572 42.906 43.494 43.125 45.042 43.639 44.171 43.636 43.938 44.840 44.133 44.997 44.733 44.363 43.065 43.275 44.511 45.888

3.7997

0.0026

44.689

3.7428

0.0025

42.216

3.7958 3.8073 3.8047 3.8004

0.0025 0.0038 0.0026 0.0029

44.513 45.029 44.914 44.719