ANYONE FOR TENNIS (BETTING)ANYONE FOR TENNIS (BETTING), Artykuły po angielsku
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ANYONE FOR TENNIS (BETTING)? Abstract The most robust anomaly noted in the literature on wagering markets is (positive) longshot bias: over a period of fifty years, it has been well documented in horse betting that higher expected returns accrue to short- than to long-odds bets. However, a few examples of betting markets with zero or negative bias have been found, for example in certain American sports. The understanding of longshot bias is likely to be informed by comparing and contrasting conditions in markets displaying positive, zero and negative bias but, to date, relatively few markets have been examined. This paper employs a large data set on professional men’s tennis matches and a new econometric approach to the estimation of the relationship between returns and odds. It finds positive bias throughout the range of odds. It discusses this finding in the context of the debate on why biases exist and persist in wagering markets, focusing particularly on bettor attitudes to risk and skewness. keywords: sports betting; longshot bias; risk preference 1 ANYONE FOR TENNIS (BETTING)? 1. Introduction Wagering markets are specialist financial markets where bettors purchase state contingent assets. As in other financial markets, most studies (Sauer, 1998 and Vaughan Williams, 1999 provide excellent surveys) indicate that, broadly, prices are efficient but, again as in other financial markets, anomalies have been noted. The most celebrated and robust of these is termed longshot bias : in American, British and Australian horse betting markets, whether organised by bookmakers or on a pari mutuel (tote) basis, superior returns accrue to a strategy of placing short-odds bets relative to a strategy of placing long-odds bets. This stylised fact has been repeatedly confirmed by empirical studies dating as far back as Griffiths (1949) and a similar pattern has been shown to characterise dog race betting markets (Cain et al., 1996, for the UK, Terrell and Farmer, 1996 for the US). It represents an anomaly because in most conventional financial markets, expected return is higher in respect of assets associated with greater risk. In horse and dog betting markets, the opposite occurs. A number of explanations have been proposed to account for the anomaly; for a survey see Vaughan Williams (1999). Many start from the notion that the market is inefficient because of the presence of noise traders and high transactions costs that discourage arbitrage. 1 But, in the present paper, we are concerned principally with explanations based on bettors’ risk preferences. Golec and Tamarkin (1998) suggest that bettors might be risk-averse but ‘skewness-loving’. In this explanation, the assumption made in most economic analysis, 1 namely that investors are risk-averse, is retained; but it is hypothesised that at some level of wealth the utility function would become risk-loving and so betting at sufficiently long odds would be attractive. On this view, longshots provide evidently poor value (low expected return, high variance in return) in equilibrium but bettors still accept the odds because they are compensated by high positive skewness. One of the implications of risk aversion, combined with a taste for skewness, is that there should be a non-monotonic relationship between odds and returns. The present paper tests whether this implication of the Golec and Tamarkin approach is supported by the data from a betting market with a very wide range of odds A way forward for the literature may be to compare the extent to which different hypotheses can account not just for the dominant stylised fact of positive longshot bias in horse and dog betting markets, but also for any exceptions to the general rule that bets on short-odds events are financially superior to bets on long-odds events. And exceptions have been found. For example, no bias has been detected in Asian racetrack markets (Busche and Hall, 1988, Busche, 1994, Busche and Walls, 2000) and Vaughan Williams and Paton (1998) found bias absent also in the case of wagering on ‘higher-grade handicap’ races in Britain. Beyond racing, Forrest et al. (2005) reported unbiased odds from examining bets available on nearly 10,000 English football matches; and Woodland and Woodland (1994, 2001, 2003) have even identified reverse, i.e. negative, bias in respect of betting on the American team sports of baseball and (ice) hockey 2 . As noted by Vaughan Williams and Paton (1998), a successful general theory of wagering markets would explain any contrast in the pattern of returns as observed in different sub-sectors of betting. 2 This paper tests for the direction of bias in a hitherto unexplored betting market, that on men’s professional tennis. This adds to the existing taxonomy of which markets display positive and which negative bias. Evidence to date relates to horse and dog betting and certain team sports. Attempts to account for different directions of bias have been based mainly on contrasting conditions in the horse and baseball betting markets. To be convincing, such explanations should be able to predict direction of bias in other sub- sectors, such as tennis. Hence evidence is needed from markets not previously studied in order to discipline the debate on longshot bias. We seek to provide such evidence for tennis and to examine the extent to which it is consistent with previous attempts (particularly those linked to specific hypotheses about bettor risk preferences) to explain why bias is positive and negative in different markets. We argue below that tennis is an especially valuable source of evidence because of the very wide range of odds available on singles bets. 2. Width of odds One reason for contrasting patterns between different areas of betting may be that different widths of odds are observed in different markets (Woodland and Woodland, 1999). Consider some relevant facts, first from racing. Vaughan Williams and Paton (1998) found no bias in English horse racing odds when their sample was confined to handicap races. By design, runners in a handicap race are intended to have fairly equal chances of winning and the odds range may be expected therefore to be relatively narrow. This is indeed the case. We recently reviewed odds data collected on 31,037 runners in British (jumps) races. The 3 proportion of runners that were strong favourites, defined as having odds of evens or shorter, was much lower in handicap than in non-handicap races (0.7% compared with 2.8%). The reason for the failure of an odds bias to emerge in handicap races might be that one observes only a compressed range of odds compared with other racing. In sports betting markets, one does not generally find extreme favourites or rank outsiders. In English soccer and in the American team sports, all contests are prospectively quite close because the sport is organised to promote competitive balance. So true probabilities of a particular team winning will almost never justify odds like 10/1 which are available routinely in, say, the British racing programme. And whereas, in our large sample of British (jumps) races, much less than 3% of runners had starting odds at evens or shorter, it is not unusual in a sports fixture to find both teams quoted at odds-on. In this setting of team sport where all bets are in a short range either side of evens, positive longshot bias is not found. By contrast with most sports leagues, Singapore’s S-League (soccer) is spectacularly unbalanced 3 and extreme odds are often available. For example, one team was recently 1/20 to win, notwithstanding that it was playing away. Forrest and Simmons (2001) found that odds on S-League games did display marked positive bias in contrast to the difficulty in establishing any bias in the odds on English football and the clear negative bias in American team sports. Moreover, within English football, betting on exact scores (rather than on the home/ draw/ away result) does offer the possibility to wager on highly unlikely events (such as a scoreline of 6-5), and in this sector positive bias has again been reported (Cain et al., 2000). 4 [ Pobierz całość w formacie PDF ] |
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