5.2 Data
5.2.3 Descriptive Statistics
The total of 80,871 horses started in 8,834 races and 72,556 of them (89.7%) fin- ished. There is a large variability in the data. The average number of horses in a race is 9.15. The minimum is two horses (for as many as two races) and the
4http://www.betfairpromo.com/betfairsp/prices/index.php.
5http://www.sportinglife.com/.
6Betfair allows for quotes from 1.01 to 1,000. The grid becomes increasingly coarser, ranging from one penny increments between odds of 1.01 to 2.00, to 10 pounds increments between odds of 100 to 1,000.
maximum is 34 horses (for only one race). There are only 76 races with more than or equal to 20 horses.
The mean race duration is 173.14 seconds and the median is 129.07 seconds.
There are 2,644 races which finished in 90 seconds or shorter, and there are 4,836 races which lasted longer than 120 seconds.
The mean pre-race trading volume is 71,094 (GBP) and the median is 27,387.
The mean in-play trading volume is 20,665 (GBP) and the median is 4,089. The event that attracted the largest amount of money in our dataset is Cheltenham Gold Cup. This is a Grade 1 National Hunt race in which horses run three miles and two-and-half furlongs (5,331m) and jump 22 fences on the way.7 The race is a part of “Cheltenham Festival,” which takes place annually at March and is the highlight of the National Hunt season. The total pre-race trading volume in this only one race amounted to over nine million GBP.
The distribution of winning probabilities implied by pre-race volume-weighted average odds is shown in the left panel of Figure 5.1. The mean implied prob- ability is 0.115 and the median is 0.083. The red line represents the maximum likelihood fit of beta distribution B(α,β) with the estimated shape parameters α = 0.975 and β = 6.988. The right panel of Figure 5.1 illustrates the dynamics of implied probabilities during Cheltenham Gold Cup. Before the race started, two horses namedBobs Worth andSilviniaco Conti were strong favorites (volume- weighted average odds for those two horses before the race were 2.66 and 4.03, respectively). Implied probabilities were relatively stable until around 350 sec- onds after race started. Then, the dynamics became busy: implied probabilities for two favorite horses became volatile but suddenly, the third horseLord Winder- mere(highlighted red in the right panel of Figure 5.1) took the lead and won the race at the very last moment.8
The left panel of Figure 5.2 shows a time series of median (together with 25- and 75-percentile) amount of cumulative money (in the unit of 1,000 GBP) traded on the exchange before races start. Notice that about 80% of the money is bet in the last five minutes before races start. This shape is consistent with the finding in a U.S. racetrack parimutuel betting market reported in Camerer (1998). Similarly,
7National Hunt racing is the official name of the type of horse racing in which horses jump fences and ditches.
8Note that the European/U.K. style of racing is quite different from the typical American style.
American races are faster-paced, and it is common for a few horses to vie for leadership early in the race, and change positions frequently. In European/U.K. style the pace is slower early in the race and horses do not switch positions as frequently; they save energy for a mad scramble in the last 30 seconds of the race. This is reflected in the typical odds profile in the right panel of Figure 5.1 in which the implied subjective probabilities do not change much until late in the race.
02468Density
0 .2 .4 .6 .8 1
Implied probabilities
0.2.4.6.8Implied probability
0 100 200 300 400
Race time (s)
Figure5.1: Probabilities implied by pre-race trading volume weighted average odds with estimated Beta density (left) and the dynamics of implied probabilities during a long race, the Cheltenham Gold Cup (right).
050100150200250Volume (1000 GBP)
−1800 −1500 −1200 −900 −600 −300 0
Time to start (s) Median
Inter−quartile range
200220240260280300Volume (1000 GBP)
−60 −40 −20 0
Time to finish (s) Median
Inter−quartile range
Figure 5.2: Median and inter-quartile range of cumulative trading volumes before start (left) and finish (right).
the right panel of Figure 5.2 shows the same series before races finish. While the magnitude of increase is less pronounced compared to the series for pre-race, the shape exhibits slight convexity.
It is a general tendency in this market that we observe relatively stable paths of implied probabilities before races start. This is reasonable since traders in the market receive virtually no additional information in this time window. This tendency holds until 30 to 40 seconds before races finish. Implied probabilities then become much more volatile. Some approach toward 1 while others approach toward 0. See Figure D.1 for an illustration of dynamics of implied probabilities pre- and in-race (an extension of the right panel of Figure 5.1). Given those typical patterns of the dynamics of implied probabilities, in the following analyses we divide the entire race duration into two categories. The first category is pre-race,
and in particular we focus on 10 minutes before races start. The second category is the last phase of the races. Since most of the dynamic aspects of horse racing appear in the “last straight,” we look at up to 40 seconds before races finish.