Over the years sport has acted as a useful domain to study decision making under risk and uncertainty. This is because incentives are at work in semi-structured environments where participants mostly have had the chance to learn. A curious and quite old finding, where people make such ‘real-life’ probability estimations, comes from studying the behaviour of gamblers at race tracks.
The End-of-Day effect involves choosing bets that have a lower probability of occurring but higher payoffs, in the later stages of a round of gambling, and is one of many cognitive biases psychologists and behavioural economists have discovered. The problem at hand is intuitively quite simple. Imagine you are at a racetrack where eight races are going to post throughout the day. You have a fixed budget of a €10 bet per race. Let’s assume that you are not having any luck; you are backing favourites and none of them have won!
By the time the last race goes to post you are €70 out of pocket after seven previous failed bets. Given that you only have €10 euros left, what do you choose to place your final bet on? Do you a) bet on a horse that is clearly odds on favourite at 1/7, as you have been doing all day, or do you b) shift your preference to an outsider horse who has a chance but is priced at 7/1? If you stick with the 1/7 favourite and are successful (which is most likely to happen) you will leave the racecourse with €14.28 (a lot less than the €80 you arrived with). If you switch to the 7/1 long-shot however there’s an outside chance you will leave with your original budget of €80. Of course, as it’s a long-shot it’s more likely you’ll leave the race track penniless!
The most famous study on this idea was conducted in the middle of the 20th century when William McGlothin (1956) collected data on 9,605 horse-races, primarily from California tracks from 1947-1953. He was interested in the stability of risk taking behaviour over a series of events, in particular the constancy of subjective probability and subjective utility of those who place bets over the course of a day. On-course betting allowed the preferences of gamblers to be measured that were of equal expectations but different probabilities of success. McGlothin (1956, 615) concluded that “the group behaved in a manner such as to increase the variability of their assets as a series of risk-taking events preceded”. In the last race risky decision making increased as bettors shifted towards horses that held longer odds.
Further evidence of the end-of-day effect in the race course is provided by Muktar Ali (1977) who analysed 20,247 horse races over a five year period. Again, horses with a high objective probability of winning were seen to be understated and horses with a lower objective probability of winning were overstated. This relationship was shown to be robust across different race tracks and alternative race conditions, supporting the original McGlothin (1956) study.
Why is this interesting to economists? The answers is because such behaviour is inconsistent with the predictions of subjective expected utility theory - a central theory in the discipline. This theory suggests that when offered a risky gamble we make a rational choice by weighing up probabilities and likely consequences, consistently choosing the best outcome. In the thought experiment given above, you should treat the races independently. On average punters wouldn’t back a 7/1 shot over a 1/7 shot in the first race, so why would more people do so in the last? The problem is because it is psychologically challenging for any race-goers to treat their wealth level and races independently; logically one should not seek out a long-shot in the final race but rather incur a small gain of €4.28 (but retain a net loss) and treat the first race of the next meeting you attend as your next bet.
While the End-of-Day effect is outside of the predictions of the traditional utility theory in economics, it can be accommodated by Prospect Theory. Perhaps we shift toward more risky bets as the day goes on because we form reference points in regards to profit making? The reference profit is commonly zero. If gamblers are incurring high loses by the last race of the day they would prefer to substitute away from gambling on favourites, towards horses that have a lower likelihood of winning, in an effort to return to this reference point of zero.
My advice would be to keep the End-of-Day effect in mind the next time you head to the race track, casino or even when you see your bookmakers offer a boosted price for long-shots in later races. By that last race of the day you’ll probably see punters who just don’t care about their final €10 and irrationally take a big punt that could, but probably won't, come off! .