Apr 15, 2020
Apr 15, 2020

The element of randomness in sports betting

Why is sports betting random?

How random in sports betting?

Measuring the extent of randomness in sports betting

The element of randomness in sports betting

By its very nature, betting on sport is an uncertain business, so how can bettors keep a tight grip on the randomness of it all? Joseph Buchdahl looks at the best way to tackle the inevitable randomness that occurs in sports betting.

Why is sports betting random?

In the article The illusion of control, we looked at the risks and dangers associated with the misinterpretation of meaningless correlations in data that are inherently random, uncontrollable and unpredictable.

Similarly to weather forecasting and the stock market, sports betting is inherently a very uncertain business.

In sports betting, the idea that outcomes can directly rate to information and knowledge about a team or player can give rise to an exaggerated sense of belief in one’s predictive ability. As mentioned in the article, a little information can be a dangerous thing.

Furthermore, our self-serving attribution bias ensures that we are more likely to associate forecasting successes with internal attributes (such as the thought that a bettor is a skilled forecaster possessing skills capable of leading to a correct call), whilst associating failures with external attributes (for instance, if the bet lost then the bettor was simply unlucky).

Despite a craving for control, the reality is that similarly to weather forecasting and the stock market, sports betting is inherently a very uncertain business. The evolution of a game or match is complex, chaotic and conceivably even non-deterministic if we concede that what takes place might be entirely dictated by chance.

Most bettors do appreciate that on a bet-by-bet basis either good or bad luck can serve a pivotal role in whether they win or lose. But exactly how much does the element of chance influence outcomes over long periods of time?

How random is sports betting?

To ensure that we are not entirely fooled by randomness, a useful exercise is to analyse exactly how much inherent random variability actually exists in sporting outcomes.

A method of ascertaining this is to plot a time series of hypothetical betting returns from fair odds to see how much they vary over different time scales. Betting odds merely represent probability estimates for our expectations.

The Wisdom of the Crowd ensures that on average, these odds prove to be a very reliable indicator of ‘true’ probabilities. However, randomness ensures that outcomes frequently deviate from idealised market expectations.

Firstly, the graph below plots the ten-match moving average level-stakes return on investment (or yield) for betting on all home, draw and away outcomes for ten seasons of English league soccer matches (specifically from 2005-06 to 2014-15).


The fair betting odds are based on real market average match betting odds with the bookmaker’s profit margin removed.

As you can see, the sheer deviation in results makes it difficult to draw any reasonable conclusions. The majority of bettors will recognise and accept that over small samples of just 30 bets, unexpected results will cause significant deviation from the expected yield of 0%.

For instance, lucky underdog winners will push the line well above zero, while an excess of winning favourites that offer proportionally smaller level stake returns will drop it below zero.

However, is it worth noting that the magnitude of the fluctuations occasionally reach high enough to exceed 50%. If a bettor was exhibiting a yield of over 50% after 30 wagers, there would presumably be an equal temptation to attribute this to either skill or good fortune.

On the other hand, if they were down by 30%, doubts would likely form in their confidence to eventually regress towards the mean.

The second graph shows the 100-match moving average level-stakes return for the same fixtures. As you will see, there remains considerable inherent random variability, with the largest deviation producing a formidable 23.5% yield from 300 bets.


Even the graph for the 1000-match moving average level-stakes return exhibits a notable residual inherent random variability.


What can be learned from this?

While the quantity of bets in this study is more than the vast majority of bettors will wager during several soccer seasons, they still highlight sizeable deviations of several percent in yield across a considerable period of time.

The sharpest bettors are more effective at forecasting sporting outcomes, but will still recognise that this is a matter of chance.

The case also stands that no bettor blanket bets on all home, draw and away outcomes for every soccer match. Nonetheless, a sample of your own bets over a long period of time will likely exhibit a similar extent of random variability among your returns that is comparable to any complex system for which outcomes are shrouded in significant uncertainty.

The key point to take away from this is just because you might have achieved a 20% yield after 300 wagers or a 4% yield after 3,000 wagers, there is no means of confirming that any degree of skill caused that to happen. Unless you are aware of the level of randomness in sports across all time scales, you are likely be fooled by your own self-serving attribution biases.

Even the sharpest bettors will recognise that while they may be more effective at forecasting sporting outcomes than other bettors, most of what happens in sports is largely a matter of chance.

Nate Silver demonstrated that the world’s best poker player can still lose money from 100,000 unlucky hands. As some might say, the signal is weak and the noise is loud.

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