What is Variance?
Variance, in the realm of statistics, is a quantitative measurement that captures the dispersion or spread of data points around their average or expected value. It reflects the extent to which individual values deviate from the mean or average, illustrating the degree of diversity or variability within a dataset. Essentially, variance quantifies the average squared difference between each data point and the overall mean, providing valuable insights into the distribution and overall pattern of the data.
Ok, on to the fun part..
Why Does Variance Exist?
Variance exists based on the inherent randomness and unpredictability of sporting events. When placing bets, there are always multiple potential outcomes, and variance quantifies the degree of variability in these outcomes. It accounts for both positive and negative deviations from the expected results, reflecting the natural fluctuations that occur within sports betting.
Even in situations where the odds may seem favourable, variance can lead to unexpected results.
Examples of Variance in Everyday Life
- Weather Forecast: Variance can impact everyday life, such as in weather forecasting. Despite advanced meteorological models, the weather can deviate from predictions due to the inherent variance in atmospheric conditions, resulting in unexpected changes like sudden rain showers or temperature fluctuations.
- Stock Market: Variance plays a significant role in the financial world, particularly in the stock market. The value of stocks can fluctuate significantly due to various factors, including market trends, economic news, and investor sentiment. Investors must consider variance when making decisions to manage risks and maximize returns.
- Traffic Congestion: Variance affects traffic patterns and congestion. While traffic planners use historical data and predictive models, unexpected incidents like accidents, road closures, or sudden influxes of vehicles can lead to significant deviations from predicted traffic flow, causing delays and congestion.
What is Variance in Sports Betting?
Variance in sports betting refers to the statistical measure of the distribution of outcomes and the degree of uncertainty in the results of bets placed. It represents the fluctuations or deviations from the expected or average outcomes. Basically, even if you are a profitable punter, your results will be all over the place in terms of winning and losing!
Why is Variance an Important Factor in Sports Betting?
Variance is a crucial factor in sports betting because it directly impacts the potential outcomes and short-term profitability of bets. Understanding variance, helps bettors make informed decisions, minimize risks, and maximize rewards. By considering variance, bettors can assess the range of potential outcomes and adjust their betting strategies accordingly.
Examples of Variance in Sports Betting
- Football: In football betting, variance is evident when an underdog team unexpectedly defeats a favoured opponent. While the odds may heavily favour one team, the unpredictability of player performance, injuries, referee decisions, or even weather conditions can lead to surprising outcomes.
- Horse Racing: Variance is prominent in horse racing due to the involvement of multiple factors, such as horse form, jockey skill, track conditions, and race dynamics. Even the best-prepared horses can face unexpected challenges, resulting in high-variance outcomes, where long shots can win, causing significant fluctuations in your profit.
- Tennis: Tennis betting can experience variance when a highly ranked player unexpectedly loses to an underdog. Factors like injuries, fatigue, or mental resilience can influence player performance, creating opportunities for unexpected outcomes with your bets.
What Causes High Variance in Sports Betting?
High variance in sports betting can be caused by several factors. These include the odds bet at, unpredictability of individual player performances, injuries, weather conditions, referee decisions, and the potential for upsets. When these factors align or deviate from expectations, it leads to larger deviations from the average, resulting in higher variance.
What Causes Low Variance in Sports Betting?
Low variance in sports betting can occur when the factors influencing the outcomes are more predictable and stable. For example, when a dominant team faces a weaker opponent, and all the conditions favour the favourite, the outcome is expected to align closely with the predictions. In such cases, the variance is lower due to the reduced uncertainty.
How to Reduce Variance in Your Sports Betting
To reduce variance in sports betting, bettors can employ various strategies:
- Bet on Lower Odds Ranges: Betting on outcomes with lower odds reduces the potential for large swings in results. While the returns may be smaller, the variance is generally lower, resulting in more consistent and predictable outcomes.
- Diversify Bets: Spreading bets across multiple events, sports, or markets can help mitigate the impact of variance. By diversifying their portfolio, bettors reduce their reliance on a single outcome and create a more balanced risk profile.
- Practice Betting Fund Management: Proper fund management is crucial in managing variance. Setting a budget for betting, wagering a reasonable percentage of the fund per bet, and avoiding overexposure to high-risk bets can help minimize the impact of variance on the overall betting performance.
More on Betting Fund Management
Managing a betting fund and understanding variance are crucial for punters. It’s important for bettors to be able to quantify their edge as far as possible and know when a ‘run’ of results is good or bad luck or something more.
Consider a bet at evens (2.0) and assume a simple model with no commission, which would mean a probability of 50%. If you know that the true probability of your bet landing is 52% (a price of 1.92) the expected return for each bet made at 2.0 will be 4.2% (2.0/1.92 – 1(100)). This is the value element from the bet.
Let’s say you start with a fund of 100 points and bet a fixed 1 point per bet. After 100 bets, your betting fund could be anywhere between 0 to 200 point, but it is expected to be 104 point, reflecting your 4% value edge.
In the simulation below, the strategy is run 10,000 times, and we can get a good idea of the effect of variance on your betting fund.
What the Graph Tells Us
While the average is a shade under a four point increase in the betting fund, the difference between the best outcome at +38 points and worst outcome at -30 points, is quite considerable. It’s important that you realise that a 4% edge doesn’t guarantee a 4% profit, certainly not over the short-term.
With this simulation, you can expect a return of between -12 points and +20 points, 90% of the time.
Different Drawdown Scenarios
The chart below gives you an idea of the likelihood of having certain point or unit drawdowns from your starting fund, over a sequence of between 100 to 1,000 bets. Again,10.000 simulations were used. It’s assumed that you have a 4% edge at odds of 2.0 and bet 1 point per bet.
After 1000 bets, the likelihood of experiencing certain drawdowns seems to be reaching its upper limit.
The chart below illustrates how when your value / edge increases, the chance of certain drawdowns becomes less and less.
So, for example, with a 4% edge, the chance of experiencing a 10 point drawdown during the course of having 1,000 bets at 2.0, is about 43%.
Varying the Odds
What happens to the betting fund if we keep the bet size (1 point) and the value / edge percentage (4%) the same but change the odds? The chart below shows the probability of different drawdowns from your starting fund, when you place 1,000 bets at different odds. Once again, each batch of 1,000 wagers was simulated 10,000 times.
When betting at odds of 2.0, there is around a 43% chance of being down 10 points at some stage over a series of 1,000 bets. At odds of 5.0, the chance of a 10 point drawdown increases to around 78%. Importantly, this is with an identical stake, edge and expected return from a series of bets. Backing at bigger odds dramatically alters the implications for your betting fund in terms of variance.
It is important to understand what kind of bettor you are. What is your likely reaction to different betting fund situations?
Looking at Value / Edge
In the chart below we take a run of 1,000 bets once again. By varying the odds and value edge, we can look at the standard deviation of returns.
You can see that the variance increases as the odds increase. Making 1,000 1 point bets with a 10% edge at odds of 5.0, you get a standard deviation of about 6.3%. If you bet at lower odds of 1.67, standard deviation drops to 2.5%. In both cases the expected return is +100 points (+10%).
An interesting result is that for odds shorter than 2.0, as edge (and thus expected return) increases, standard deviation actually decreases. Finding an increasing edge in odds shorter than 2.0 is rewarded not only by the increase in expected return but with a decrease in variance.
My football service lays bets at an average of around 2.30, which effectively means we back at around odds of 1.70, below 2.0. This is very good for minimising variance.
Summarising the Data
We know that the bigger the value / edge, there is an increased chance that you will overcome more quickly a run of bad luck. The data also shows that it is a mistake to lose confidence in a drawdown, as this is just a natural part of betting.
Equally, however, it would be a mistake to become over-confident or increase stakes over a short run of positive results.
We also saw how increasing the odds, increases the variance, even where the edge and potential return are the same. This is an important consideration for your betting fund.
We also found out how even over reasonable sample of bets, variance can distort the ‘true picture’ regarding your betting.
How is Variance Related to Standard Deviation?
Variance and standard deviation are closely related statistical measures. While variance quantifies the average squared deviation from the expected outcome, standard deviation is the square root of variance. Standard deviation provides a more interpretable measure of the dispersion or spread of outcomes, allowing bettors to gauge the potential range of results.
How is Variance Related to Randomness?
Variance is intrinsically linked to randomness. In sports betting, the outcomes of events are influenced by various random factors, including player performance, external conditions, and unforeseen events. These random elements introduce uncertainty, which leads to the observed variance in betting results. Variance provides a statistical framework for quantifying and understanding the impact of randomness on outcomes.
Variance can be exasperating, trust me I know, but it’s an unavoidable part of sports betting. Get used to it and condition yourself against it. Understanding variance is crucial for bettors to make informed decisions, manage risks, and optimize their betting strategies. By recognizing the impact of variance on your sports betting, you can implement appropriate risk-management techniques, enhance their long-term profitability and navigate the inherent uncertainties of the betting world.
Charts reproduced with kind permission from Pinnacle Sports