Fri, Feb 7, 2025
By
Veri.bet
Betting accumulators, also known as parlays, are a popular choice among sports bettors due to their promise of high returns from small stakes. They allow gamblers to combine multiple bets into one, offering a payout that multiplies individual odds together. However, the very nature of accumulators introduces a significant statistical disadvantage. In this article, we will explore the underlying mathematics that makes betting accumulators a risky endeavor, backed by probability theory and external authoritative sources.
An accumulator bet combines multiple selections (legs) into a single wager. For the bettor to win, every leg must be correct. For example, if you combine five selections, and any one of them loses, the entire bet is lost.
If each leg has odds of , the overall probability of winning the accumulator is:
The payout is calculated by multiplying the odds of each leg together and then multiplying by the stake. While this multiplication increases the potential reward, it also compounds the risk exponentially.
Assume that each event in your accumulator has a 60% probability of success (which is optimistic for most betting scenarios). With five legs in the accumulator, the probability of winning is:
This means there is a 92.224% chance of losing the bet. As you increase the number of legs, the probability of success declines rapidly due to compounding risk.
Thus, even with reasonably favorable odds on individual bets, the overall likelihood of winning an accumulator quickly diminishes as more selections are added.
Bookmakers add a margin (overround) to each event, which ensures their long-term profitability. In simple terms, this means that the odds provided are slightly lower than the true probability of the event occurring.
For example, if a fair bet would have odds of 2.0 (implying a 50% probability), a bookmaker might offer odds of 1.91. This difference accumulates in an accumulator bet.
If the overround on each leg is 5%, and you include five legs in your accumulator, the effective margin compounds:
Thus, while the stated odds might look attractive, the hidden costs of compounding margins significantly reduce expected value.
To understand why accumulators provide a disadvantage, consider expected value (EV). EV measures the average return of a bet over the long run:
Let’s assume you place a 5-leg accumulator with a stake of €10. The combined odds are 20.0, and the true probability of winning is 7.776%.
While this example shows a potential profit, it assumes no bookmaker margin. Introducing a 5% margin per leg yields:
In this case, the adjusted EV is negative, illustrating the cumulative impact of margins and low probabilities.
Several studies on sports betting outcomes support the mathematical disadvantage of accumulators. According to a report by The Economist, accumulators are among the most profitable bet types for bookmakers due to the low probability of success and compounding margins.
Moreover, a study by the UK Gambling Commission (source) found that accumulator bets accounted for a significant portion of losses among recreational bettors, further demonstrating their poor expected value.
Bookmakers actively encourage accumulator bets through promotions, enhanced odds, and bonuses. The reason is simple—accumulators maximize bookmaker margins while minimizing payouts. Even when offering bonuses such as "accumulator insurance" (where bettors get their stake back if only one leg fails), bookmakers remain highly profitable.
Consider the following benefits for bookmakers:
Higher Hold Rates: Bookmakers retain a larger share of the total wagered amount.
Increased Betting Volume: Accumulators encourage larger bets due to their promise of outsized rewards.
Psychological Appeal: Bettors are drawn to the allure of small stakes turning into massive wins, despite the low probability.
While accumulators are statistically disadvantageous, bettors can apply some strategies to minimize losses:
Limit the Number of Legs: Keep accumulators short (e.g., 2-3 selections) to reduce the compounding effect of risk.
Focus on Low-Margin Events: Select events with minimal bookmaker margins.
Use Bonuses Wisely: Accumulator bonuses and insurance can partially offset losses but should be viewed with caution.
Betting accumulators promise high payouts but come with an inherent statistical disadvantage due to probability decay and compounded bookmaker margins. Understanding the mathematics behind accumulators highlights their negative expected value for bettors, making them a risky choice in the long term. For recreational bettors, accumulators may provide entertainment value, but they should be approached with caution and awareness of their underlying risks.
For further insights into betting mathematics, see Joseph Buchdahl’s book on sports betting analytics and explore statistical analyses on betting theory at Rowdie.co.uk.