Accumulators and compounding

A bit of a departure from my usual favoured topics, but I have been inspired by a seeming lack of articles around this subject, which is relatively simple but often…

Categories: All Sports, Prices, Statistical models, The basics

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A bit of a departure from my usual favoured topics, but I have been inspired by a seeming lack of articles around this subject, which is relatively simple but often underplayed or underestimated.

The entire concept goes right back to the cornerstone of the high-margin business that high street bookmakers in the UK used to enjoy after their legalisation back in the 60s. Finally punters could combine events, across matches, leagues, countries and sports, in the hope of landing a massive payout.

The price at which these payouts came, however, was very high. Still to this day do we (very occasionally!) see the betting press run a story on a punter winning hundreds of thousands, or even a million, from a small stake. Why are these stories still so popular?

Many know that coupon bets or “acca” bets are so often a mugs bet. However, they are not quite as clear as they should be on why. The answer is relatively simple; think of it as the same effect as compound interest has.

If I borrow £100 at a rate of 10% over a 10 year term, and make no payments in the interim, but merely pay the entire sum back at the end, the interest accumulates on the interest. Thus, I accrue £10 of interest in the first year but £11 in the second year, £10 on the principal and £1 on the existing interest. This phenomenon, compound interest, means I accrue £159.37 interest over the term. If I only paid interest on the principal, I would have accrued £100. So, I have paid nearly 60% more thanks to compounding.

Happily, for the savers out there, the same phenomenon applies and this effect turned around the other way helps make mountains out of relatively small investments, if they are left to accrue for long enough. The same logic applies to an accumulator bet.

Imagine two punters – Average Joe and Sharp Steve. Joe picks 10 bets he thinks will win, 10 favourites which for the sake of argument all have a 10% edge to the house. He bets £10. His £10 is exposed to the edge, compounded, 10 times. On a £10 single he would lose £1 on average to the edge.

On a £10 accumulator he loses £6.51 on average to the house edge, so his money disappears 6.5 times as quickly. He faces (essentially) a 65% house edge – such a game is incredibly difficult to beat of course!

Steve picks 10 outcomes where he estimates that the player edge in his favour is 10% on each bet. If he bets a £10 single, he would win £1 on average.

On a £10 accumulator he wins £15.94 on average (returning £25.94) – a 159% advantage.  Truly a crippling edge.

Of course, Steve has to factor in the probability of his outcomes to optimise such situations. If each bet he combines he is receiving 1000/1 on a true 900/1 shot, and he has to combine such bets, the odds are overwhelming that he will die before he ever cashes in. Using the Kelly Criterion to determine optimum stakes, the determined stake for almost any bankroll would be effectively zero.

A further benefit to Steve, however, is that the use of the accumulator offers him a smokescreen. Accumulators are rarely used by sharp punters – the variance that they introduce can offer an extremely rough ride – however, if used sparingly and wisely, they can also turn a comparatively small edge of 1-2% into a large one, through the “magic” of compounding advantage.

About Adam Lawrence

Adam divides his time between betting for profit and the property business. His background is varied including a strong academic pedigree alongside international experience in finance and wealth management, but he has found his niche now and is busy settling into it for the long haul.
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