How Much Of Your Bankroll Should You Bet?

There are two essential characteristics to being a successful long term sports bettor. The first is the ability to recognise value in a given market, and the second is how to manage your investment bankroll. In other words, how to optimise that value and manage risk.

Many bettors have the ability to recognise value in a particular sports betting market, whether that be by ‘gut’ and ‘feel’ or some statistical model to asses the probability of an outcome. But once value has been identified, how much do you invest in that wager to make the most of that value while protecting your bankroll?

There are many and varied investment strategies that can and have been applied to sports betting, a number borrowed from the world of finance. Any Google search however will surely confuse the uninitiated, as a carnival of mutant theories and strategies parade down the page. Regardless, by the end of this article it’s hoped even the most inexperienced of sports bettors will be familiar with the most popular money management strategies, will have a better understanding of the fundamentals behind money management and how to increase their chances of joining the small percentage of sports gamblers who make a long-term profit.
A Slice Of The Pie

One strategy is to maintain a constant percentage of your bankroll with each bet. It’s assumed that this method will protect any bettor from losing their entire bankroll as the amount to be bet diminishes as your bankroll diminishes. It’s a little like Zeno’s paradox. The arrow will never reach its target as it halves the distance at each interval. However, while unlikely, even betting 5% of a €1000 bankroll will leave you with a bankroll of less than €200 after 33 consecutive losses.

But more to the point, it assumes equal value for each bet and additionally it expects equal odds being offered for each bet. Let’s say that bookmaker bet365 are offering odds for a team to win of 1.70. Would you really want to bet the same percentage on a 1.70 favourite as a 3.50 outsider without any recognition of their respective value? The answer should clearly be no. Further, even if you only bet on 1.70 favourites, is the probability of each 1.70 favourite winning identical in each instance? In other words, does each 1.70 favourite offer the same value? It could be the case, but its unlikely.

The Slice of the Pie strategy while offering a manner of managing your bankroll, fails to recognise value as a key part of a successful management strategy. Essentially, in the end, it will only manage the way you lose your money.
Inside out

This method is similar to the Slice of the Pie, except that it takes the further step of taking into account the odds being offered for a particular bet. So for example, you bet 5% of a €1000 bankroll as a standard unit, €50. If betting on 2.00 odds, the unit remains €50, but when betting on say a 11.00 outsider, that unit becomes €5. It can be calculated like this:

eg. (€1000 * 0.05) / (11 – 1) = €5

This works fine when betting on outsiders but what if we wish to bet on short priced favourites? If betting 5% of any bankroll, betting on a 1.05 favourite would mean betting your entire bankroll. Now I would never recommend betting on anything remotely close to a 1.05 favourite let alone your entire bankroll, (unless the odds were on the sun rising tomorrow, but even then I would probably spend a nervous night watching the darkened night sky). Regardless, the limitations of the Inside Out strategy should be clear as it still fails take into account the recognised value of a particular betting proposition.
K is for Kelly

While it still has its critics, the Kelly Method has stood the test of time since its creation in the mid 1950′s. Essentially this method takes into account both the probability of a given team or player winning and the value of the odds offered in relation to that probability – also known as ‘the overlay’. This means that it suggests you bet more depending upon how great the overlay is, but it also means you have to assess the probability of a given outcome with consistency.

The overlay is calculated simply as:

Overlay = (probability * odds) – 1

There have been many amendments to the Kelly method over the years, and although the fundamentals remain the same, each edition of the method offers its own insights.

The Full Kelly – While a proven method, the Full Kelly can make a wild ride of your betting experience and can suggest risky amounts be bet. It can easily recommend a bet of even 50% of your bankroll, which can reduce your bankroll to merely nothing in a short time. On the other hand, a winning streak can send your banroll into orbit

It is calculated as:

Percentage of bankroll to bet = Overlay / (Odds – 1)

e.g With an overlay of 0.20 and odds of 2.40 and a bankroll of €1000, the Full Kelly would recommend a bet of €143, or 14.3% of the bankroll.

The Fractional Kelly – This is a simple and conservative amendment to the Full Kelly method whereby the bettor only bets a certain fraction of the recommended bet. It could be 50%, known as the Half Kelly, 25% the Quarter Kelly or any percentage you feel comfortable with. Further, while the intuition may be that this will reduce your winnings according to the percentage you choose, it can be shown that a fractional Kelly method can return better results long term than the Full Kelly method.

The Constant Kelly – The same as the Full Kelly method, but rather than recommending a percentage of a varying amount, it recommends a percentage of a constant. So for example, instead of suggesting 15% of a diminishing or improving bankroll, it recommends 15% of a constant amount.
Busy Busy Busy

One of the drawbacks of any Kelly method is the issue of betting on multiple events at the one time. Let’s say there are 4 games you want to bet on, all being played at the same time. And what if the recommended percentage of bankroll for Bet A is 25%, Bet B is 35% and Bet C 35% and Bet D 40%? This amounts to betting 135% of your bankroll, which is obviously impossible.

One solution to this problem is to adjust the percentages proportionally so that 100% of the bankroll can be bet. i.e Bet A would proportionally become 19% and so on, as 25% is a proportional 19% of the 135% recommended. The issue with this is that firstly, you’re still betting 100% of your bankroll on 4 events which could all easily lose, and secondly, it means you’re not giving the same value to say a 25% bet on a busy day (where in this example it becomes 19%) as you would on a day when it might be your only bet.

One way to solve this is to use a fractional method so that no matter how many events you want to bet on in a single day, the total recommended is unlikely to eclipse 100% of your bank. This could well work, but as I know myself, it is easily possible to be betting on up to and over 20 events in a single day, meaning the 100% could still be eclipsed.
So What Do I Suggest?

Personally, I use a 10% fractional Kelly method. This allows me to protect my overall bankroll while I diversify and place many bets on sporting events being played daily.

So let’s say my bankroll is €5000, and I am betting on a team to win at odds of 2.60 offered by bookmaker Pinnacle Sports. Now let’s say I have assessed the probability of this team winning to be 50%, the recommended bet amount would be calculated as:

(bankroll * chosen fraction) * (overlay/(odds – 1))

i.e ($5000 * 10%) * (0.30 / 1.60) = €93.75
Try It Out For Yourself

While many bankroll management strategies are available to apply, I believe that the fractional Kelly method is best, as it takes into consideration the odds on offer, the probability assessed of a team or players winning and the resulting value identified in order to recommend a bet amount that will optimise that value without risking your bankroll and an early end to your career as a sports bettor.

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