Bankroll Management: How Bet Sizing Impacts Your Sports Betting

Proportional or Flat stake sizing

Bet sizing plays an extremely important role in any profitable betting strategy, and in this article I'm gonna try to give some insight into exactly how important it is. 

In the sports betting community, there are mainly two general staking strategies bettors use. A flat stake, and a proportional stake. With a flat bet size, you either put the same wager on every single game, or you put the same wager on games that have the same odds and edge. Flat bet sizing is fairly easy to use, but it's hard to select a proper size. A size too big will increase the chance of going broke, while a size too low will not yield big enough profits.

As an alternative to this article, you can watch this video. Or you can do both:

 

The Kelly Criterion: A Proportional Stake Sizing Strategy for bankroll management

A proportional strategy is where you place a certain percentage of your current bankroll on each bet. Kelly's Criterion is a formula that maximizes the growth rate of your bankroll. The formula for the Kelly's Criterion is

Kelly Criterion Formula

Kelly Criterion Formula

where P is the probability of success and G is the odds you're given. Let's take an example.

If you were to bet on a coinflip - in a fair world you'd get an odds of 2. If you were to get odds of 2.1, you would've had an edge (you can read more about how edges occur here) of 2.12=0.05=5%2.12=0.05=5% and kelly would suggest

Percentage of bankroll you should stake according to Kelly

Percentage of bankroll you should stake according to Kelly

This means you should bet 4.545% of your current bankroll. Let's take the scenario where this is ran 2 times with a starting bankroll of $100, you win one and lose one.

  1. You bet 0.04545∗100=4.5450.04545∗100=4.545 and lose, now you've got $100−$4.545=$95.455$100−$4.545=$95.455 left.

  2. You bet 0.04545∗95.455=4.3380.04545∗95.455=4.338 and win, now you've got $95.455+$4.338∗(2.1−1)=$100.227$95.455+$4.338∗(2.1−1)=$100.227 left. (4.338 * 1.1 is the net return of the bet)

The interesting thing, is that the order of the bets does not matter. You would've ended up with $100.227 if you'd won the first one and lost the second one.

example of Results Distribution with Different Kelly Percentages

Now over to a practical scenario. The example written over is not exactly representative for the common bettor, because it assumes that you know the outcome of the previous bet before placing the next one. In the sports betting world, one would usually have between 5-50 open bets at the time. This obviously affects the bet sizing. If you were to place 10 bets in a row with similar odds and edge, the bet sizing would decrease as your current bankroll decreases with each bet. If every single bet were with the odds of 2.1 and edge of 5%, you would expect to win 50% of the bets. This gives you the possibility of losing all your biggest bets and winning all your smallest bets - hence ending up in the negatives after placing nothing but profitable bets. It's worth noting that the other way around could occur, you could win all your biggest bets hence flipping a huge profit.

Here is a distribution of all possible combinations of bets with odds of 2.1 and edge of 5%, giving a win rate of 50%. There are 20 open bets, and it randomly picks 10 winners and 10 losers, so it's running perfectly every time - and only a matter of how the wins and loses are distributed. The x-axis shows the bankroll after the bets are settled relative to the starting bankroll, and the y-axis shows the number of occurences (out of the 184756 possible combinations). It follows the kelly bet sizing, so the bet size decreases for each bet as it's always placing 4.545% of its current bankroll. The blue shows the results for 100% of kelly, the orange for placing 50% of kelly, and the green for placing 30% of kelly.

Distribution of simulation outcomes with different Kelly Criterion Percentages

Distribution of simulation outcomes with different Kelly Criterion Percentages

As we can see from the plot, the 100% of kelly (blue line) yields the highest possible return, and the highest average (~1.03). However the spread is huge. One could end up with everything from 88% to 117% of your starting bankroll. As you decrease the fraction of kelly to 50% and 30%, the spread gets alot smaller. The probability of ending up in profit skyrockets, where as the average return gets lowered ever so slightly. It's very important to note that by betting a lower fraction of kelly, you risk less money. By betting 100% of kelly, you risk ~60% of your bankroll to grow it to an average of 104%. By betting 50% of kelly, you risk ~37% of your bankroll to grow it to an average of 102%. By betting 30% of kelly, you risk only ~24% to grow your bankroll to an average of 101%.

You can read more about what you can expect from your results as your sample size increases in this article on the Law of Large Numbers and how it relates to sports betting. 

Stats for 3 Different Kelly Settings 

Table showing Expected Value, Variance, Standard Deviation, best and worst case scenarios for 3 different Kelly Criterion Percentages

Betting less than full kelly to reduce variance

There is no doubt that following full kelly is the strategy that would maximize the growth of your bankroll. Many people will tell you to bet less than the Kelly formula tells you to. Two reasons are generally given for this.

  1. The edge may change. If you place a bet 10 hours before kick off, the odds can swing both in and out of your favor. By placing a fraction of kelly, let's say 50% you have more rooms for error if the edge slightly decrease. If it increases, you can simply place more money on that bet.

  2. The Kelly formula leads to extreme volatility, the probability of being badly down for an unacceptable long strech may occur (You can read more about variance here, and how to reduce variance here).

Additionally, placing a lower fraction of kelly would generally decrease your bet size, making the probability of getting limited by the bookmakers smaller. You can read more about how bookmakers profile winning players here, and  how to avoid bookmaker limitations here

Do not bet more than Kelly suggests, so if you chose to go high risk (100% of kelly), do not over-bet. That will actually decrease the growth of your bankroll - as the full kelly value is a maximizer.

I really hope this gave some insight into how important bet sizing is. Additionaly, I want to point out that there are no perfect bet sizing that fits all. The fraction of kelly you're comfortable with placing depends on your personal risk profile. Do whatever you're comfortable with. In Trademate Sports - you can now select between 3 different betting sizes, 100%, 50% and 30%. Just go to your profile, and it'll be an option.

Source: http://blog.edgebet.net/betsize-and-simula...

Bankroll Management for Sports Trading and Betting Using the Kelly Criterion for Stake Sizing

Sports Betting 101

Understanding the Kelly Criterion is key for any bettor with a goal of becoming a professional sports bettor and do sports betting for a living. This video explains the following topics

  1. What is the Kelly Criterion?

  2. How to apply it when trading sports and betting.

  3. How it relates to profits and risk.

  4. Why the Kelly Criterion is superior to flat stake sizing for bankroll management.

It is hosted by Marius from Trademate Sports. 

Hedging Bets: A strategy for reducing your risk when trading sports?

Key takeaways

  • Hedging sports bets can enable you to reduce your risk, but it will also reduce your potential ROI. Therefore it is a tradeoff between risk and reward that you as a trader have to make.

  • Be aware of potential pitfalls such as bookmakers voiding your bets as they can leave you exposed with high risk and no upside.

“A hedge is an investment to reduce the risk of adverse price movements in an asset.” - Investopedia

Russian Premier League: Ural vs Rostov

Russian Premier League: Ural vs Rostov

An Example of Hedging a Sports bet in a Russian Premier League Game

As a sports trader you can reduce your risk by hedging a trade you have placed. For instance on November 30th, 2016, Ural played Rostov in the Russian Premier League. The opening odds for the game offered by Pinnacle is included in the table below. Rostov both being higher placed in the League and being a team that beat Bayern Munich at 15 in odds in the Champions League the week before was the favorite to win the game.

Soft bookmakers typically place their odds lower than the odds offered by the sharp bookmakers such as Pinnacle, because they have a lower payout rate. 2,5 hours before kick-off, November 30th, the Norwegian bookmaker Norsk Tipping (NT) offered the game at 2.95 for a Ural win. However at this point in time the odds at Pinnacle had dropped to 2.17 (removing their 2,5% vig, the true odds would be 2.26) resulting in a 30.5 % edge [ ((2.95 / 2.26) -1) *100% ]. Next, Norsk Tipping most likely noticing a large amount of money placed on a Ural win adjusted their odds to 2.6 resulting in the odds below.

However, this was still a 15% edge versus Pinnacle. I placed the bet at 2.6 on NT with a stake of 850 NOK or approximately 100 USD. If Ural wins I would get a return of 260 USD and a profit of 160 USD (Stake returned - Initial stake). After I had placed my initial bet, I kept monitoring the odds at Pinnacle, which kept dropping. With such a large edge I now had the opportunity to hedge my bet to completely eliminate any potential losses if Ural failed to win, while making a smaller profit if they win. This was achieved by placing a bet on Rostov to win on the Asian Handicap line of +0.5 at Pinnacle at 1.96 in odds about 20 minutes after taking my initial position. Meaning that if the match ended in a draw, Rostov would have a 0.5 goal handicap, the result being a Rostov win. By hedging on Pinnacle I would have a return on investment of 11,7% given a Ural win [ 1 / (1/2.6 + 1/1.96) ]. While breaking even on any other outcome (a draw or a Rostov win), so basically I was freerolling the game without any risk of potential losses. An important point to note is that hedging differs from arbitrage, because the bets take place at different points in time. This enabled me to get a much higher ROI while taking positions on both sides than what I would have achieved through arbitrage at the time I placed my initial bet. 

Odds for hedging my bet

Odds for hedging my bet

Expected profits after hedging my bet

Expected profits after hedging my bet

New Information in the form of Lineup Changes Made the Odds Drop

The odds at Pinnacle kept on dropping all the way until kick-off as new information became known to the market. Most likely due to Rostov resting several key players, the pictures below compare the lineup Rostov fielded vs Bayern on the left and Ural on the right.

 

Lineup comparison for Rostov in this game vs their last game

Lineup comparison for Rostov in this game vs their last game

When the match started Ural had become the favorite and Rostov the underdog. Pinnacle offered the following odds:

Closing odds at Pinnacle

Closing odds at Pinnacle

The vig-free closing odds offered by Pinnacle at a Ural win would be 1.76 [ 1.71 / 0.973 ]. (You can read more about why the closing line is a good approximation of the true odds of a game here). The closing edge versus my initial trade at 2.6 would have been a 47,7% edge [ ((2.6 / 1.76) -1) * 100%) ]. It is also worth to note that I would have had better odds on my hedge trade if I had placed it closer to kick-off.

The Pros and Cons of Hedging a Sports Trade

The game ended with Ural winning 1-0, giving me a profit of $60. However, if I had simply stuck with my initial trade of a Ural win at 2.6 in odds without hedging I would have made a profit of $160. This highlights the pros and cons of hedging sports. The advantage of hedging was that I managed to eliminate my risk on the game. However, the disadvantage was that I reduced my potential ROI.

Btw, the winning goal was incredible! (27 seconds into the video)

Now, because of Norsk Tipping’s specific rules, the Ural - Rostov game was not offered as a single, meaning that I had to match it with another game to form an accumulator. I ended up combining it with another team scoring 2 goals or less in another game at 1.01 in odds. They ended up scoring 2 goals, so it was a close call, that ended with the trade being good. However this also meant that in reality my hedge trade was not completely risk free. If the 1.01 game had not gone in, I would have ended up losing the $100 I placed through Pinnacle. Also, bookmakers often reserve the right to void bets where the odds is wrongly set. This could potentially have left me with a huge -EV trade. So if you are going to hedge your trades, make sure you are familiar with your bookmakers rules and practices. 

Lessons Learned from Hedging a sports bet

What did I learn from this experience? One can only make decisions with the information one has available at that point in time. I could not know whether the market would continue dropping in odds on a Ural win after I placed my initial trade or whether it would swing the other way. Therefore I made the decision to hedge my trade and freeroll the game for a guaranteed profit if Ural ended up winning. In hindsight, I would have made the same decision if the trade had been a single on NT. However if I come across trades in the future where there are hedging opportunities, but the game is not offered as a single I would rather run the risk with the potential upside of a larger return on investment

Key takeaway

To sum it up hedging a sports bet can enable you to reduce your risk, but it will also reduce your potential ROI. Therefore it is a tradeoff between risk and reward that you as a trader have to make. In addition, you should be aware of potential pitfalls such as bookmakers voiding your bets as they can leave you exposed.

By

Marius Meling Norheim