This info was in an email I get from a company called Betitup .. who are basically youngsters who specialise in sports modelling.
The info is v well presented, and newbies might find it useful.
I have no financial link to the company, apart from buying services.
I am having to cut/paste pics .. hope they in the right place. Will try 3 pics at a time // hmm dont seem to be able to post more than 3 pics, per post. There are like 11 pics. Will try dropbox it.
With the MLB season being just around the corner and after loads of feedback from you readers... It's time to start a series around the "mechanics" of profitable sports betting. One of the most misunderstood aspects of being a winning player is bet sizing. Bet sizing for + EV bettors is critical for those taking an investment like approach to sports betting, Here at Betitup we view it as our responsibility to provide you readers with the very best information
we can find and today's contributors are no different. Dan Rubin and his team at Cleat-street.com / @Cleat_Street came to us highly recommended by a very trusted source and in this article you will see why. Dan is analytically-minded and financially trained. His passion for sports now meets profession as he aims to usher sports gambling into a mature asset for fans and investors. Enjoy and please share your feedback at [email protected]
What’s My Unit?
Position Sizing, Money Management, and More
Finding the right picks and establishing conviction is one of the more difficult aspects of sports gambling. However, money management is usually glossed over and can be the difference between zero and hero.
The money management advice that we usually find lies in the units ascribed to a pick. We’ve all seen a version of this before:
Portland Trailblazers -9.5 at Cleveland Cavaliers, 1.5 units
Sports gamblers refer to units as a standard of communicating conviction. The more units cited, the more confident a recommender is in his or her pick.
But what does 1.5 units really mean?
The rule of thumb is that 1 unit = 1% of a bettor’s bankroll, and analysts typically recommend between 1 and 5 units. This rule of thumb can be misleading. The truth is – it means something different to everybody and is determined by the following four factors:
1. Risk Tolerance
2. Bankroll
3. Odds / Payoff
4. Expected Win Rate (%)
Once we have a deeper understanding of these four factors, we can better interpret just how much a unit means to us.
Risk Tolerance
Sports gambling outcomes are binary – either a team covers the spread or it doesn’t – but win rate is a spectrum. This key difference drives wealth volatility that even the best sports gamblers experience over time. To accommodate this volatility, sports gamblers have stuck to a series of frameworks beginning with the Kelly Criterion.
The Kelly Criterion was published by J.L. Kelly Jr. (with the help of Claude Shannon) in his 1956 piece entitled “A New Interpretation of Information Rate” in The Bell System Technical Journal. In short, Kelly argued that sports gamblers should wager amounts tied directly to their “edge” or conviction in a pick in order to maximize their median wealth over a betting horizon. For example, a sports gambler that has a 54% win rate would bet 3.4% of his or her bankroll on each bet with -110 odds based on the Kelly Criterion.
While the Kelly Criterion is designed for maximizing bettor returns, it still leaves open the possibility of boom and bust scenarios. To control this volatility, many sports gamblers apply a risk tolerance framework to mute the wild swings. Today, this is generally referred to as Fractional Kelly Criterion (e.g. “Half-Kelly” or “Quarter-Kelly”). These approaches simply take a fraction of what the Kelly Criterion suggests for a given win rate. For example, a Half-Kelly approach to the same 54% win rate / -110 odds bet would recommend a bet of 1.7% of one’s bankroll (vs. the Full-Kelly recommendation of 3.4%)
Fractional approaches reduce the median final wealth created by a winning betting strategy but also reduce the standard deviation of returns. This allows investors to accommodate their risk tolerance across different betting strategies and uncertainty with respect to expected win rate (%). Most sports gamblers avoid a Full-Kelly approach for these reasons.
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Bankroll
Throughout our lives, we’re bombarded with investment rules of thumb: max out your IRA contributions, invest (100 – your age)% in stocks with the rest in bonds, the list goes on. While these can be broadly helpful, most recommendations boil down to a balance between risk and reward and can be easily applied to sports gambling.
The Sharpe Ratio is the most familiar risk-reward framework in finance. Conceptually, it balances:
Expected Return
Alternative Risk-Free Expected Return
Risk Exposure
Consider two potential investments:
A: You expect a ~20% return in one year, but this could range from 0% to 40%
B: You expect a ~10% return in one year, but this could range from 8% to 12%
Which of these two investments would you prefer?
At first glance, it isn’t easy to compare the two investments. On the one hand, you stand to earn almost twice as much with security A; on the other hand, security B feels less risky because you will create wealth across all scenarios. The Sharpe Ratio simplifies this – security B is more attractive on a risk-adjusted basis
pic 5 here
Using these same parameters, we can easily calculate the Sharpe Ratio of a successful sports gambling strategy and compare this to other investments, such as the stock market.
In order to calculate the Sharpe Ratio of the sports gambling asset class, we need to make a few assumptions. First, let’s assume that the strategy has a win rate of 54%. Second, we will assume that each bet is made at -110 odds (the combination of the first two assumptions implies an expected return of 3.1% and a standard deviation of 95.1% for each bet made). Third, we expect to place ~350 bets in a given year as we play selectively through the NFL, NBA, and MLB seasons
pic 6 here
In the context of the assumptions that we’ve made, sports gambling appears to have a Sharpe Ratio of 0.03 for each wager made and 0.61 after the year is finished. It’s important to note that the Sharpe Ratio of the betting portfolio is independent of the Fractional Kelly Criterion applied, but each framework has materially different expected returns and standard deviation as illustrated above.
These assumptions can change materially depending on the strategy that you end up implementing. Generally, the most important assumptions are the win rate and the number of bets placed in a given year. In practice, one’s win rate intuitively goes up as one gets more selective and bets on fewer games.
pic 7 here
Now that we understand sports gambling’s risk and reward, we can compare it to other asset classes. For now, we’ll continue to use our example strategy that has a Sharpe Ratio of 0.61. This compares to the S&P 500 average of 0.82 over the last 30 years. Investing in the S&P 500 provides a better expected return for the amount of risk assumed than our example strategy.
However, traditional financial frameworks recommend investors to diversify across various asset classes. So how many eggs belong in your sports gambling basket? In other words, what percentage of your portfolio should be allocated to your sports betting bankroll?
Unfortunately, the answer is: it depends. It depends on the amount of risk you are willing to take. Some useful questions on this front include (but aren’t limited to):
• When will I need this money next?
• If I lost 50% of my bankroll, would I keep the remaining 50% invested?
• How stable are my current and future income sources?
pic 8 here
Using diversification as a guide, it is reasonable to include a winning sports gambling strategy as a part of your overall investments. Ultimately, it is up to you to decide what extent you invest in sports gambling relative to other asset classes.
Let’s follow an example:
Assume that an investor, Jake, has saved about $30,000 and decides to invest ~10% into sports gambling. This implies Jake’s bankroll is about $3,000. Given Jake’s desire for reduced risk, he decides to implement the Quarter-Kelly Criterion in the example betting strategy with a 54% win rate. Jake will therefore start out betting about $25 on each wager he places, which will increase from there as the strategy profits thus compounding returns. All else equal, $25 per wager is Jake’s initial “unit” until his bankroll changes.
Odds / Payoff
Thus far, we have simplified the betting landscape to the standard -110 odds generally applied to ATS and over/under picks with reasonable trading volumes. The reality is the betting landscape is much wider than this niche, though the principles we have discussed still apply. In fact, odds / payoff may be the most certain of the four parameters for an investor. While odds can differ from one sportsbook to the next, investors can effectively “price shop” to find the best lines at a sportsbook that they are comfortable with and then use this as input to implementing a strategy.
While we can explore the arbitrage opportunities across sportsbooks with differing lines and how lines tend to evolve over time, we will save these concepts for a later date.
Expected Win Rate (%)
Estimating a reasonable win rate for a basket of picks is crucial to money management, but a lack of transparency in the industry should keep investors on their toes. So far, we’ve explored independent strategies with static win rates but the world is much more complicated than that. Within a given strategy, win rates can differ materially year-to-year and across types of picks. This gets even more complex as we combine picks from a basket of different strategies to ultimately build a “portfolio” and these different strategies do not always have a transparent track record available. Without perfect information, investors should be duly cautious of strategies that overfit trends or analysts that embellish their track record.
Win rates are inherently volatile and this is linked directly to the volume of picks a strategy spits out. The more picks, the less volatile the win rate. Ironically, more picks and less volatility also tend to accompany lower win rate strategies – nobody ever said this would be easy.
pic 9 here
So how does a strategy’s win rates vary then?
Most obviously, win rates vary over time; a strategy’s overall win rate is always evolving and we attribute this to several reasons:
1. Causal relationships strengthen or weaken
2. The market becomes more efficient
3. Plain-vanilla randomness
Bettors need to always keep their eye on the ball. While short-term volatility in a given strategy is to be expected, there is an acute difference between this volatility and structural change. Over time, it will become (painfully) apparent whether or not the win rate has devolved.
Win rates can also differ within a strategy’s types of picks. This applies to residual-based strategies that recommend picks based on the difference between the market price and the fundamental forecast; the greater the difference between the market and the forecast, the higher the conviction. Many analysts will segment recommendations from the same model, offering a buffet of conviction and subsequently win rates. For example, a single strategy may forecast a mispriced NBA spread by 2 points for one game and 1 point for the second game; assuming data integrity, the first recommendation has greater conviction than the second and should thus have a greater win rate. The units an analyst recommends should be tied to the tiering of picks within the strategy, reflecting the relative win rates.
So are all units created equal? Resoundingly, no!
Different strategies have different win rates. Unless the analysts behind two strategies coordinate their unit recommendations to accommodate this fact (highly unlikely), the units are unique to their respective strategy and cannot be directly compared to each other.
This is especially precarious when we scroll through our Twitter feed, cherry-picking recommendations from our favorite analysts to build a portfolio of bets on a single day. Money management now becomes convoluted and imprudently brushed to the side.
While more complicated, it is still crucial for investors to understand the composition of their portfolio and how they should be managing their money. Ultimately, we believe a portfolio approach is the best way to reduce volatility and is well worth the extra brain power it takes to pull together.
A portfolio approach is a multi-step process in which the investor builds the portfolio from a selection of picks, determines the characteristics of the combination of these picks, and then allocates bankroll appropriately.
Let’s follow an in-depth example:
Jake has just refreshed his model for tonight’s slate of NBA games and is determined to bet on two picks. As he is scrolling through his Twitter feed later that afternoon, he finds two more picks from two separate analysts. Jake now has four at-the-spread picks that he will bet on tonight and needs to determine how much money to place on each wager.
Strategy A: Jake has the most visibility into his own model. The two picks he’s found for tonight fall into his Tier One and Tier Two buckets, with respective out-of-sample win rates of 56% and 53.5%.
Strategy B: An industry veteran who has publicly published her picks for two years now, recommends one pick for tonight and ascribes 5 units to it. Jake judges that she has a historical win rate of 54%. Tonight’s pick is clearly higher in conviction based on the number of units recommended and so Jake conservatively estimates the win rate to be 55%.
Strategy C: A relative newcomer to the industry has been publishing his picks for two months now and has a win rate of 56%. He recommends one game tonight and ascribes 1 unit to it. Jake recognizes the small sample set for the overall win rate and that this pick is lower in conviction; he conservatively estimates the win rate to be 53%.
Jake usually applies Quarter-Kelly Criterion to a single bet to reflect his risk tolerance. Using this framework, he realizes that he will be wagering more than 4% of his bankroll across the four picks and quickly becomes uncomfortable with this figure. His gut instinct is to cut the allocations across the board.
pic 10 here
Upon further investigation, Jake realizes that the combination of the four picks actually cuts the riskiness of the portfolio in half. This is the power of diversification.
Because the portfolio is less risky than the sum of its parts, Jake can even apply a Half-Kelly Criterion to the portfolio as a whole. In this way, Jake is creating a more attractive investment than any of the individual picks by themselves (higher Sharpe Ratio) while still accommodating his own risk tolerance.
pic 11 here
At Cleat Street, we take a strictly financial approach to sports gambling as an asset class, using many of the concepts discussed in this article. As we launch over the next month, we plan to offer a recommendation engine to our customers that balances risk and reward in a portfolio framework. Our fundamental thesis is that a disciplined portfolio framework combined with prudent money management practices is critical to successful investing. If you’re interested in learning more or becoming a customer, head over to cleat-street.com to sign up!
Footnotes and Disclaimer
1: The absence of readily available track records makes it easy for analysts to misrepresent their win rates in the pursuit of making more money. This is a subject unto itself that we will dive into at a later date.
Disclaimer: Investments in sports gambling are higher risk instruments and should be approached with precaution. The views expressed above are our own opinion and we do not make any warranties about the completeness, reliability, and accuracy of this information. You are cautioned not to place undue reliance on these statements, which reflect our opinions only as of the date of this presentation. Any action you take upon the information in this article is strictly at your own risk. It may be prudent to consult a financial advisor before taking such steps.
Discussion of betting units - Good stuff
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sorry for the necro-post. Liam - this is exactly what i do too and wondered if it had an official title (kelly on fixed bankroll - variable staking ).
having tried all the other variants of fractional kelly on a compound bankroll, i look at this as the best long(er) term fit.
my *studies* have gone thro all sorts of variants on staking from level, to percentage to kelly. i did of course in the *early* days dabble with receovery methods as i too was one of those that believed in the gamblers fallacy and was certain that 2 losers meant that a winner was on the way -lol. a bankroll refresh (or two) soon disabuses you of that notion!!.
there is no nirvana (tho there is a foo fighter in us all
) - but evaluating your strategies and determining a staking plan that DOES NOT involve recovery but does party on value has to be one step closer.[edit] - in truth, to undertake this type of discipline, you either need to code up yourself against the api, or use a 3rd party application that has kelly built into the staking options. to manually apply them in BA would be a tad cumbersome on a bet by bet basis as it is pretty much dictated by the current odds, your bankroll and your own implied odds (or strikeweight of your strategy). Could stored values be used i wonder if push came to shove??
since this post has been brought to general attention again, seems worthwhile adding a little primer on kelly:
https://www.bettingexpert.com/academy/a ... ained#gref
[edit] - i also think that the title is the main reason why it was either missed or ignored. potentially renaming it to something like Money Management - What's your angle!?! or something along those lines would give more insight to the content..
https://www.bettingexpert.com/academy/a ... ained#gref
[edit] - i also think that the title is the main reason why it was either missed or ignored. potentially renaming it to something like Money Management - What's your angle!?! or something along those lines would give more insight to the content..
Tbh not sure if it an official name but I know a few syndicates use the same.jimibt wrote: ↑Fri Feb 28, 2020 11:56 amsorry for the necro-post. Liam - this is exactly what i do too and wondered if it had an official title (kelly on fixed bankroll - variable staking ).
having tried all the other variants of fractional kelly on a compound bankroll, i look at this as the best long(er) term fit.
thanks liam - that's more than good enough for me. have a grt wknd.LinusP wrote: ↑Fri Feb 28, 2020 4:08 pmTbh not sure if it an official name but I know a few syndicates use the same.jimibt wrote: ↑Fri Feb 28, 2020 11:56 amsorry for the necro-post. Liam - this is exactly what i do too and wondered if it had an official title (kelly on fixed bankroll - variable staking ).
having tried all the other variants of fractional kelly on a compound bankroll, i look at this as the best long(er) term fit.
Haha, I never really looked into the whole math behind Kelly etc, although I understand why there would be a need for it when it comes to betting/gambling strategies with tight edge margins since afaik the whole point of it is to try and maximize the expected value and I'm aware that some of the richest people on the planet used different types of Kelly methods, but I always thought that it was a bit of an overkill when it comes to pure trading strategies because the edge margin should be greater on average, at least on the sports exchange. That was at least part of the lessons learned after a tilting situation at the start that cost me a good chunk, albeit a minuscule price to pay for changing direction, because it wasn't the staking that got me into trouble, it was the psychology behind it, so all my staking decisions since then were pretty much entirely based on psychology instead of numbers. Had a reckless start but since adopting a more calculated approach the only goal was to slowly start taking on more and more risk by expanding that comfort zone which is by far the most important thing for me. Since then, I've capped out staking-wise on some markets and gotten used to risking the entire stake at times, so this approach has obviously been working for me. Making one concrete step at a time instead of trying to make 10 at once and falling flat on my face.jimibt wrote: ↑Fri Feb 28, 2020 1:33 pmmy *studies* have gone thro all sorts of variants on staking from level, to percentage to kelly. i did of course in the *early* days dabble with receovery methods as i too was one of those that believed in the gamblers fallacy and was certain that 2 losers meant that a winner was on the way -lol. a bankroll refresh (or two) soon disabuses you of that notion!!.
Yeah, I feel it entirely depends on your strikerate and type of approach etc, tbh I don't really see any real benefit for the bread and butter trading approach that I used the most, I only see it needlessly overcomplicating things. Can't really see how a higher frequency trading strategy with an innately higher strike rate benefits from it, perhaps if it was automated, but I haven't had the chance to look deeper into that option yet and haven't really consulted too much with experienced botters. I did share a random clip with Shaun once but he never mentioned anything about automation potential, I'm sure he would have told me!jimibt wrote: ↑Fri Feb 28, 2020 1:33 pm[edit] - in truth, to undertake this type of discipline, you either need to code up yourself against the api, or use a 3rd party application that has kelly built into the staking options. to manually apply them in BA would be a tad cumbersome on a bet by bet basis as it is pretty much dictated by the current odds, your bankroll and your own implied odds (or strikeweight of your strategy).
The losses are obviously there but for the most part they can't really be seen on a P&L due to the higher frequency of trades/bets per market, although in fairness I do in general try to avoid most of the losses by avoiding unsuitable markets, so the scratch results that should be losses are mostly just me ditching an unsuitable market. I see something as simple as that often overlooked, with people trying to force an approach on a market that is just not suited for it.
And when I compare some of my trading with the very best traders out there, like with Psychoff's bread and butter trading approach on the image below (which granted most people don't really see or care about), the interesting bit for me is that he achieved different results with the same/similar stake sizes, because he chose a market that's even more suitable to these types of approaches, market with a bit more risk but with a lot more volatility, and due to the gulf of experience it makes sense that his comfort zone is far greater than most traders. Which was a bit of a breakthrough for me, realizing that even though I was trading the right markets it turned out that I was trading the "wrong" ones and basically mismanaging a good chunk of my skillset. So since then I've tweaked my approach and made a switch to a very different market, different to his as well, but automation aside I think that ultimately I'll almost certainly end up utilizing this approach on cricket as that's as far as it can probably go.
So in a nutshell the staking itself is probably one of the last things on my mind, I only want to use whatever stakes I feel comfortable using, depending on the type of approach and the quality of opportunity. That's just my 2 cents at least.