As one can imagine, we are not running into a unique problem by looking at this. In fact, since this problem touches anything where winnings compound and losses accumulate, basically all of the work has been done for us by clever people in the 1950s. Whilst it isn’t quite DNA or the polio vaccine, for us we’re looking at John Larry Kelly Jr.’s ‘Kelly Criterion’, which maximises the log-growth of the bankroll per-bet.

Intuitively, if we have an edge, we want to bet as big as possible, unless we’re betting so big that we’re in mathematically unsound levels of danger of our bankroll dropping to 0. And that is likely to depend on the size of our edge, and the likelihood of a winning payoff.

However, we do need to caveat our excitement slightly. Full-Kelly (betting the full fraction suggested) is brutally heavy on variance, sometimes requiring atomic-grade wagers of 20-40% of our bankroll depending on the probabilities involved. To retain the benefits of dynamic staking whilst minimising variance we typically pick a fractional Kelly regime, which significantly reduces the variance whilst preserving proportionally more bankroll growth. In past experiments I’ve used quarter-Kelly which has generally served me well, preserving 44% of the bankroll growth of full-Kelly, whilst subjecting our wallets and blood pressure to a much-reduced 6% of full-Kelly’s variance.

But, as nice as this has been so far, does it actually make a significant difference versus flat staking? In particular, if we’re going to implement this we at least want to be confident it will increase the growth of our bankroll. Let’s imagine we’ve found 1,000 bets, ranging from 2-8% in edge, and at odds 2.0 to 5.0. Unit staking or Kelly?

So in the figure above, we see that by varying our stake sizes with our estimate of the true edge, we generate an additional 0.6% ROI over the simulated runs. This is pretty significant; inevitably in the world we’re going to inhabit we’re going to have different projected edges and different odds, and a staking regime that ups our ROI by 0.6 percentage points is a very tidy outcome.

As with seemingly everything we cover, a word of caution is required. Whilst the above experiment enjoys the absolute privilege of knowing its exact edge, we almost certainly won’t in the strategies we’ll cover over the rest of this series. If a miscalibrated model starts putting more capital behind bets which have a lower true edge, far from enjoying a higher ROI we’ll instead suffer decreasing returns.

Speaking of knowing our true edge, the central thrust of Q1-03 was that this is actually really quite complicated. For good, liquid markets, we can use CLV. The statistical bar for proving our strategy is valid using CLV is much lower than drawing conclusions from our betting history. Our outcomes are no longer either winning or losing a bet, with all of the accompanying variance, but a comparison of the odds we’ve bet at versus the CLV, which is much more stable.

But if we want to go into more niche markets, CLV is less accurate for comparison. We need to look at our dataset and analyse it to identify whether there’s sufficient evidence to reject the null, and rather depressing hypothesis that we’ve not achieved anything meaningful edge-wise. This is simply a function of lower limits leading to less intensive price-discovery.

Source (exact figures aren’t watertight but there is a significant difference in limits for player props versus moneyline bets).

Does our newfound knowledge of staking regimes change the picture? Not in the strict sense. Adjusting our stakes up and down doesn’t change the underlying maths, which are entirely a function of betting outcomes. We can't manufacture evidence that an edge exists by deciding to risk more or less money on it. But in discussing staking we’ve opened up the dataset to be a better fit for reality — varying odds, varying edges. This can lead to alternative statistical methods that attempt to quantify whether our estimates of our edges is correct, such as log loss and brier score, meaning there is more out there to explore once we’re up and running some strategies.

But for now, where do we stand:

• Staking regimes in dynamic edge environments actually matter and yield additional ROI over sequences of bets.

• Quarter-Kelly is our regime of choice to preserve bankroll growth whilst minimising variance.

• Proving our strategies are +EV is still painful unless we have strong CLV data.

• Looking at alternative statistical methods can yield additional information about our betting performance.

Theory over, next post we’re going to finally delve back into The Research Desk and discuss a specific strategy I’ve been running over the past few weeks, which has yielded positive results. Looking forward to seeing you there.

The Alternative Desk
Still a going concern

The purpose of these posts is to deep-dive into a quantitative topic, from the generally rather dry theory to the more interesting question of how it can be exploited to create profitable strategies. It should also function as a helpful primer to much of the theory behind what we’re going to cover in the more strategy-driven ‘Research Desk’ posts, keeping them free of definitions and focused on the more interesting bits.

Those who’ve followed the desk for the past month will know that our universe for the quarter is betting markets. Specifically betting exchanges, which was picked for the astute reason that they were the only venues which I could both access and hadn’t been stake-restricted on.

The fundamental driver of winning strategies in all betting, including across betting exchanges, can be boiled down to one concept: Expected Value (EV). It’s both easy to define and difficult to confirm the existence of. Not quite God, but for our purposes it may as well be. So today we’re going to explore EV for betting markets, from theory, to practice, to statistically significant amounts of practice to minimise variance.

So a sportsbook has cost-cut a little bit too aggressively in its odds team, and now has a line on its website at 2.1 for a fair coin-flip. Using our formula to sum the products of the different payoffs and probabilities, we can see we’ve found a tidy little 5% edge. Unfortunately, we’re going to spend the rest of this post discovering that a 5% edge is difficult to both identify and use, but at least that gives me some content to write about while I try to do something actually interesting for the next editions of The Research Desk.

But, whilst this was a nice example in isolation, what with its known true probabilities and all, how about something we’ll actually see on a sportsbook, and how does this relate to EV? Well as we know every price implies a probability of the event occurring (the decimal odds’ reciprocal, which is yet another reason to move from the ghastly American odds format). In absolute isolation we might not know whether this is a fair price. But if we add up the implied probability across all the lines, representing all the outcomes of a market, we can get a mathematical idea of just what the margin is on a sportsbook’s market.

Here we can sum the reciprocals and we get 105.3%. That excess above 100% is known as the ‘vig’. Sometimes also referred to as the overround, juice, or if you’re feeling a touch archaic, ‘vigorish’. This is essentially the average margin the bookmaker will make on a bet, and the lower the vig, the more competitive odds you’re seeing.

As we previously mentioned, the true price of an event is ‘discovered’ on sharp books which charge a very low vig, taking money from high-value bettors and syndicates, with the lines being adjusted based on this action until the market reaches an approximate consensus. From there, the number travels. Data companies buy the sharp lines, package them into a feed, and sell them on. The household sportsbooks sponsoring the shirts are, for the most part, displaying a bought-in price rather than one they worked out themselves, then marking it up with their own margin on top. So the price a casual punter sees has already passed through several hands, discovered by people who bet for a living, wholesaled by a middleman, and vigorously vigorished by a brand whose entire model depends on that markup.

But of course, we don’t care about soft books, although knowing the mechanics may give you a few ideas of how to find +EV bets on them (see: Steam Chasing). What we care about is finding the true price of an event, and we’ve just stumbled on how to do this. Strip the thin vig out of a sharp line to recover the true probability, and you have a benchmark. A bet is positive expected value if, and only if, you can get odds better than that devigged sharp price. There are multiple ways to devig these lines, but on relatively low vig markets it’s sufficient to just divide the implied probabilities by (1 + vig %) and you’ll have an accurate-enough set of probabilities to base your assumptions off.

Excellent. Maybe? We do appear to have gone round in a circle here. The sharp odds are generally the best odds, both in terms of highest odds available to the bettor and accuracy, that we can access. If we can even access them. And it’s also our benchmark for the true odds (once devigged). And the sportsbooks are for the overwhelming majority of the time taking these odds and adding an extra margin on top of them. So how are we going to actually find any winning bets?

As the old saying goes, if you want EV done properly, you have to do it yourself. It’s up to us to come up with models, or identify inefficiencies, that would mean the odds we’re being offered imply a lower percentage of winning than the true probabilities. Luckily, I have some interesting posts coming up on that. But the hard part is the input. Let’s imagine we’ve endeavoured to create a football model, that predicts the true probabilities of teams to win a match. You’ve bought a nice new bag of locally roasted coffee, and had an afternoon in with the seminal paper on football modelling by Dixon & Coles. And now your model’s up and running and firing out predictions hither and thither.

Most excitingly of all, it keeps telling you that there are some very nice looking bets knocking around. In particular, tonight, your model thinks there’s a 50% chance Rayo Vallecano will beat Barcelona (at this point you may want to check your model hasn’t mixed the team names up), which would correspond to fair odds of 2.0. You smile to yourself at how simple the reciprocals are to calculate and thank the universe that you don’t use American odds. But lo and behold, on your betting venue of choice, you see Rayo Vallecano priced at 2.1. Repeating our coin-flip maths from earlier, we know we have a 5% edge.

Don’t we? Well according to our model yes we very much do. But that model relies on its own calculations to give us a probability estimate. And being the ever cautious young padawan that you are, you have a simple question: how do I know my model’s estimate of the true probability is any good?

Closing Line Value (CLV)

Well there are a couple of ways to answer that question. Our first is CLV. We already said the devigged sharp closing line is the market's best estimate of the truth. How good is that estimate? Pretty good actually. Not perfect, but actual research is published on these things and the general consensus is that where the market settles before the event starts on sharp books is a high-quality predictor of the true probabilities of the various outcomes.

So what’s our plan? Beat this line. Prices will move around significantly between when they first become available to bet on and the close. If you’re consistently taking prices better than the CLV, you are consistently beating the most informed opinion available, and you can know it without a single result coming in. And not needing results to come in is a big pro. Aside from the admittedly major bankroll and staking considerations, we can almost ignore the actual outcomes of individual bets, safe in the knowledge that we’ll win in the long run.

But there are downsides. The ultra-efficient price-discovery type process happens on the biggest markets on the sharp books. If you were say, running a desk that wanted to focus on slightly niche strategies, possibly betting on exotic corners of the book, there is not going to be a tightly efficient CLV for you to use for comparison. Most of these sharp books do exotic lines, but the limits are smaller and it’s hard to call a price efficient when £14 moves the line.

Outcome Validation

It’s time to strap up and get statistical. The second way to confirm your probabilities are any good is to place the bets and measure what actually happens. Track your realised return and see whether it’s statistically convincing that you’re actually doing something useful. Simple in principle. Unpleasant in practice, due to the very thing we’ve been trying to avoid talking about the whole time: Variance. Enjoy your one-way ticket to statistical despair.

Consider a bettor with a real, genuine, not-imagined 5% edge. The best kind. And ask a simple question: after 100 bets, in a normal odds range, how likely are they to be sitting on a loss?

Oh dear. Nevermind 100 bets, our condolences are going to have to go the poor Joes who are 1000 bets in and still net-negative. All 15% of them. Of course seeing the individual paths at least provides some intuition for the level of variance a particular bettor can expect over 1,000 bets.

So if we’re taking my fairly strong hint from a few paragraphs ago that the CLV isn’t always going to be available or useful to us for some of the strategies we’re going to explore this quarter, then what the hell are we going to do with this? If we want to prove our edges exist with statistics, so far the only reliable way to do this is to bet more. At last, a methodology the degenerates and statisticians can both support.

In fairness, it does at least seem to work effectively. Mathematically speaking, as the number of bets n grows, your expected profit grows in proportion to n, while the noise around it grows only with √n. That means, over enough bets, the signal from a genuine edge grows faster than the noise created by variance. But have we factored in the parameters of these simulations into this? As those who bother to read graph legends can see, we have assumptions around edge %, odds and staking. By tweaking these, can we make our lives easier in terms of validating our strategy?

Here are three bettors with a 3%, a 5% and an 8% edge, each after a full thousand bets. The distributions overlap so heavily you couldn’t confidently tell which bettor was which from their results alone. Even a large edge hides in the noise for longer than intuition allows. Are there any more variables we can tug at to try and improve things? Is there an alternative method of suffering around which odds we bet at?

That's the number of bets required before a 5% edge becomes statistically distinguishable from no edge at all, broken down by odds bands. Down at short odds, it’ll take around 2,000 bets on average to get a statistically significant result versus circa 32,000 for our longshots. We can at least take some comfort in having a way to improve our ability to verify edges. If we can decrease the variance per bet, we should be able to verify whether we’ve found a winning strategy much sooner.

And what about staking? Staking is unfortunately a big enough issue to get its own post. Under certain staking regimes +EV strategies are guaranteed to go to zero, so it’s a vital piece of the puzzle which we can use to validate strategies more effectively.

But where does this leave us for now? Well, if we want to test our models against the main lines that attract big money, we can compare against the CLV and should get a fairly good feel for whether we have something worth running. If we want to go into the more niche corners of betting we’re probably going to have to take a statistical approach to confirm our edge post-hoc. Of course, we should have some level of conviction behind our strategy before running it. There should be a logical reason why our strategy is +EV, which we can verify after the fact, so we aren’t starting from zero.

In the next post we’ll cover staking with the Kelly criterion, including its impact on total profit and our ability to verify edges. We’ll then move onto our first true ‘Research Desk’ post, covering a simple exchange arbitrage strategy, which we’re now better equipped to enjoy the zero-variance nature of. See you then.

The Alternative Desk
Still a going concern

The intention is for these posts to cover everything about the novel strategies we’re attempting to find; their universes, their hypotheses, their execution and the inevitable practical issues that come with trying to find edges in more exotic environments.

With that being said, let’s introduce our universe for this quarter:

BETTING MARKETS

The Beginners’ Guide to Betting Markets

Underwhelmed? Thanks. Don’t be deceived simply because we’ve not decided to rival Jane Street in Q1. 10% of the Premier League is majority-owned by individuals who’ve made their fortune from sports betting. There are people making some very serious money in this space.

Before we delve into the wider world of sports betting, it’s important to note that the fundamentals of profitable betting rests on one concept: expected value (EV). To understand what’s below, you only need the last sentence of the next paragraph. To understand what’s coming over the quarter, we’ll have a specific first principles post dedicated to the topic of EV coming in the next newsletter.

Every line on a market implies a probability. The tidiest mathematical example is a bet priced evens (2.0, +100, 1/1, depending on your odds preference). A price at evens means your bet needs to win 50% of the time to break even. If you think it’s likelier, you should bet; otherwise you shouldn’t. Maybe you think that in reality there’s around a 45% chance of the bet winning. Then you don’t bet. But it isn’t only your view that makes a bet profitable or unprofitable, if you can find the same event priced at improved odds of 2.5, breakeven drops to 40% (the reciprocal), and the same bet is now worth taking. Fundamentally: lower odds are always worse for the bettor, so where you bet, and how competitive their odds are, matters.

Betting companies exist all over the world, from Asia, to Europe (where this newsletter is based), to now much more prominently in the US. The premise for the completely uninitiated is relatively simple. Sign up, deposit funds, find a bet that takes your fancy, and lose. At least on average. Somebody needs to pay for the shirt sponsorships. And yet where you bet can matter as much as what you bet. Almost all platforms fall into one of three categories:

Soft Books

See: Sportsbooks, Retail Books, Bookmakers

Examples: Bet365, Fanduel, BetMGM, literally thousands of others

Associated Terms: punters, casual betting, losing long-term, my parlay only lost by one leg

What makes a soft book? The business model for these is simple; offer bad odds so your customers lose quite a lot of money on average (refer back to EV paragraph if this relationship is unclear). Spend heavily on marketing, sign-up offers, sponsorships and brand visibility to attract as many casual bettors as possible to your brand, as opposed to any other sportsbook. These are the most visible and well known betting platforms, specifically because their business relies on it.

If we hypothetically could find a winning strategy, would this work well for us? No. These platforms have a rather pesky habit of outright banning any customers who manage to win long-term. There can be a delay on the banhammer, meaning there’s potentially some fun to be had in the interim on soft books (search matched betting), but it’s more of a summer project than the type of long-run quantitative strategies that we’re aiming for here. Unfortunately I’ve already completed this summer project, in several names, over several summers, and remain banned from many of these soft books. So these are a non-starter.

Sharp books

See: Asian books, Low-vig books

Examples: Pinnacle, Circa Sports, SBO Bet (still many but probably <40 true sharp books)

Associated terms: Syndicate betting, high-limit betting, low-vig, brokers

Sharp books, Asian books, or any of the derived terms, run close to the opposite model. They offer highly competitive odds, deliberately take high-limit customers and syndicates, and welcome winning players rather than banning them. They also manage their prices aggressively, moving lines in response to the action they take, including when sharp accounts pile in on value. It’s the closest thing betting has to price discovery in a financial markets sense, and the closing line on a sharp book is widely treated as the truest available estimate of an event’s real odds.

Would a winning strategy work here? Yes and no. The catch is jurisdiction. Sharp books tend to be based in Asia, and actually getting money on their system and on their lines takes a fair amount of monetary plumbing for a European. They often also come with expectations around stake volume that a four-figure, experimental bankroll can’t meet, which makes them unfeasible, or at best sub-optimal, for us.

Betting Exchanges

See: Peer-to-peer books

Examples: Betfair Exchange, Smarkets, generally more specialised

Associated Terms: Liquidity, Back/Lay, Am I the dumb money?

Betting exchanges operate somewhere between the sharp and soft books. Or maybe not between them, but on a slightly different axis altogether. The fundamental difference is that everything here is peer-to-peer. When I back (buy) a bet, there’s someone on the other side laying (selling) it, effectively short that same outcome. Their payoff is the mirror of mine: if the bet loses they keep my stake, and if it wins they pay out my winnings. The market parallels run deeper than that. Each line has a spread, the best back price you can get sits just below the best lay price next to it. Taking a bet right now means crossing that spread, exactly like paying the bid-ask to trade a security immediately rather than waiting for your price. If you want to be filled without hanging around, you pay for the privilege.

As for the business case, exchanges take a set commission on net winnings, normally 2-5%. They don’t set prices themselves, but a version of the same price discovery happens here, often more transparently, because most exchanges show the order book. And of course, the incentive to cap winners evaporates; they want your volume so they can get the commission. The catch is liquidity: your bet only exists if a peer is willing to match it. The biggest players still prefer sharp books for the high limits, so the sharpest action happens there first, and exchange market makers tend to move their prices in response to it. As for who provides that liquidity, it tends to be large syndicates and professional market-making groups. Outside Betfair, these groups can be connected in some way to the owners of the exchange itself, which I’m told regulators love.

But how well do exchanges suit our needs? For the most part, very. I have access to several exchanges in my jurisdiction, and better still, most run APIs, so odds can be pulled, processed and bet on programmatically. Of the three venue types, exchanges fit the brief by far the best.

The plan from here

So where does this leave us? If we’re going to find the consistent, scalable and algorithmic edges we want then betting exchanges are the place to look. The job is to find inefficiencies that show up in these markets, confirm they’re real rather than noise, and turn each one into a strategy that runs itself. Once a strategy is automated and behaving, move on and start hunting the next, while the last one keeps ticking over in the background. Repeat until we have a stack of small edges running in parallel and buy a Premier League football club. Simple.

After we’ve taken our deep-dive into EV, we’ll start unglamorous and venture out arb-hunting, to prove that our plumbing works before delving into the really niche stuff. See you next time.

The Alternative Desk
Still a going concern

Over the past several years I’ve found much more enjoyment ignoring almost all of this content, and trying to find edges outside of the current in-vogue ideas, which has led to a number of failures and some notable successes. But working on these experiments consistently around a full-time job meant progress was always difficult. My background is in financial analysis and reporting, paired with a curiosity about the investment-grade end of finance that never quite turned into a career in it. As a combination it’s nearly enough to put someone off equity investing; analyse enough financial statements and you’ll realise an unqualified opinion is often an unfortunate double entendre. And just to be clear we’re not here for investment-grade finance anyway.

It’s from this difficulty to make progress that the idea of the alternative desk was born. Instead of a random walk through different experiments, why not attempt to fix the parameters and really see if there’s any value to be had? Why not start with a fixed amount of capital and fixed accounting rules, and attempt to make some genuine money? And why not document it for the wider world, which keeps things honest and imposes some deadlines? But there’s a second reason too. I can’t find anyone doing these experiments. And I’ve tried; mainly because it would’ve been very useful to me over the previous years of building. So in addition to finding out whether there’s money to be made, you get to see everything. The method, execution and outcome, with results reported quarterly, so you can follow the journey.

The desk starts with £5,000. Not a bankroll likely to intimidate, but enough to benefit from scale and afford some fixed costs to implement strategies as effectively as possible. The aim of the fund is the same as almost all funds even if the methodology will be on novel ground; maximise returns within an acceptable level of risk. It’s worth mentioning that this is entirely my own capital, and this project isn’t open to outside money (and yes, this is education and not financial advice). Inevitably, there will be some losses and some unprofitable ideas that end in defeat, but such is the cost of transparency and I hope you’ll appreciate me sharing these with you.

So the natural next question: what actually makes a good strategy on the alternative desk? The traditional financial markets are too efficiently priced and the transaction fees too big for a pot this size to make a return there beyond buy-and-hold investing. The job of the desk is to hunt for edges in alternative markets which are smaller, weirder, and frankly too much effort for the institutional players to bother deploying capital towards. To do this, we’re going to explore one universe per quarter; once an edge is found within it, an appropriate slice of the capital is allocated subject to expected edge and variance, and the strategy is then actively monitored to verify the returns are in line with expectations.

Spinning £5,000 into something meaningful comes with its own practical constraints. The first is time: strategies have to lean algorithmic and automated. For the fund to reach a meaningful number of strategies my role has to remain limited to building, deploying and monitoring. Otherwise the workload will increase unsustainably and the fund won’t be able to scale. The second is what to do with any excess funding. For now, the plan is to keep any uncommitted capital in a money market fund, especially early on, when 0% of it is deployed. Avoiding an equities-based fund also dodges the embarrassment of being the only alternative investment fund in history with a beta of 1.

Now the guidelines above have been set, the overarching approach is simple. Explore the chosen universe over each quarter, find the edges and algorithmicise them into a positively returning strategy and continue. Over several quarters the desk will have numerous strategies running in different universes, all providing a source of uncorrelated returns. And of course, each one will be set out in detail as it happens.

So how does the desk keep score, and what do you as a reader actually get each quarter? Every quarter you’ll see total return, sharpe ratio, max drawdown, as well as a split of returns by strategy, both gross and risk-adjusted, to ensure the aim is being met and returns aren’t simply the product of variance. Everything is accounted for clearly, including the costs of things like VPSs and data feeds. There are of course certain other costs involved in bringing you this content such as domain names and platform fees. These are kept separate so the fund’s numbers reflect the real cost of running strategies independently. Concretely, here’s what you’ll get each quarter from subscribing to the alternative desk:

• Mark to Market: The quarterly results, including the breakdowns and analysis that inform the capital allocation strategy for the next quarter.

• The Research Desk: Where the experiments live, including the method, execution and outcome.

• First Principles: A deep dive format into quantitative topics going from the theory to how they can be exploited.

Finally, let’s set the starting position clearly. The date is August 1st 2026. There’s £5,000 seed capital. Currently 100% in money market funds. Zero novel strategies, which admittedly is quite a low bar to improve from content-wise. Onwards.

The Alternative Desk
Still a going concern