Alternative Bankroll System - Experiment Time

When I was going over past seasons of results one of the things that jumped out at me was that even over larger sample sizes profitability can be noisy. When you consider a binary Bernouilli trial with probability p, the standard deviation is given by sqrt(p(1-p)). When you extend this to n trials, the standard deviation becomes sqrt(np(1-p)). The result is a quadratic curve that it can easily verified has a maximum at p=0.5. When you go to long shot events (say p=0.01) your standard deviation is lower but anyone who has tried betting on long shots will tell you, it's very feast or famine and you can be underwater for a hell of a long time before you become profitable (and conversely you can be profitable for a hell of a long time before a gammy edge reveals its flaws). Over huge sample sizes, the long shot bets will have lower variance but over smaller sample size you notice the noise. That's why spreads and totals despite having the highest variance from a continuum limit perspective have a cleaner yield curve because no one individual result distorts the graph.

The 2024/25 picks for the European football season was done through Asian handicap betting. This time last year I did recommend a transition to moneyline for various reasons that were very relevant at the time. I have since decided to go for a hybrid approach due to better liquidity on prediction markets which enables higher edge extraction as well as more reliable variance reduction. The question of variance reduction is no small one. This past World Cup was possibly the most favourite friendly tournament from a moneyline perspective I have ever seen. I have never seen such a sequence of games where the favourite would either blow out the minnows or the minnows would put up a strong fight and yet the favourites would always find a way to squeak through. Leaving aside my annoyance at this from a sheer spectacle perspective, it does have betting implications. If you have taken underdogs on moneyline throughout the tournament, you would have witnessed a bloodbath. If you took the same underdogs on the Asian handicap line, you would have done better and maybe even profitable depending on which underdogs you picked.

I have already covered at length in previous posts why I prefer to take alt lines on football picks when one side is clearly favoured over the other. I have also covered why I sometimes prefer to take no on a team to win even if they are favoured by less than half a goal under certain circumstances. Even taking one longshot draw pick at 16c with 2% of bankroll behind it means a last minute goal can be a swing of roughly $700. A longshot at 10c with 2% of bankroll is a swing of $1000. A couple of those can heavily distort the picture of picks over the course of a year. Together that's 34 units. Notwithstanding that buying no on certain teams, especially favourites, can be advantageous from a liquidity flow perspective, it gives a cleaner picture of a strategy's rate of return over the course of a year.

There is an extra question here and that is bankroll sizing itself. The standard bankroll sixing on Sportspicks is 2% for a regular play, 1% for a "longshot" (as seen in CFB and NFL) and 5% for high conviction plays. 2% on standard spreads and totals gives a relatively predictable dispersion of results. The 1% and 5% plays are where net exposure can become larger in unexpected ways. Suppose we have 1% on a certain team to win the Super Bowl at 5c. Assuming a bankroll of $5000, this would mean said team to win the Super Bowl would be $50 for 2000 contracts. For reference a standard 2% play at 50c is 200 contracts. Of course, you can hedge out of a 1% future if it goes up in value, but that is not guaranteed. If you have multiple 1% futures you may have 5-10 units on various teams to win the Super Bowl and since some of those are inevitably going to be a bust (barring the most freakish of underdog years ever), you are almost forced to take profit on whichever ones do go up in value. The point is that the base money exposure may be relatively low but the payout exposure is much bigger than a standard 2% play. The point is not whether or not these futures have value; it's whether or not their variance is disproportionately large relative to the rest of the portfolio. If it is, it increases the chance of making a loss even when one was on the right side of the tracks from an expected value perspective.

So what I am experimenting around with is an adaptation for the prediction market era. Instead of making my unit size be enumerated in currency, I am going to experiment with enumerating it in contracts. This would make each position controlled for total exposure at position resolution, not total exposure at position entry. Instead of implementing a play as 2% of bankroll, I would implement it at 200 contracts (for a reference bankroll of $5000, you can easily convert this into contract quantity for other bankroll sizes). This would give some extra flexibility in football picks as sometimes the draw is the only undervalued option between two teams and it might be priced at 25c. 200 contracts at 25c is $50, so the lower entry price would reduce the entry exposure to compensate. a college football underdog as a long shot win at 10c would be $10 if buying 100 contracts in place of a 1% play or could still be $20 for 200 contracts, still being lower than $50 of a 1% play. A last minute goal, touchdown, run etc would only affect portfolio value by the number of contracts, so $100 or $200 rather than potentially $1000. This in turn reduces the pressure to take profits while a game is going on. Not every play would have the exact same number of contracts but it would change exactly which variable is exposed.

The equivalent translation of on a regular bookmaker is to keep the total payout (stake plus profit) relatively constant. So +300 means total return is four times stake, so dividing $200 by four give $50 and so on and so forth.