Sub-Optimal Staking Exposed

In reference to my earlier post in support of variable staking, James, currently recovering from the stress of installing IE10, had this to say:

I agree entirely. If the other side of the trade has negative expectation then you have the edge, regardless of stake. Edge and stake are not related in that respect.

Poor money management affects the variance in profits and level stakes is just as likely to destroy your bankroll by yielding less profit on a winning bet as too big a loss on a Kelly bet.

The optimal bet is to chase your winnings and not your losses. If you consistently bet less than you should then you are building a smaller cushion for when the inevitable losing streak comes.

Kelly betting conforms to "chase your winnings not your losses" by sizing the bet to your current win/loss streak. If you are in a losing streak then Kelly will make smaller bets relative to the decreasing bankroll. 

Webbo, who of course initiated this debate with his ill-considered Tweet responded with:

Largely agree with you of course and I'll just clarify a couple of the points.

By letting the bookie do the work, I mean let them decide on the exact price. It's much easier to know that a price is too big than to know by exactly how much each time.

I have to interrupt here, because I don’t understand this statement. For a start, let’s be clear that these days the bookie doesn’t ‘do the work’ –

...it is us as bettors collectively whose are those that set the odds, not the bookmakers.

Individual odds, or prices, are nothing more than an equilibrium price that is formed by matching the supply and demand [for bets] from punters. Betfair Exchange is the clearest example of a true market. On Betfair, by introducing the bets they are willing to place/lay and at corresponding odds (“supply and demand”), a market price is formed. Other bookies or betting houses are not markets as such. They determine their own odds. But deep down they cannot escape the fact that they are part of a global market and that they have to adjust their prices in response to evolving events. Bookmakers have different strategies to set their odds, but at no point can they go against the market.

Thus the market decides on the ‘exact’ price and the traditional bookies pretty much fall into line, except by offering worse odds than the exchanges and the new model Sportsbooks (e.g.Pinnacle Sports), and hoping to get some interest from non-price sensitive long-term losers and a few quid in their FOBTs. (They may not yet be long-term losers, but traditional bookies will soon limit you if it appears they won’t be).

As for the statement that “It's much easier to know that a price is too big than to know by exactly how much each time”, I think if you are serious about investing rather than looking for entertainment, you really need to have a price in mind before you can say an offer is “too big”. When you read a tipster saying that a selection “offers some value”, you can be pretty sure they really have no idea what their 'true' price is. It’s one of my gripes about tipsters that they will tip a selection at say 2.5, but not tell you at what price that selection ceases to be value. Not to mention that different punters have different thresholds for when it is worth their while getting involved. 0.1% value is one thing, 5% another, and 25% another altogether (in the case of the latter, you're probably missing some information).

The only way you can determine that you have value is by calculating your own prices, and once you have done this, it’s easy to know how large any edge is.

Webbo continues:

I'm sure bookies do hate all winners but most of those who use a variable method are less likely to be able to price up markets as accurately as the bookies on a regular basis. Of course you could be varying based on odds ranges only but this is then not much different to level stakes if that’s the case. They will also likely see more volatile swings of which they are less likely to be able to handle. I’m guessing a bit here as I’ve never been a bookie and I’m not saying that I’m correct, but after an early period of success I think they’d be more confident that the variable staker will come a cropper than the level stakes bettor.

Of course there will be some exceptions but very few people will be able to show a set of results that have been improved by variable staking.

Again, the bookies do not price up markets, we punters collectively do, and we generally do a pretty good job. 

I would argue that bookmakers are actually more concerned about variable stakers. If you consider the example of the casinos and card-counting in Blackjack, the success of the strategy hinges completely on varying stakes, and this is the behaviour that leads to one being shown the door. Level stakes bettors are free to play all night, and to come back next day. 

When someone bets to level stakes, it reveals that they don't know the size of their edge, and by extension if they even have an edge. The variable staker should thus be seen as more sophisticated and knowledgeable, i.e. just the type of client bookmakers don't want.  

  

What this sentence means - "They will also likely see more volatile swings of which they are less likely to be able to handle" – I have no idea! I thought Deepak Chopra was commenting for a moment!

Webbo followed up later with a further comment:

We are all singing from the same hymn sheet here by the way. We all know that Kelly is the optimal approach in theory but 90% (maybe more?) of punters won't be able to use it or any variable staking to their advantage. The twitter statement was merely intended as advice for most people.

It was poor or misguided advice at best. I’m not sure we do all know about Kelly, but regardless, the Tweet made no reference to Kelly anyway. It simply stated that "variable staking can leave you exposed with just one bad bet" which is meaningless. As I said previously, it’s idiotic staking that can hurt you, not variable.

Webbo changes the topic, continuing:

Anyway here's a more interesting question for you related to this. How low do you let your bank get using Kelly if you have an edge? How low would you expect it to go?

In your mathematically perfect world you would utilise as much of your edge and bank as possible but what if these sees you lose up to 40% of your funds along the way?

Our simulations over more than 10 year’s worth of data show that if we make the most of our edge in all markets we could see our bank more than 40% lower than the previous bank high and it can take up to a year to see a new high.

This does return by far the most profits in the long term but when the time comes for us to drop such a percentage, how do we know there's not some external forces that have come into play or that the edge has diminished? At the same time we want to maximize our edge as quickly as possible.

Appreciate your thoughts.

Again, I am not advocating anyone use full Kelly for sports investing - there are a number of problems, not least that to use Kelly it must be assumed that the investor is able to maintain his edge indefinitely - no easy task. As I wrote previously:

The curse of Kelly (or more conservatively fractional Kelly) is that accurately calculating your edge on a sporting event is very difficult. For that reason, sticking to a maximum bet size of 4% of your bank will serve most people well.

In the unlikely scenario that you are able to maintain an edge indefinitely, and accurately measure it, choose your bank size, apply full Kelly and go with it knowing that you are betting optimally.

The question of "how low do you let your bank go" is silly. Why choose a bank size if you are not committed to it? I like the inimitable Ian Erskine's recent take on this:

After the July seminars a guy asked me to sort his bank of 10k out which I did. He then lost £1856 which is less than 20% of his bank. He sent me a load of abuse and stated he was no longer continuing.

I replied and stated that in that case he did not have a 10k bank clearly he had a less than 2k bank and had he informed me of that I would have started him on much smaller stakes relative to a 2k bank. I then got another load of abuse. That is how so many of you operate. You do not commit, you fanny around trying to do everything to £2, £5 stakes and wonder why you're not rich. You give up as soon as a bad run comes, you stake money you don’t want to or can’t afford to lose, so have a meltdown as every bet leaves you teetering on the cliff. If you just stopped took a breath and set yourself up properly then you would see it really is not that difficult and once set you control your emotions and operate the same daily.