Wednesday, May 05, 2010

Chasing Losses and Abandoning Profits

With respect to trading, humans are better described as loss averse than as risk averse, Because the pain of a $100 loss far outweighs (between 200% and 500%) the pleasure of a $100 profit, when faced with a situation framed as a probable failure we gamble and when faced with a situation framed as a probable success we quickly take profits. In other words, we neither maximize profits nor minimize losses! This is the normal human condition.
As a result, whatever approach we take to reducing the impact of chased losses or abandoned profits must always allow for some of both. Trying to completely defy human nature is simply pointless and guaranteed to fail!
One approach that I would recommend is to use a form of session trading. Set aside a daily bankroll based on both the number of markets you wish to trade and the maximum number of units you are willing to risk for some minimum profit target. Critically, you must factor in a small percentage for the possibility of chasing losses.

Tuesday, April 13, 2010

Handicappers Edge and Traders Hedge

If you define yourself as a gambler/handicapper/punter then you are focused primarily on identifying a unique advantage in a sporting event that is not already accounted for by the public odds. By contrast, if you define yourself as an investor/speculator/trader then you are focused primarily on taking an initial position in a market and then protecting that position against a negative move.
The former approach is fundamental in nature and the latter technical. Both strategies have their respective Achilles heels! With fundamental approaches, you never know in advance if you have an edge in an upcoming sports event; with technical approaches you are uncertain when to exit a particular market by either “greening up” or “redding down” your current position.
In terms of money management, handicappers generally preach the Kelly Criterion and use Sportsbooks while traders affirm “Bold Play” and frequent betting exchanges. In general, the age profile of handicappers is higher than that of traders simply because betting exchanges are a relatively recent innovation. Handicappers try to automate their plays by using systems whereas traders use bots.

Wednesday, March 17, 2010

Absence of Proof is not Proof of Absence!

Francis Bacon (1620) “For a man always believes more readily that which he prefers.” If we leave aside the contentious issue of whether or not it is possible to be a profitable sports trader using a wholly fundamental approach to handicapping, we can readily identify three evidence-based views of ‘form’:
  • Evidence of Presence (EoP),
  • Evidence of Absence (EoA), and
  • Absence of Evidence (AoE).
The natural tendency to confirm our initial opinion leads us to look for supporting evidence (EoP) in both the historical record and in statistical trends with the obvious danger of the logical error of affirming the consequent. By contrast, evidence that eliminates a contender (EoA) is the recommended approach with its natural link to the logically correct method of denying the consequent. Finally, lack of evidence (AoE) neither confirms nor denies the status quo but many neophytes seem to confuse it with EoA.

Thursday, February 25, 2010

Even-Equivalent Probability of Ruin

Epstein (2009) provides a detailed, mathematical analysis of the risk of ruin within the broader context of the basic theorems of gambling. Without loss of generality, it is worth providing a layman’s interpretation of how the probability of ruin impacts the choices made by the average handicapper.
In the classic treatment of ruin, there is a working assumption of unit bets at even-money in order to make the calculation of the risk of ruin more tractable. To avail ourselves of this analytical solution, we need to transform our real-world bets into their even-money equivalents, see Krigman (1999).

For example, if you are in the fortunate position outlined above with a 42% strike rate at an average price of 2.50 then your advantage is the equivalent of having a win probability of 52.02% at 2.00 with both the same expected value and standard deviation (0.25, 6.169) as the original bet and with a probability of ruin equal to 24.07%. Obviously, it is also possible to estimate stake size given a specific price and preferred risk of ruin.

Thursday, January 21, 2010

Gamblers Ruin at Casino Incroyable

A nice mixture of mathematics and humor - Gamblers Ruin at Casino Incroyable with passing reference to "Bold Play", "Minimum Gain", and "Gamblers Ruin".

Saturday, January 09, 2010

ZEER: Zero Evens-Equivalent Rate

When comparing handicapper performances across different circuits, it is better to zero the tax rate at evens using ZEER:
ZEER = (StrikeRate * (Odds + Tax - (StrikeRate * Tax))) / 2
Edge = ZEER - (1 - ZEER)

For example, comparing handicappers (see above) at Aqueduct, Gulfstream, and Santa Anita gives ZEERs of 52.94%, 54.04%, and 53.00% respectively.
This yields equivalent edges for the three handicappers of 5.89%, 8.08%, and 6.00%, identifying the Gulfstream handicapper as the most successful.
In summary, ZEER allows a group of handicappers to compare their
performances on a common scale (evens at zero tax level)!

Friday, January 01, 2010

Kelly Horse Race or Ziemba Roulette

In the spirit of the New Year, I offer the following thought-provoking argument:
Betting is often described as a competition between you and the "Crowd" (i.e. Pari-Mutuel market) on which you can better estimate the true distribution of odds in a particular sporting event. In that context, a good starting point is to ask Bill Benter's fundamental question of handicapping: what additional variables (if any) explain a significant proportion of the variance in results to date that is not already accounted for by the public odds (Wisdom of Crowds)? By keeping records, it is possible to determine whether or not you have been successful over time in so doing. However, it is not possible to know (in advance) if you have an overlay in an upcoming event. This is the fundamental flaw of handicapping and, eo ipso, the flaw of fundamental handicapping.
The alternative approach is technical trading and an often underestimated strategy is "Bold Play" and its variants. Bold play is recommended for subfair games (i.e. p < 0.5, assuming even money bet) and, given the high-level of taxation, one can argue that horse-racing qualifies. Without going into the mathematical details and assuming a little "poetic licence", bold play reduces to an algorithm comprising two rules:
__a) Bet amount to reach target bankroll in single event (e.g. one race); or
__b) Bet amount in current event to reach bankroll level from which it is possible to attain target bankroll in next event.
You will no doubt immediately recognize that it is possible to iterate rule b) over many events (e.g. complete race card) but, ideally, you want to minimize the number of iterations. This technical trading approach only requires information on current bankroll, target bankroll, number of remaining events, house limits, and access to the public odds.
In summary, the advice to use fundamental handicapping to find overlays which you then exploit using edge-based staking (Kelly, 1956) assumes a superfair game but if, in fact, the game is essentially subfair then technical trading is recommended using bold play (Ziemba, 2002) or one of its variants in as few iterations as is feasible given whatever constraints are in place (e.g. maximum stakes).