From an economics viewpoint (expected utility theory), the prescribed way to approach a series of bets is to focus on expected utility (for example. wealth). This leads invariably to Kelly staking and maximizing the long-term expected growth rate of one's bankroll. With this approach, the handicapper is advised to play every race where he has an edge (namely, "bet your beliefs"). By contrast, from a psychology viewpoint (prospect theory), the prescribed way to approach a series of bets is to focus on loss aversion (pain of losses far outweighs joy of wins). This leads invariably to session handicapping and minimizing regret.

If for example, we define session handicapping as a day's wagering, then it is possible to adapt Belgian mathematician Thomas Bruss’s Odds Algorithm (http://www.ems-ph.org/journals/newsletter/pdf/2006-12-62.pdf) to determine when is the optimal time to stop betting to enhance the probability of ending the day in profit. In other words, the odds algorithm works out after which race during a day's session you should quit assuming you are ahead!

## Monday, October 19, 2009

## Tuesday, October 06, 2009

### Trade Selection (Trailing Stop Loss / Take Profit)

## Friday, October 02, 2009

### Sample Size: Confidence Interval and Confidence Level

There are two key factors to consider when estimating sample size for testing a betting rule: confidence interval and confidence level. Confidence interval refers to the range within which you expect the correct strike-rate to fall and confidence level refers to how certain you are that this range holds the true value. For example, with a confidence interval of +/-5% and a confidence level of 99%, using these values and without going into the exact calculations [=POWER(PRODUCT(PRODUCT(NORMSINV(PRODUCT(SUM(ConfLevel,1),1/2)),1/SQRT(2)),1/PRODUCT(SQRT(2),ConfInterval)),2)] gives a sample size of approximately 664 (663/664). What this means is that testing a betting rule on 664 races drawn randomly from, for example, 2008 (i.e. different population from that used to discover betting rule), you can be 99% certain that the strike rate your betting rule generates from this new random sample will be within +/- 5% of the true strike rate.

## Tuesday, September 29, 2009

### Negative Expectation Misconception

Some handicappers believe incorrectly that, if they play a negative expectation game, they will lose a percentage of their initial bankroll equivalent to that expectation. This is incorrect.

For example, assuming that the expectation of randomly betting favorites at Track X is -17% and that Joe Punter starts with a bankroll of $1,000, he expects to lose (randomly betting favorites at Track X) $170 (17% * $1,000) over a season. In fact, he can expect to lose 17% of his total bets (turnover), not of his initial bankroll. Suppose he makes 250 flat $30 bets on favorites giving him a total turnover of $7,500 ($30 * 250), he can expect to lose $1275 (17% * $7,500) - not $170! In other words, he stands to lose (on average) $275 more than his initial bankroll!

For example, assuming that the expectation of randomly betting favorites at Track X is -17% and that Joe Punter starts with a bankroll of $1,000, he expects to lose (randomly betting favorites at Track X) $170 (17% * $1,000) over a season. In fact, he can expect to lose 17% of his total bets (turnover), not of his initial bankroll. Suppose he makes 250 flat $30 bets on favorites giving him a total turnover of $7,500 ($30 * 250), he can expect to lose $1275 (17% * $7,500) - not $170! In other words, he stands to lose (on average) $275 more than his initial bankroll!

## Thursday, September 24, 2009

### Calculating Initial Bankroll

The first decision you make as a professional sports trader is to calculate the size of your initial bankroll.

This task is like tackling a 'chicken and egg' problem. On the one hand, you need to know your average strike rate in order to calculate a starting bankroll. On the other hand, this is difficult to accurately assess before you begin to trade. However, assuming you can generate a conservative estimate of the strike rate, Peter Webb provides a simple formula:

LLR = ROUND(LN(NumBetsPerYear)/-LN((1-

StrikeRate%)),0)

for calculating the longest expected losing run relative to strike rate. Using this value, initial bankroll can be calculated, as follows:

IB = ((LLR * 2) * UnitStake)

For example, with a projected 25% strike rate and an average number of bets per year of 1000, you can expect a longest losing run of approximately 24 so, given a unit stake of $25, the recommended initial bankroll is (24 * 2 * $25) = $1,200.

This task is like tackling a 'chicken and egg' problem. On the one hand, you need to know your average strike rate in order to calculate a starting bankroll. On the other hand, this is difficult to accurately assess before you begin to trade. However, assuming you can generate a conservative estimate of the strike rate, Peter Webb provides a simple formula:

LLR = ROUND(LN(NumBetsPerYear)/-LN((1-

StrikeRate%)),0)

for calculating the longest expected losing run relative to strike rate. Using this value, initial bankroll can be calculated, as follows:

IB = ((LLR * 2) * UnitStake)

For example, with a projected 25% strike rate and an average number of bets per year of 1000, you can expect a longest losing run of approximately 24 so, given a unit stake of $25, the recommended initial bankroll is (24 * 2 * $25) = $1,200.

### Fundamental (Weighing) or Technical (Voting) Analysis

In essence, there are two major schools of analysis among traders in the world's stock markets - fundamental and technical. Fundamental analysis is a weighing machine that measures the intrinsic value of a company. By contrast, technical analysis is a voting machine that measures the historical trends in the company stock price

With sports trading (e.g., horse-racing), there are two markets available on most betting exchanges (e.g., Betfair): pre-event and in-play. The pre-event market is similar to the standard bookmaker or pari-mutuel equivalent with respect to the back side (i.e. punting) of the equation. However, the addition of a lay option generates a highly liquid market for technical traders as they negotiate the ebbs and flows of money for the market leaders in the last fifteen minutes before the start of the event. Though there is some scope for a solely technical or fundamental approach to the in-play market, it actually requires a form of fusion analysis (i.e. blend of fundamental and technical) because, unlike stock markets, there is only one winner and many losers at the end of a finite time interval (i.e. end of race). Thus, even though the sports trader can punt (i.e. back OR lay) a single selection, the recommended approach is to trade (i.e. back AND lay) one or more selections to either "green up" (i.e. guarantee return regardless of outcome) or "red down" (i.e. spread liability across all selections to minimize loss regardless of outcome) the trader's overall position.

With sports trading (e.g., horse-racing), there are two markets available on most betting exchanges (e.g., Betfair): pre-event and in-play. The pre-event market is similar to the standard bookmaker or pari-mutuel equivalent with respect to the back side (i.e. punting) of the equation. However, the addition of a lay option generates a highly liquid market for technical traders as they negotiate the ebbs and flows of money for the market leaders in the last fifteen minutes before the start of the event. Though there is some scope for a solely technical or fundamental approach to the in-play market, it actually requires a form of fusion analysis (i.e. blend of fundamental and technical) because, unlike stock markets, there is only one winner and many losers at the end of a finite time interval (i.e. end of race). Thus, even though the sports trader can punt (i.e. back OR lay) a single selection, the recommended approach is to trade (i.e. back AND lay) one or more selections to either "green up" (i.e. guarantee return regardless of outcome) or "red down" (i.e. spread liability across all selections to minimize loss regardless of outcome) the trader's overall position.

### Back Story: As Time Passes Things Change

A simplistic interpretation of the Second Law of Thermodynamics is that as time passes things change. Though fundamental to our world, change is very difficult for most adults. In that respect, I am no different from my peers. According to my career script, I expected to become a successful, self-employed, consultant and to retire in late middle-age to the west coast and study mathematics. Actually, I achieved the initial career goal relatively quickly and lived the lifestyle I had anticipated for a short while only to be trumped by entropy. Facing an uncertain market for my expertise and experience, I decided on a complete change of direction. This is the continuing story of that journey...

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