Small Fields And Exotic Convex Bets (Part 1)

Small Fields And Exotic Convex Bets

In horse-racing, Convex betting is predicated on frequent small losses and infrequent big wins. But in order to take advantage of this strategy, we require markets with fields of 11+ runners to generate live outsider prices.

Unfortunately, in the last couple of years, British racing has begun to noticeably decline in terms of competitive fields in both Flat and Jump codes with the consequential drop in price ranges! We, sports traders, cannot fix the current problems facing British racing so we must either adapt or die!

One possible solution for us is to look for better prices in the exotic (e.g. Betfair's 'Forecast' and 'Reverse FC') markets.

To that end, using an Excel spreadsheet, we can set up a table as follows to generate either 'Forecast' or 'Reverse FC' tickets subject to the following conditions:

• Runner saddle numbers as both row and column labels,
• Populate the table with 1s and 0s subject to the following constraints:
  • Row totals must equal two.
  • Column totals must equal two.
• Use Solver to generate a possible solution. Otherwise, use trial and error.
• Read off the row labels of the columns containing 1s to generate a subset of all possible tickets.
• There are multiple valid combinations of tickets.
• No matter what is the winning combination of the race, the generated set will contain two tickets with at least one of the winning numbers.

This is an example of generating a 'Reverse FC' solution for an eight-runner field.

and this is an example of generating a 'Forecast' solution for a five-runner field.

Enjoy!

Automatic Trading Using WCMI

Explore And Exploit

On which sports-trading events should we risk our capital? A good starting point is to ask the fundamental question of sports markets:

"Is the public market well-informed with respect to a specific event (Wisdom of Crowd)?"

Our proxy for identifying such events is to calculate the Wisdom of Crowd Market Index (WCMI) for all markets and to select only those events for which the market falls below a specific WCMI threshold (for example, 0.15). By focusing on these less well-informed markets, we are dramatically increasing the chances of identifying at least one overlay. In other words, the guiding principle is to explore all markets but only exploit those markets with low WCMIs. For UK Flat horse-racing markets, FlatStats is the logical starting point in this process.

Market Selection Using WCMI

The following Betfair simulation shows how an automated trading solution would first filter those markets with low WCMI and then, having identified at least one overlay, bet on one or more selections as calculated by the Single Event Multiple Selections variant of the Kelly Criterion:

• Filter markets (e.g. identify 5f sprints);
• Calculate WCMI for each filtered market;
• Rank contenders in market on fundamental factors;
• Create odds-line for contenders based on ratings;
• Check market contains at least one overlay;
• Make selections using Kelly Criterion; and
• Submit bets.

Betfair Pari-Mutuel Equivalence

For those handicappers fortunate enough to have access to both Betfair and Pari-Mutuel markets for the same events and who wish to arbitrage their positions for a "no loss" outcome, they should add the following formulae to their toolset:

• o = 1 - (d * 1/(x - 1)) and
• d = -((o - 1) * (x - 1))

where o = betfair decimal odds, d = pari-mutuel dollar payoff, and x = betfair tax (combination of commission and discount). These prices are equivalent in terms of expectation and volatility..

Betfair InPlay Hedge Stake

Trading an event in-play on Betfair is not for the feint of heart as, ultimately, no position is safe until it is successfully hedged. Psychologically, however, if you have carried out a fundamental analysis of the event then you want to be paid a premium for that analysis should your selection prove to be successful. On the other hand, Cumulative Prospect Theory confirms that we hate losing (loss aversion >= 2.25) more than we enjoy winning. In order to balance those conflicting forces, you could calculate a hedge stake to green-up your position, as follows:

  z = (s*(o+m-1))/(h+m-1)
  where  z = hedge stake
        s = original stake
        o = original price (back)
        m = win multiple (ratio of win payout to loss payout, if greened up)
        h = hedge price (lay)

For example, if I back a selection for $100 @ 6.00 and wish to green-up at 2.00 then the default option is to lay $300 @ 2.00 for a guaranteed $190 whatever the result of the event. By contrast, the above calculation (e.g., m = 2.25), gives a stake of $223.08 with a win payout of $264.74 and a loss payout of $117.66 giving you a win premium!

Betfair In-Play Trading (Minimax Regret)

Opportunity Loss (Regret) plays havoc with the emotions of In-Play Traders. One psychologically valid approach is to use Minimax Regret. For example, in a horse-race, assume your selection (AtTheWire) is on offer to back at 3.50 (Win Market) and to lay at 1.80 (TBP Market) and your calculation of edge dictates a stake of 100. In the Win Market, at what price and with what stake should you trade out In-Play to minimize regret? As the above table shows, trading out at less than or equal to 1.80 for 100 is the optimal choice! Note that backing your selection in the Win Market is equivalent to stating that, at a minimum, you expect your selection to contest the finish. Marked-to-Market (TBP Market), your selection is on offer pre-race at 1.80 to contest the finish and this price represents your best exit point In-Play (Win Market).