In betting analysis, there is a strong emphasis on only selecting Value Bets. To this end, we are advised to calculate the Expected Value (EV) of a proposed bet and, if the result is positive, then we have a potential value bet. However, this approach is very short-sighted as outlined below. This will lead us to add an additional metric - Likely Profit (LP) - and the Dual-Metric Decision Algorithm (DMDA).
We will focus on this canonical betting example:
Parameter | Value |
---|---|
Initial Bankroll (B) | $10000 |
Markets (M) | 1 |
Decimal Odds (O) | 1.9091 |
Win Probability (P) | 55.00% |
Stake Fraction (F) | 1.00% |
First, let us calculate the Win Balance (WB) and the Loss Balance (LB) in percentage terms. WB is the state of the bankroll after a winning bet and LB is the state of the bankroll after a losing bet. WB and LB are calculated as follows:
The is equal to:
EV represents the average profit or loss per unit staked over a large number of bets, assuming the same odds and probability hold true.
But, to evaluate the bet in terms of our specific circumstances, we need an additional metric - Likely Profit (LP).
The is equal to:
LP represents the expected growth rate of the bankroll over a series of bets, assuming the same odds and probability hold true. It takes into account the compounding effect of wins and losses.
Also, the and the are equivalently:
Note: Likely Profit (LP) is equivalent to expected bankroll growth!
This leads naturally to our Dual Metric Decision Algorithm (DMDA), which is best exemplified with the following Python snippet:
if ev_per_unit > 0 and lp_per_unit > 0:
decision = 'Favorable bet; consider proceeding.'
elif ev_per_unit > 0 and lp_per_unit <= 0:
decision = 'Positive EV but negative LP; reconsider stake size.'
else:
decision = 'Negative EV; generally avoid this bet.'
Returning to our example above, we can calculate the various metrics as follows:
- WB
- LB
- EV
- LP
- B_EV
- B_LP
Decision: Since both EV and LP per unit are positive, this is a favorable bet.
While the traditional EV approach can be useful for identifying potential value bets, it fails to capture the full picture when considering the long-term impact of betting decisions. By introducing Likely Profit (LP) as a complementary metric, we can gain a more comprehensive understanding of the expected bankroll growth over a series of bets. This dual-metric approach allows for a more nuanced decision-making process, enabling bettors to make informed choices that align with their individual risk profiles and long-term goals. However, the DMDA is a simplified approach and should be further refined. What is presented here is a starting point for this approach, and further research and development are needed to refine and optimize this framework for practical application in real-world betting scenarios.