Practical Dominance Revisited

Practical Dominance Revisited

In Practical Dominance, we outlined an adaptation of the 'practical dominance' algorithm from Smart Choices to help us identify likely convex bets. On this occasion, we will further extend the algorithm in order to automate it. Though obviously heretical to those of an 'Even Swaps' persuasion, nevertheless our adaptation will ultimately prove to be of value. Effectively, we will loop over 'alternatives' and 'criteria' in successive iterations to reduce our initial table to as few selections as possible.

In each pairwise comparison, if one alternative has more wins than losses than the other alternative (comparing ranks across criteria) and the latter has no more than one win, then the first alternative practically dominates the second one. A similar explanation applies if the second alternative has more wins than losses compared to the first alternative.

Iteration 0 - Ranks

We begin our process by converting the raw ratings of 13 alternatives across 8 criteria into the equivalent table of ranks. In so doing, we are implicitly creating a level playing field allowing us to proceed by successive iterations to reduce both alternatives and criteria.

Alternative	A	B	C	D	E	F	G	H
Alpha	6	11	13	5	11	9	2	8
Bravo	7	7	6	9	9	10	6	12
Charlie	8	12	6	4	5	3	5	11
Delta	9	5	11	10	12	6	9	4
Echo	1	4	6	1	1	12	3	8
Foxtrot	4	9	12	5	7	5	9	6
Golf	10	5	6	12	13	12	1	2
Hotel	13	2	1	13	6	2	8	3
India	2	3	5	2	2	8	7	12
Juliet	5	7	2	7	3	6	12	5
Kilo	3	13	4	3	10	1	13	10
Lima	12	1	2	11	8	3	11	1
Mike	11	9	6	7	4	10	4	6

Iteration 1 - Remove Alternatives

Alternative	A	B	C	D	E	F	G	H
Delta	9	5	11	10	12	6	9	4
Echo	1	4	6	1	1	12	3	8
Foxtrot	4	9	12	5	7	5	9	6
Golf	10	5	6	12	13	12	1	2
Hotel	13	2	1	13	6	2	8	3
India	2	3	5	2	2	8	7	12
Juliet	5	7	2	7	3	6	12	5
Kilo	3	13	4	3	10	1	13	10
Lima	12	1	2	11	8	3	11	1

• Alpha is dominated by Foxtrot (practical)
• Bravo is dominated by Echo (practical)
• Charlie is dominated by Echo (practical)
• Mike is dominated by Juliet (practical)

Iteration 2 - Remove Criteria

Alternative	A	B	C	E	F	G	H
Delta	9	5	11	12	6	9	4
Echo	1	4	6	1	12	3	8
Foxtrot	4	9	12	7	5	9	6
Golf	10	5	6	13	12	1	2
Hotel	13	2	1	6	2	8	3
India	2	3	5	2	8	7	12
Juliet	5	7	2	3	6	12	5
Kilo	3	13	4	10	1	13	10
Lima	12	1	2	8	3	11	1

• D is dominated by A (practical)

Iteration 3 - Remove Alternatives

Alternative	A	B	C	E	F	G	H
Echo	1	4	6	1	12	3	8
Golf	10	5	6	13	12	1	2
Hotel	13	2	1	6	2	8	3
India	2	3	5	2	8	7	12
Juliet	5	7	2	3	6	12	5
Kilo	3	13	4	10	1	13	10
Lima	12	1	2	8	3	11	1

• Delta is dominated by Hotel (practical)
• Foxtrot is dominated by Hotel (practical)

Iteration 4 - Remove Criteria

Alternative	A	B	C	E	H
Echo	1	4	6	1	8
Golf	10	5	6	13	2
Hotel	13	2	1	6	3
India	2	3	5	2	12
Juliet	5	7	2	3	5
Kilo	3	13	4	10	10
Lima	12	1	2	8	1

• F is dominated by C (practical)
• G is dominated by E (practical)

Iteration 5 - Remove Alternatives

Alternative	A	B	C	E	H
Echo	1	4	6	1	8
Hotel	13	2	1	6	3
India	2	3	5	2	12
Juliet	5	7	2	3	5
Lima	12	1	2	8	1

• Golf is dominated by Echo (practical)
• Kilo is dominated by Echo (practical)

Iteration 6 - Remove Criteria

Alternative	Echo	Hotel	India	Juliet	Lima
B	4	2	3	7	1
C	6	1	5	2	2
E	1	6	2	3	8

• A is dominated by E (absolute)
• H is dominated by B (practical)

Iteration 7 - Remove Alternatives

Alternative	B	C	E
Hotel	2	1	6

• Echo is dominated by Hotel (practical)
• India is dominated by Hotel (practical)
• Juliet is dominated by Hotel (practical)
• Lima is dominated by Hotel (practical)

This leaves us with 'Hotel' as the only remaining alternative in a 13 runner field and as long as the odds meet our minimum convex bet requirement of twice the natural odds $(2*(13-1))/1 \approx 25/1)$ it is our selection.

python PD_Revisited.py -h

PD Revisited - Ex Novo
(c) 2022, matekus, All Rights Reserved.
https://vendire-ludorum.blogspot.com/

usage: PD_Revisited.py [-h] [-f FILENAME] [-x THRESHOLD]

optional arguments:
  -h, --help            show this help message and exit.
  -f FILENAME, --filename FILENAME
                        Csv file name (default: Sample_Racecard_Ranks.csv).
  -x THRESHOLD, --threshold THRESHOLD
                        PD threshold (default: 1).

If more than one choice remains because no alternatives are eliminated in the last iteration, then we can either increase the practical dominance threshold (default = 1) or leave our final decision to a combination of the average ranks and available odds.

Obviously, there is no guarantee that we will end up with a viable option.

Enjoy!