5 Deck analysis

This analysis attempts to use regression to determine the cards with the best performance inside archetype or base archetype.

A binomial regression is initially trained on a set of decks. In order to be included in this analysis the archetype must be present at least 50 times in the dataset.

In order to be considered a card must be included at least 50 times in either the main deck or the sideboards, one or the other being considered separately. In models comparing the number of copies of each card, when a number of copies is less than 50 it is grouped with an adjacent number of copies. For example, a card that is present 32 times in 1 copy 200 times in 2 copies, 15 times in 3 copies and 47 times in 4 copies would lead to the following result 1/2 : 232 and 3/4 : 62. The formulation 2-4 indicates that the numbers of copies 2, 3 and 4 have been grouped together.

Be careful, this part leads to results that I’m not really sure of. The interpretation of the regression coefficients seems really questionable, particularly in relation to the collinearity problem and the very large number of variables with sometimes small sample sizes. I would therefore encourage you to be very careful.

Templates are created separately for the maindeck and the sideboard and maindeck and side board pull together (Total 75) according to the following scheme :

Base Cards cards systematically present in decks with an almost fixed number of copies less than 50 decks that do not have the most common number of copies. decks with zero copies are grouped with the majority class) contained in the decks, for which the number of copies varies, quasibinomial regression models are created using the wins and losses of each deck :
- Comparing for each card presence Most common count vs absence Other
- Comparing each card count with a sufficient sample size Most common count vs 1 vs 3-4 for example
Uncommon Cards, These cards are not always included in decks, quasibinomial regression models are created using the wins and losses of each deck :
- Comparing for each card presence +1 vs absence 0
- Comparing each card count with a sufficient sample size 0 vs 1 vs 3-4 for example.

Model produce odds ratio, an odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first cards count. And an odds ratio less than 1 indicates that the condition or event is less likely to occur in the first cards count.

If the probabilities of the event in each of the groups of cards count are p1 (first group 4 copy of a cards) and p2 (second group 0-3 copy of the cards), then the odds ratio is:

\[OR = \frac{p_1/(1-p_1)}{p_2/(1-p_2)}\]

6 Archetype

6.1 B Demon : Demons

Number of deck : 60 for 130 wins over 238 rounds

6.1.1 Main deck

6.1.1.1 Base Cards

Cards Always in deck with nearly fix count

Total number of most common count : 50

Mainboard_CardName	WR	Mainboard_Count	most_common_quantity	Card_not_in_deck	Not_most_common_count
Basic land	0 %	2-4/8/11/13-15	3	0	28
Duress	1.75 %	1-3	2	9	27
Fatal Push	-0.15 %	2-4	4	1	2
Land_tot	0 %	20/22-26/34	25	0	10
Mutavault	1.92 %	4	4	6	0
Shock land	-0.26 %	4	4	10	0
Thoughtseize	0 %	3/4	4	3	1
Unholy Annex // Ritual Chamber	1.57 %	3/4	4	7	3

6.1.2 Side Board

6.1.2.1 Base Cards

Cards Always in deck with nearly fix count

Total number of most common count : 0

Sideboard_CardName	WR	Sideboard_Count	most_common_quantity	Card_not_in_deck	Not_most_common_count
Land_tot	0 %	0	0	0	0

6.1.3 Total 75

6.1.3.1 Base Cards

Cards Always in deck with nearly fix count

Total number of most common count : 51

Mainboard_CardName	WR	Mainboard_Count	most_common_quantity	Card_not_in_deck	Not_most_common_count
Basic land	0 %	2-4/8/11/13-15	3	0	28
Duress	0.49 %	2-4	3	4	20
Fatal Push	-0.15 %	2/4	4	1	1
Land_tot	0 %	20/22-26/34	25	0	10
Mutavault	1.92 %	4	4	6	0
Shock land	-0.26 %	4	4	10	0
Thoughtseize	-0.15 %	3/4	4	1	2
Unholy Annex // Ritual Chamber	1.57 %	3/4	4	7	3

6.2 Mono Red Aggro

Number of deck : 109 for 249 wins over 476 rounds

6.2.1 Main deck

6.2.1.1 Variable Cards

Cards not always in deck using binomial regression for WR

Any
Count

	Mono Red Aggro N :476
Characteristic	N	OR	95% CI	p-value
Color
R	167	—	—
Other	309	0.44	0.09, 2.08	0.3
Number_of_cards	476	1.02	0.95, 1.10	0.5
Den of the Bugbear
1-4	273	—	—
Other	203	0.94	0.52, 1.72	0.9
Fast land
1-5	262	—	—
Other	214	0.73	0.25, 2.09	0.6
Kumano Faces Kakkazan
0	234	—	—
Other	242	0.86	0.41, 1.77	0.7
Monstrous Rage
1/3/4	278	—	—
Other	198	0.67	0.31, 1.41	0.3
Pain land
0	249	—	—
Other	227	0.89	0.41, 1.92	0.8
Ramunap Ruins
1-4	264	—	—
Other	212	1.10	0.52, 2.32	0.8
Shock land
2-4/6/8/12	285	—	—
Other	191	0.61	0.16, 2.13	0.4
Sokenzan, Crucible of Defiance
1-4	270	—	—
Other	206	1.17	0.73, 1.88	0.5
Abbreviations: CI = Confidence Interval, OR = Odds Ratio

	Mono Red Aggro N :476
Characteristic	N	OR	95% CI	p-value
Color
R	167	—	—
Other	91	0.53	0.10, 2.62	0.4
WR	97	0.76	0.10, 5.67	0.8
RG	80	0.69	0.09, 5.18	0.7
BR	41	0.47	0.06, 3.40	0.5
Number_of_cards	476	1.01	0.94, 1.10	0.7
Den of the Bugbear
1-4	273	—	—
0	203	1.04	0.56, 1.97	0.9
Fast land
1-5	262	—	—
0	214	0.77	0.25, 2.30	0.6
Kumano Faces Kakkazan
0	234	—	—
1/4	242	0.88	0.41, 1.87	0.7
Monstrous Rage
1/3/4	278	—	—
0	198	0.63	0.28, 1.38	0.3
Pain land
0	249	—	—
1-4	227	0.76	0.31, 1.82	0.5
Ramunap Ruins
1-4	264	—	—
0	212	1.08	0.51, 2.32	0.8
Shock land
2-4/6/8/12	285	—	—
0	191	0.72	0.18, 2.78	0.6
Sokenzan, Crucible of Defiance
1-4	270	—	—
0	206	1.15	0.70, 1.89	0.6
Abbreviations: CI = Confidence Interval, OR = Odds Ratio

6.2.2 Side Board

6.2.2.1 Base Cards

Cards Always in deck with nearly fix count

Total number of most common count : 0

Sideboard_CardName	WR	Sideboard_Count	most_common_quantity	Card_not_in_deck	Not_most_common_count
Land_tot	0 %	0-2/15	0	0	4

6.2.3 Total 75

6.2.3.1 Variable Cards

Cards not always in deck using binomial regression for WR

Any
Count

	Mono Red Aggro N :476
Characteristic	N	OR	95% CI	p-value
Color
R	167	—	—
Other	309	0.48	0.10, 2.05	0.3
Number_of_cards	476	1.04	0.97, 1.12	0.3
Den of the Bugbear
1-4	273	—	—
Other	203	0.92	0.51, 1.68	0.8
Fast land
1-5	262	—	—
Other	214	0.74	0.25, 2.10	0.6
Kumano Faces Kakkazan
0	234	—	—
Other	242	0.83	0.40, 1.72	0.6
Monstrous Rage
1/3/4	278	—	—
Other	198	0.68	0.31, 1.43	0.3
Pain land
0	249	—	—
Other	227	0.94	0.43, 2.04	0.9
Ramunap Ruins
1-4	264	—	—
Other	212	0.99	0.46, 2.13	>0.9
Shock land
2-4/6/8/12	285	—	—
Other	191	0.62	0.17, 2.06	0.4
Sokenzan, Crucible of Defiance
1-4	270	—	—
Other	206	1.16	0.72, 1.87	0.5
Torch the Tower
0	250	—	—
Other	226	1.31	0.85, 2.00	0.2
Abbreviations: CI = Confidence Interval, OR = Odds Ratio

	Mono Red Aggro N :476
Characteristic	N	OR	95% CI	p-value
Color
R	167	—	—
Other	91	0.55	0.11, 2.47	0.4
WR	97	0.80	0.11, 5.27	0.8
RG	80	0.66	0.09, 4.29	0.7
BR	41	0.48	0.07, 3.13	0.5
Number_of_cards	476	1.03	0.95, 1.12	0.5
Den of the Bugbear
1-4	273	—	—
0	203	1.03	0.55, 1.94	>0.9
Fast land
1-5	262	—	—
0	214	0.77	0.25, 2.29	0.6
Kumano Faces Kakkazan
0	234	—	—
1/4	242	0.83	0.38, 1.77	0.6
Monstrous Rage
1/3/4	278	—	—
0	198	0.63	0.28, 1.37	0.2
Pain land
0	249	—	—
1-4	227	0.83	0.34, 2.00	0.7
Ramunap Ruins
1-4	264	—	—
0	212	0.97	0.44, 2.11	>0.9
Shock land
2-4/6/8/12	285	—	—
0	191	0.72	0.19, 2.58	0.6
Sokenzan, Crucible of Defiance
1-4	270	—	—
0	206	1.13	0.68, 1.85	0.6
Torch the Tower
0	250	—	—
1-4	226	1.33	0.85, 2.07	0.2
Abbreviations: CI = Confidence Interval, OR = Odds Ratio

6 Archetype

6.1 B Demon : Demons

6.1.1 Main deck

6.1.1.1 Base Cards

6.1.2 Side Board

6.1.2.1 Base Cards

6.1.3 Total 75

6.1.3.1 Base Cards

6.2 Mono Red Aggro

6.2.1 Main deck

6.2.1.1 Variable Cards

6.2.2 Side Board

6.2.2.1 Base Cards

6.2.3 Total 75

6.2.3.1 Variable Cards

7 Base archetype