A Thought About Sideboards

[Illissius]

When building a deck, it's common wisdom that you should put the best cards in your deck and play 4 of them. You should also use cards which are generally useful. It's not a good idea to play 2 Red Blasts against blue decks, 2 Blue Blasts against red ones, 2 Engineered Plague against tribal, and 2 Orim's Chant against combo (yeah, the colors are fucked, ignore that); a better idea is 4 Spell Snare and 4 Swords to Plowshares.

I've had the idea that maybe for sideboards, it's the opposite. You have to go into every first game with the maindeck you have; contrarywise, you get to choose which sideboard cards to bring in for which matchup. And there are a huge variety of decks out there. Red Elemental Blast and Spell Pierce are both good against blue Counterbalance decks; but Red Elemental Blast is also great against Merfolk, while Spell Pierce is also useful against Stax and better against combo. Rather than play 4 of either, wouldn't it be a better plan to have two of each? And then make the same choice consistently when faced with similar decisions, opting for 1- and 2-ofs rather than 3- and 4-ofs, with the exception of cases where a card clearly has no equal (like Firespout). You still get to board in a similar amount of cards against the primary targets, while diversifying your options against the rest of the field, as opposed to nuking one deck and being totally unprepared against another. In cases where what you're boarding can be classified as "hate" which the opposing deck has to board in counterhate for, this also makes their job even more difficult.

Obviously a lot of people already do this -- you don't see the same rigid adherence to 4-ofs in sideboards as you do in maindecks -- and they probably already know about what I'm writing here. But I haven't seen it explicitly stated. A sideboard with a clean 4-4-4-3 of powerful cards can still look attractive to many people (including me), and maybe that's just wrong. Going Nassif with a highlander sideboard is perhaps too extreme, but maybe he had the right idea.

[chokin]

It might seem like an obvious thing to say, but it depends for what deck I'm playing. In a Painter Survival deck, I ran a Highlander sideboard because I could E.Tutor or Survival everything. In Ichorid, I run more 4s and 3s with my 2s and singles being able to come back from the yard either by Flashback (Grudge, Ray) or DR (any utility creature). My Zoo generally runs 3s all the way across.

It just depends on how consistently I want or need the answers. I'm pretty open to less uniform boards. Sometimes you need varying answers. If I don't run card draw or cantrips, I tend to run more copies of a card or more copies of a card role if that makes sense. Like Thresh decks can get away with having 2s in my opinion because they can dig. Zoo has a little bit of dig midgame, but in order to have answers early, it needs more copies.

I think that Nassif took it to the extreme. Even though he still had multiple answers to arifacts, enchantments, graveyard, etc he had some odd choices in there. I think Kataki stands out. I could see it being pretty good against Stax and Affinity, but weak artifact hate against decks that only need one or two artifacts.

Nassif is a vastly greater player than I am though. Dark Confidant probably helped out a lot in being able to sift through his deck a little more. And the singleton Tutor grabbed almost everything as well. I guess those have to count for something.

[IsThisACatInAHat?]

Nassif played that sideboard on a dare and still had groups of multiple cards with similar roles (ex. Planar Void/ Relic of Progenitus/ Tormod's Crypt, Kataki/ Energy Flux/ Enlightened Tutor). The logic of including multiples of great cards is so you see them more often. Just because sideboard cards are narrower doesn't mean you necessarily want to see them any less in matchups you side them in for.

[KrzyMoose]

Here's my favorite article on Sideboards:

http://www.starcitygames.com/magic/misc/17726_PVs_Playhouse_Last_Minute_Sideboards.html

It's premium, but I'm pretty sure it's been 90 days.

[Forbiddian]

The advantage of ANY sideboard card is the difference in win percentage between not having it and having the weakest card in your deck (for all the matches).

If you're a deck like Zoo, most all of your cards have some marginal value in every matchup. You board out your worst cards, but if you're only boarding in marginally powerful cards, your deck won't improve very much.

If you're playing more of a control deck, you'll tend to have a lot of dead weight in different matchups, so you should have a more diverse board. Generally if you're control, you're best suited by having a wide array of cards that come in under different circumstances, particularly against opponents where you have a lot of dead weight. If you're aggro, you'll want a tighter board with more powerful effects.


For control, if you're against Goblins and your worst card is a 1/1 for 1, you'd have to have a damn good sideboard card to make boarding it in worth it. A 1/1 for 1 is pretty good against Goblins. And it probably wouldn't be worth it to board in 6 or 8 cards at any rate, since there's just nothing that "wants" to come out.

If you're against The Epic Storm and you have 4 Swords to Plowshares, 2 WoG, and 1 Humility, you're much better off trying to find 7 cards that have marginal use in that matchup than 2 or 3 cards that win the game outright.

If I had a maindeck like that, I'd be looking specifically to find strong hate spells against aggro and then diverse hate spells against Combo (that won't clog up sideboard slots by only affecting one matchup, but will still be useful) and other decks. Cards like Enlightened Tutor are strong options because they have good use in multiple matchups instead of very strong use in a single matchup.


The real cause for so many bad sideboards is that people tend to look at the sideboard independently of the maindeck. The standard process is that you build a maindeck and then tinker your board to filling in the holes, but I've frequently found that if you have strong sideboard options in certain matchups, that should weigh in on your maindeck decisions.

Say you found a theoretical card that perfectly fits your sideboard. It destroys Goblins and Zoo, But you calculate and realize that the card doesn't fit your maindeck, and that the rest of your maindeck already beats Goblins and Zoo. You might only put 1 or 2 copies of it in the "just in case." You're probably better off keeping four of those bombs in the sideboard and slightly tanking your game 1 matchups against Goblins and Zoo in order to shore up other matchups. Specifically keeping in mind that whatever the four worst cards are against Goblins and Zoo, you'll only see those cards for 1 out of the three games. In other words, look back at your maindeck after creating your board to see if there are more things you can optimize.


I also hear these a lot:

"I have a slightly negative Goblins matchup, but if I board enough cards, I should win." This might not be true at all. If none of your cards is dead against Goblins, boarding in more won't help very much. Even if you bring in 8+ cards, you might only get a 10 or 15% increase in game win. You'd be better off using those board slots on matchups that will be affected more.

"That matchup is so low game 1, so I should just write it off and hope not to play against it." It might be so low because you have a bunch of dead cards game 1 that you can replace with great cards for the back two games. In this case, sideboarding would have the strongest effect and you might even get a good matchup out of it.

[mchainmail]

"That matchup is so low game 1, so I should just write it off and hope not to play against it." It might be so low because you have a bunch of dead cards game 1 that you can replace with great cards for the back two games. In this case, sideboarding would have the strongest effect and you might even get a good matchup out of it.

There are some match-ups where this is the case though; 43 Lands (Cedric Phillips's list from GenCon) versus Dragon Stompy is mostly a lost cause; Even bringing in 15 cards might not swing the matchup to 50/50.

Sure burning wish + hull breach could help, but from experience it's not a winnable matchup.

[pi4meterftw]

There are some match-ups where this is the case though; 43 Lands (Cedric Phillips's list from GenCon) versus Dragon Stompy is mostly a lost cause; Even bringing in 15 cards might not swing the matchup to 50/50.

Sure burning wish + hull breach could help, but from experience it's not a winnable matchup.

50/50 isn't some fairy-tale magical number though. It's pretty silly to pretend that winning 40% is not better than winning 20%.

[Maveric78f]

The advantage of ANY sideboard card is the difference in win percentage between not having it and having the weakest card in your deck (for all the matches).

This is quite a good definition, but it's not accurately true. Let's model this a bit to show how it can be wrong.

You play deck X. For every deck Y you might face, you first want to consider the probability you might face it: p(Y).

Let MDp be your average MD win when you're on the play.
Let MDd be your average MD win when you're on the draw.
Let SBp be your average SB win when you're on the play.
Let SBd be your average SB win when you're on the draw.

The probability you win game 1 is: p(W1) = (MDp+MDd)/2
The probability you win game 1 and game 2 is: p(W12) = SBd * (MDp+MDd)/2
The probability you win game 1, lose game 2 and win g3 is: p(W13) = SBp * (1-SBd) * (MDp+MDd)/2
The probability you lose game 1 and win game 2 and game 3 is: p(W23) = SBp * SBd * (1-(MDp+MDd)/2)
The probability you win the match is: p(W) = p(W12)+p(W13)+p(W23)

Say, you gain P% after SBing meaning that SBp = MDp+P and SBd = MDd+P. P can be negative if opponent's SB is better than yours. This assumes that -P<p(W1)<1-P. How much did you gain for each scenario?
p(W12#P)-p(W12) = P*p(W1)
p(W13#P)-p(W13) = (P-P²)*p(W1)-2P*p(W1)²
p(W23#P)-p(W23) = P²+(2P-P²)*p(W1)-2P*p(W1)²

How much did you gain overall?
p(W#P) - p(W) = P² + (4P-2P²)*p(W1) - 4P*p(W1)²

If the MU is balanced, meaning that p(W1)=0.5, you come up with this equation:
p(W#P) - p(W) = P
Which was your approximation Forbiddian.

However when p(W1) is low, it's more difficult to reverse the probabilities since you'll have only the P² factor remaining. In the symmetrical problem, when a MU is very easy preSB, your only risk is to lose -P².

Overall the metagame, the SB optimisation tends to optimise the sum on the metagame of the p(W#P) - p(W) we computed earlier (sorry the notations get messy):
perf(SB) = sum(Y in the metagame, p(Y)*(p(W#P/Y) - p(W/Y)))

Usually, the best mlove for a SB is indeed to win the MUs that are equilibrate before SB.

[Cthuloo]

This is quite a good definition, but it's not accurately true. Let's model this a bit to show how it can be wrong.

You play deck X. For every deck Y you might face, you first want to consider the probability you might face it: p(Y).

Let MDp be your average MD win when you're on the play.
Let MDd be your average MD win when you're on the draw.
Let SBp be your average SB win when you're on the play.
Let SBd be your average SB win when you're on the draw.

The probability you win game 1 is: p(W1) = (MDp+MDd)/2
The probability you win game 1 and game 2 is: p(W12) = SBd * (MDp+MDd)/2
The probability you win game 1, lose game 2 and win g3 is: p(W13) = SBp * (1-SBd) * (MDp+MDd)/2
The probability you lose game 1 and win game 2 and game 3 is: p(W23) = SBp * SBd * (1-(MDp+MDd)/2)
The probability you win the match is: p(W) = p(W12)+p(W13)+p(W23)

Say, you gain P% after SBing meaning that SBp = MDp+P and SBd = MDd+P. P can be negative if opponent's SB is better than yours. This assumes that -P<p(W1)<1-P. How much did you gain for each scenario?
p(W12#P)-p(W12) = P*p(W1)
p(W13#P)-p(W13) = (P-P²)*p(W1)-2P*p(W1)²
p(W23#P)-p(W23) = P²+(2P-P²)*p(W1)-2P*p(W1)²

How much did you gain overall?
p(W#P) - p(W) = P² + (4P-2P²)*p(W1) - 4P*p(W1)²

If the MU is balanced, meaning that p(W1)=0.5, you come up with this equation:
p(W#P) - p(W) = P
Which was your approximation Forbiddian.

However when p(W1) is low, it's more difficult to reverse the probabilities since you'll have only the P² factor remaining. In the symmetrical problem, when a MU is very easy preSB, your only risk is to lose -P².

Overall the metagame, the SB optimisation tends to optimise the sum on the metagame of the p(W#P) - p(W) we computed earlier (sorry the notations get messy):
perf(SB) = sum(Y in the metagame, p(Y)*(p(W#P/Y) - p(W/Y)))

Usually, the best mlove for a SB is indeed to win the MUs that are equilibrate before SB.

Interesting results with such a simple math. It's nice to look that the gain goes like:

p(W#P) - p(W) = P²(1-2*p(W1)) + 4P*(p(W1) - p(W1)²)

So, when p(w1) is small you are the dominant piece will be P², meaning that you should choose to side very strongly or not side at all, as a small to medium gain in P is suppressed by having to take the square. But looking closer to the numbers, let's say that p(w1) is 1/3, so we have:

p(W#P) - p(W)= P²/3 + 8*P/9

and the linear term is still dominant (and a 33%-66% is generally considered a really bad matchup).

Even in the case of p(W1)=0.2 you have:

p(W#P) - p(W)= 2*P²/5 + 16*P/25,

so what you board in is still relevant for more than 2/3 of what you board in in the even case. Forbiddian approximation was quite good after all. ;)

Edit:

What it's interesting is actually that the gain can indeed be greater than the 50-50 case.

In fact you can have

p(W#P) - p(W) | (p(W1) =1/3) > p(W#P) - p(W) | (p(W1) =0.5) if P>1/3, *

and also

p(W#P) - p(W) | (p(W1) =1/5) > p(W#P) - p(W) | (p(W1) =0.5) if P>9/10. (Edit#2: this result is meaningless, because you need to have a 110% probability to win post board, sorry)

Even if we can't unfortunately quantify P, the result it's still interesting. It really reinforces what I stated before, that in a difficult matchup you should side a lot (high P) or not at all.

* | means "in the case of" , sorry for the messy notation.

[lebarion]

* | means "in the case of" , sorry for the messy notation.

This thread needs to be re-written using TeX :wink: .

[johanessen]

Nassif was not the first to play single cards in sideboard.. just see this list:

http://www.deckcheck.net/deck.php?id=16631

BGwr Good Stuff by Jordi Estrela (4th of 89)

creature [21]
4 Birds of Paradise
1 Countryside Crusher
4 Dark Confidant
1 Dryad Arbor
2 Eternal Witness
1 Mystic Enforcer
4 Tarmogoyf
1 Terravore
3 Vinelasher Kudzu

instant [3]
1 Berserk
2 Enlightened Tutor

sorcery [10]
4 Burning Wish
3 Cabal Therapy
3 Duress

enchantment [1]
1 Rancor

artifact [5]
1 Engineered Explosives
1 Pithing Needle
1 Sensei's Divining Top
1 Umezawa's Jitte
1 Zuran Orb

land [21]
2 Bayou
3 Bloodstained Mire
3 Forest
1 Plateau
3 Swamp
2 Taiga
1 Volrath's Stronghold
3 Windswept Heath
3 Wooded Foothills

61 cards

Sideboard:
1 Armageddon
1 Cranial Extraction
1 Damnation
1 Deathmark
1 Hull Breach
1 Life from the Loam
1 Pyroclasm
1 Thoughtseize
1 Unearth
1 Vindicate
1 Engineered Plague
1 Eyes of the Wisent
1 Engineered Explosives
1 Pithing Needle
1 Tormod's Crypt

15 cards

[Rico Suave]

For me, my CB/Top list is essentially 3-4 copies of the spells maindeck, with a couple 2-ofs, but the SB has no more than 2 copies of any one card.

There are a few other factors that haven't been mentioned yet though.

1) Red Elemental Blast vs. Pyroblast (and similarly Blue Elemental Blast vs. Hydroblast)

While some will think these cards are identical, they aren't. Due to the wording on the cards, the biggest difference is that Pyroblast can actually target non-red cards. As such you can Pyroblast an opponent's land if you really wanted to, although it won't have any effect, but with REB you are unable to do as such.

For a storm deck then, it makes little sense to run REB when you can run Pyroblast. After all, you can Pyroblast any random permanent just to build storm, even if that permanent is not blue.

The card Misdirection is something else to note. Granted it doesn't see much play in Legacy, but I have won games in the past by Misdirecting a Pyroblast away from my only blue permanent onto one of my lands. I would not have been able to protect that permanent if REB was cast.

Lastly there are Cabal Therapy, Meddling Mage, and other such cards which have to name a specific card. These are perhaps the most relevant issues for a CB/Top deck. It only took one game loss for me to figure out that splitting 2/2 between REB/Pyro is a LOT better against Meddling Mage than 4 REB. Similarly, there are some R/b decks that show up where Hydroblast/BEB are strong but they have Cabal Therapy. I have seen my opponents whiff on a Therapy simply because they named BEB (of which I had a copy already in the graveyard) while sitting on a game winning Hydroblast in hand.

Even if your initial SB plan was this:
3 BEB
2 REB

It might simply be better to run:
2 BEB
1 Hydroblast
1 REB
1 Pyroblast

2) Hate cards

A common theme in Vintage against Dredge decks is to diversify the hate brought in from the SB.

Since Dredge decks can typically get shut down by as little as 1 card, they often bring in counter-hate cards which will answer your hate, allowing them to proceed with their normal game plan. Unfortunately they need specific counter-hate to fight you, and the cards they will use depend heavily on what you bring in.

For example there is little point for Dredge to bring in artifact removal if they know your only Dredge hate is Leyline of the Void. Similarly there is little reason to bring in enchantment removal if they know you only bring in artifacts.

What is extremely difficult for the Dredge player to fight, however, is a variety of cards across several different card types. Imagine you run 4 anti-Dredge cards, but it looks something like this:
1 Ravenous Trap
1 Yixlid Jailer
1 Relic of Progenitus
1 Leyline of the Void

Now they have to bring in *everything* to try and stop your hate cards. They need an answer to enchantments or they might get wrecked by Leyline. They need an answer to Jailer or they could simply scoop. The inherent benefit to this is that they can simply draw the wrong answers at the wrong time, like if they draw Ancient Grudge against your Jailer, Unmask against your first turn Leyline, or Chain of Vapor against Ravenous Trap. Let's not forget it is tougher to hit something with Cabal Therapy too.

Even if you don't have access to black, you could run this:
2 Tormod's Crypt
2 Relic of Progenitus

And now at the very least you are safer against Pithing Needle.

I believe this tactic also applies to Legacy, although it may not be as pronounced as it is in Vintage. Nevertheless it can lead to further cards in your SB that may only be present in 1 or 2 copies.

However, there are other examples of this beyond Dredge. As a CB/Top player, I can lose to PoP or Choke. While PoP may be better/worse than Choke, the different is almost irrelevant because if either one resolves (and sticks) I will frequently just be taken out of the game.

If I know my opponent only brings in 4 PoP, I can safely ignore my enchantment removal and that makes my job a little easier.

But if they run 2 PoP and 2 Choke, now I can end up in situations where I draw Grip against PoP and BEB against Choke. When a hate card takes the opponent out of the game, simply playing different kinds of hate cards will make it very difficult for your opponent to have the right answer at the right time.

3) Extensions of the maindeck

When playing against Stax, I know my Trygon Predator will wreck them if it gets as much as a single attack, and I feel very comfortable winning with 3 Trygons in my deck. The problem of course is that I don't want 3 Trygons maindeck because it's not justified against the rest of the field just to improve one prison match.

As such I maindeck 2 Trygon, side a 3rd, and bring in additional artifact/enchantment removal to supplement this approach. That 3rd Trygon in the SB will enhance my maindeck cards and as a result I end up with this:
1 Trygon Predator
2 Krosan Grip

I feel that Trygon is generally better than Grip, so I run more Trygons than Grips, however it's not that good enough to play 4 Trygon because the card can be clunky and slow - especially if you draw multiples. I'd much rather draw a split of 1 Trygon and 1 Grip as opposed to 2 Trygon, especially in the face of cards like Tabernacle or Ghostly Prison.

There are many cards that fit into this category. The point is that we may have cards which are really strong in a particular match but not be able to run a full set of those cards maindeck. We can include an extra copy or two in the SB to boost that match-up, but sometimes it will end up in weird looking SBs.

Conclusion

If you were to take just the SB cards I've outlined above and throw in a couple cards to help shore up against combo/control you end up with the following:

1 Trygon Predator
2 Krosan Grip
2 BEB
1 Hydroblast
1 REB
1 Pyroblast
2 Tormod's Crypt
2 Relic of Progenitus
2 Spell Pierce
1 Firespout

Does this SB look odd and unfocused? Yes. It is, nevertheless, quite effective at helping the maindeck win and performs a better job than if I ran a narrow set of 4-ofs and 3-ofs.

[Illissius]

Yeah, that's basically what I was getting at. We are trained to look at lots of 4s and a few 3s and think "good", and look at 1s and 2s and think "bad". I suspect we should train ourselves to think the opposite when looking at sideboards, or at the very least not think anything.

[Maveric78f]

It's much more difficut to build a 15-1-of SB than a 5-3-of SB. I think that's the main reason explaining the playset SBs. Everybody shold be aware it's generally better to have complementary cards in your SB. For instance, I've always advocated for having 1 threads of disloyalty, 1 mind harness, 1 control magic and 1 submerge instead of a playset of any of these.

[Maveric78f]

In order to illustrate the results of post 8 of this thread, I made a table and a graphics.

http://img193.imageshack.us/img193/3254/sbperftab.png (http://img193.imageshack.us/i/sbperftab.png/)

http://img199.imageshack.us/img199/1896/sbperffig.png (http://img199.imageshack.us/i/sbperffig.png/)

It shows clearly that the MUs you want to improve are the MUs that are slightly unfavorable pre-SB. And inversely, the MUs you want to protect post-SB are the MUs where you are slightly favorable.

[Cthuloo]

It depends on what you mean by "slightly". Even in a 25-75 matchup, the efficiency of the sideboard is really close to the 50-50 case (a 10% or less difference, going down as you go up with P, and in that case you will want an high P anyway).

However, good job, the results are definitely interesting.

[FoulQ]

I'm surprised nobody else has really commented on Maveric's data yet. If the conclusions he draws are correct (and I have no idea, but I trust him), this could have serious implications on a lot of sideboards. The main one being, the combo matchup for many decks, like goblins. Some say you need it, some say forget it. This gives mathematical evidence to the forget it side, if it holds up. Thanks for the data.

However, in legacy, I've never been a fan of devoting your SB to MU philosophy. Sure, some cards for your sideboard will be devoted to certain very popular MUs, but the format is so diverse that I don't think you can design a sideboard as narrow as you would in other formats. At least, with some decks. It seems to all be very complex and vary from deck to deck quite largely as to what are the best sideboard strategies, both in construction and in use.

[Illissius]

Apologies for being dumb, but could you explain what's on each axis and what the values assigned to the colors represent?

[Anusien]

For me, I build it like this:
I look at all the decks I think are relevant to fact at an event, and I write them down. Then I go through and list under each one the cards that I actively want to side out (and how many cards I want to bring in). Then I write out which cards I want to bring in there.

If you're lucky, there are 15 cards in total. If you're not, there aren't. So what you do is go through a process of tweaking where you try to combine cards for matchups. So maybe Llawan is better against Merfolk, but you don't have enough slots, so you just cut the Llawan and sideboard an extra Firespout instead. You go back and forth balancing this out until you get 15 cards. So maybe you find you don't have enough slots in your Zoo list to board in Magus of the Moon against 43land, because you have 8 slots dedicated to ANT. So instead you just bring in Sulfuric Vortex that you also have in the board.

In other words, the reason why we have 4s and 3s in the sideboards is because we have to generalize our sideboard hate because we need too many cards in too many matchups.

[Atwa]

Yeah, that's basically what I was getting at. We are trained to look at lots of 4s and a few 3s and think "good", and look at 1s and 2s and think "bad". I suspect we should train ourselves to think the opposite when looking at sideboards, or at the very least not think anything.

I must say I have applied this thought on maindecks too, and had some decent success with it. I've always been an advocate for this approach in rogue decks I play. Both in the sideboard and maindeck, this way of selecting cards can rewarding. You have lots of different cards, which makes you more flexible when playing a game (and sideboarding), and your opponent will never know what to expect.

I honestly think we are all staring ourselves blind on the fact decks should be consistent, but are forgetting flexibility also is a road to victory. Now I'm not saying every deck (or sideboard) should start playing lots of singletons and 2-offs. However I think people should have a more open mind in the thought of flexibility over consistency when constructing a deck or sideboard.

[Forbiddian]

@Maveric: Thanks for yet another insightful use of mathematics. I used something similar (the same equations you ended up using), but never looked at them in this manner.

@FoulQ: The mathematics is accurate, but the crux of this problem is not finding the equations, but the applying them in a useful manner.

I was going to comment earlier, btw, but had to go to lab.


@Thread
There aren't very many cards that would strictly go like:

-5% Chance to win game 2 against Goblins.
+5% Chance to win game 2 against TES.


Usually, combo gives you the highest delta. It's mitigated somewhat by the fact that you need to dig yourself out of a hole, but drawing a Mindbreak Trap is going to affect your probability of winning the Belcher matchup a hell of a lot more than drawing Krosan Grip is going to help an even matchup.


I'll note that Maveric's data has a ton of applications. When I looked at the data, I actually came to basically the opposite conclusion that Maveric did. Proximity to 50% does make the delta more important, but it's only by a very small factor.

Say that there are two matchups, both equal in metagame saturation. Then you need to choose between a card that gives +20% chance to win a 30% game 1 matchup and another card that gives a 15% better chance to win a 50% game 1 matchup.

If you blindly go with the conclusion that you should concentrate on the "about even" matchups, then you're missing out that the first case gives you 18.4% more match win and the second case only gives you 15% more match win.

Matchups proximity to 50% should break any ties, but the effect is extremely small next to the card's power in a given matchup.

In fact, if you look at all the rows, virtually regardless of the game 1 probability to win (as long as it's realistic, e.g. >20%), you're better off with any card that provides 5% more swing.



For example, Mindbreak Trap is extraordinarily powerful in the Belcher matchup. Drawing it you'll probably win 80% of the games and not drawing it, you'll probably win 20%. Regardless of the original probability to beat Belcher, it's still going to have a profound effect on the match win percentage.

Of course, that might not be enough because Mindbreak Trap is so narrow that it might not be worth it, but you get the idea that powerful board cards can still be the best pick even if they only affect low or high win percentage matchups.

[Maveric78f]

Apologies for being dumb, but could you explain what's on each axis and what the values assigned to the colors represent?

P(W) is the overall probability of win g1 (it's the average probability of winning g1 on the draw and winning g1 on the play).

P is the overall probability of win gain post SB. Meaning that post SB, you have P(W) + P chance of winning a game, regardless who plays and draws.

P(W#P) - P(W) is probability of winning the round. A lot of people think that P(W#P) - P(W) is linear with P, but it's wrong and that's the first thing (if not the only) I wanted to stress on. The graph clearly shows that it's more relevant to improve a close-to-even-pre-board MU than an impossible-to-win-g1 MU.

But, as forbiddian pointed out, this must be put into perspective with a lot of considerations:
- the metagame is the first relevant parameter. It will alsmost allways be better to improve a MU that represents 20% of the field than a MU that represents 10% of the field.
- the second important parameter is the P value: if you can improve an impossible-to-win-g1 MU by 80%, then it's probably worth it.
- the third important paramater is the compactness of the SB: if you gain 10% of MU1 with 1 card and 10% of MU2 with 4 cards then the first SB option is probably better.
- the fourth important paramater that is very often forgotten (a lot of people think that a MU is always improved post SB), is also the opposing SB.

Once you've taken into account all these parameters, you can probably take some conclusions of my experiments/tables/graphs.

[Illissius]

Oh. Okay. So what it's saying is that changing the probability of post-sideboard game wins by an equal amount has a bigger effect on the probability of match wins if the matchup was even pre-sideboard than if it was lopsided. Makes sense. Thanks.