# How to Approach Sideboarding (Mathematically, sorry)

Note: I understand that you can never get exact numbers, but that is not the point. The point of this is to give you an idea on how to think about sideboarding, because it is easy to make mistakes with it.

I know it is little sad to think of tournaments as optimizing win percentages, but that is what is actually about. You might just not talk about it in the sense of numbers, but that is what is often hiding behind those converstations on how popular a deck is going to be and what’s going to be good against it.

The key is that you will never find a deck that is going to be good against everything (okay, it happens every once in a while), so you need to hedge your bets on what you should play based on how good you think it’s going to be against the field. For this, you need to figure out what the meta is going to look like, which is a skill in itself. Than you need to know what is going to be good against the popular decks.

Okay, suppose you have chosen to play deck A, because of the expected field of decks, which looks like this:

Deck Metagame share Win%
Deck B 20% 60%
Deck C 15% 70%
Deck D 10% 60%
Deck E 10% 55%
Rest of the Field 45% 45%

In this case you have found a deck that you think is going to have a positive match-up against all the popular decks in the field. However, you are taking a hit in your win% against the rest of the field, perhaps because you have optimized your deck so strongly against the specific decks you are expecting.

Based on these numbers, your win% against the field on any given round is .2*.6 + .15*.7 + .1*.60 + .1*.55 + .45*.45 = 0,5425. So, positive, but not very much so.

Suppose you only have five different cards you can choose from for you sideboard (just for the sake of simplicity, as it would be kind of difficult to cover dozens or possibly hundreds of options).

The effect on the matchups for each card looks like this (with no negative effects as you can always choose not to sideboard it in):

 Card B C D E Rest 1 0,02 0,05 0,05 0,1 0,01 2 0,03 0 0 0 0,03 3 0 0 0,05 0 0,01 4 0,01 0,01 0 0,04 0,05 5 0,05 0,04 0,01 0 0

How to figure out from here which cards to put into the sideboard? One assumption I’m making here, which is not true, is that each copy will have the same effect, when often you might want to bring in just one just in case or you might bring in two, because there are two cards in your deck you need to upgrade. You should always remember to use your common sense on top of any theory.

There’s also diminishing returns on each card. Your second Rest in Peace drawn just isn’t going to be as good as the first, but you also want a better chance of drawing that one, which makes it more difficult to figure out how to approach this.

You can also use transformative sideboards, where you change your approach to the match-up completely, not just try to answer specific strategies.

Also, this is somehow a situation where each match-up is better after sideboarding, which obviously can’t be true in all cases, but there are decks, where this is largely true (usually control or midrange decks, which can customize their interactive cards after sideboarding), so just go with it. Gladly, that doesn’t even matter.

You see, the thing we are interested in is how much better each card can make the match-up, not what the win% is after changes.

 Card B C D E Rest 1 0,004 0,0075 0,005 0,01 0,0045 0,031 2 0,006 0 0 0 0,0135 0,0195 3 0 0 0,005 0 0,0045 0,0095 4 0,002 0,0015 0 0,004 0,0225 0,03 5 0,01 0,006 0,001 0 0 0,017

So, based on this, we should have 4 copies of card 1, 4 and 2 as well as 3 copies of card 5, in which case we would be able to .

Obviously, as I’ve said before, it’s not this simple, but again, I’m trying to explain that since you can’t optimize each match-up with your 15 card sideboard, you need to try to find the best percentage gains you can, which is a combination of understanding the match-ups and predicting the metagame. Neither of these is ever going to be perfect and even if get your metagame analysis 100% correct, you still can’t predict exactly which decks you will face. I’ve been in a tournament with over 30% of one deck and not playing against it once in eight rounds. That is unlikely, but that is how probabilities work. They are just probabilities. You just need to optimize them.

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