A Thought About Sideboards

[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.