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7 months ago ::
Oct 28, 2012 - 12:48PM
#1
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Date Joined:
Jun 15, 2009
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So I was trying to come up with this on my own, and I wasn't sure of the best way to go about this. What is the formula for determining how often a player would win in the absence of mana issues, based on their observed record in games where they had no mana issues, the liklihood mana issues are hit and the general record for players who hit mana issues. Or is there a formula that uses variables different from these?
What I'm trying to get at is, let's say a given player wins 80% of their games when they have no mana issues. You can't say that they would win 80% of their games if mana issues were taken out, because some of those wins came in games where their opponent lost due to mana issues when they would not have won otherwise. I'd like a formula to figure out what the adjustment should be.
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7 months ago ::
Oct 28, 2012 - 1:21PM
#2
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- Volunteer Community Lead
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Date Joined:
Feb 27, 2002
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Best place to start would probably be Elo.
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7 months ago ::
Oct 28, 2012 - 2:27PM
#3
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Date Joined:
Jun 15, 2009
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Best place to start would probably be Elo.
How so? I'm not looking for the answer for a specific matchup. I'd like to be able to say a person who wins x% of the games where they had no mana issues would win y% of their games if mana issues never occured.
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7 months ago ::
Oct 28, 2012 - 2:28PM
#4
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Date Joined:
Jul 20, 2007
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So I was trying to come up with this on my own, and I wasn't sure of the best way to go about this. What is the formula for determining how often a player would win in the absence of mana issues, based on their observed record in games where they had no mana issues, the liklihood mana issues are hit and the general record for players who hit mana issues. Or is there a formula that uses variables different from these?
What I'm trying to get at is, let's say a given player wins 80% of their games when they have no mana issues. You can't say that they would win 80% of their games if mana issues were taken out, because some of those wins came in games where their opponent lost due to mana issues when they would not have won otherwise. I'd like a formula to figure out what the adjustment should be.
Honestly I don't think such a formula is possible since mana issues are built into the game. Even if you could design the game so that mana was never an issue you would really be talking about another game. Part of a person's cumulative experience is in how they deal with mana issues and at what point they make decisions because they recognize their situation.
For example if you know your deck is 30% 3cmc or lower and you keep a 3 land hand expecting of course to draw more at some point not drawing that 4th mana means making decisions about casting the spells you CAN cast even if they aren't advantageous to do so at the time. And so on.
There is also the notion that your opponent may actively try to hurt your ability to produce mana in timely fashion (kill your land or your mana producer before you can ramp up for example.) At what point does that behavior become critical to your win/loss is a factor that can't be decided by a general formula.
You could I suppose come up with something that factors in such variables as unknown quantaties so that you can solve them when such data becomes available but that seems sketchy at best and fruitless at worst.
Winter.Wolf
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7 months ago ::
Oct 28, 2012 - 2:55PM
#5
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Date Joined:
Jun 15, 2009
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What I'm looking for should be a simple formula and would likely be based on the variables I described. For example the end result might be: "A person with an 80% win rate across games where they hit no mana issues would have a 75% win rate in games where neither he nor his opponent hit mana issues" Something along those lines.
Mana issues in this case are defined as either missing one of the first 3 land drops, drawing more lands than spells over the first 17 cards, or drawing more lands than spells over the first x cards drawn if the game ends before 17 cards are drawn. I'm looking to remove all games in which either player hits mana issues to see what percentage of games player 1 (the player who wins 80% of their games where they don't hit mana issues) wins after mana issues are removed. It won't be the exact value, but it should be easy to get a pretty good appropimation. For example, if player 1 won 100% of the games where they had no mana issues, the formula I am looking for will state that they are expected to win 100% of their games if mana issues did not exist, because any game their opponent lost via mana issues they were going to lose anyway.
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7 months ago ::
Oct 28, 2012 - 3:02PM
#6
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Post your initial simple formula you've worked out based on your variables and we can help to tweak it.
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7 months ago ::
Oct 28, 2012 - 3:10PM
#7
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Date Joined:
Jun 15, 2009
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Post your initial simple formula you've worked out based on your variables and we can help to tweak it.
I started it a few times and stopped. I wanted to see if someone could come up with a formula and I'm worried about prejudicing the people who might write in. If I don't see a formula that looks correct by tomorrow I will post my second attempt.
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7 months ago ::
Oct 28, 2012 - 8:03PM
#8
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Date Joined:
Oct 27, 2012
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Several caveats:
1) Magic is too complicated. A reductive approach is inherently flawed.
2) Different decks have different probabilities of mana issues, and some are more injured by poor mana than others.
3) There are different degrees of mana issues to have.
I. That said, here's the formula under the following assumptions:
1) Win percentage of the player with no mana issues: A
2) Typical win percentage with mana issues: B
3) Probability of mana issues: p
Then the win percentage in general is (1-p)A + pB.
For example:
1)Let's say A is 80%, as you had in your example.
2)It's not clear what we should take p to be. This is where caveats 2 and 3 above become apparent. I'm just going to say .1, i.e. 10%. (See footnote.*)
3)I also don't know what to put for B. For the sake of argument, let's have it be 10% if your opponent has no mana issues, and 50% if your opponent also has mana issues. That makes, with p = .1, B = 10%*.9 + 50%*.1 = 14%
Then win percentage in general for this example would be .9*80% + .1*14% = 73.4%
*Footnote:
The probability of, for example, a limited deck on the play with 17 lands not hitting its third land drop, assuming you keep 7 card hands with 2-5 lands, 6 card hands with 2-5 lans, and any 5 card hand is roughly .09, i.e. 9%.
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7 months ago ::
Oct 29, 2012 - 6:22AM
#9
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Date Joined:
Jun 15, 2009
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Based on the last post I'm not sure that people understand what I am looking for. So let me state it again. Player A wins 80% of the Magic games they play where they hit no mana issues. I would like to know the rough percentage of games they won in games where neither they nor their opponent had mana issues. I'm pretty certain there can be a rough calculation for this based on parameters like the average liklihood of mana issues and the average win rate for people hitting mana issues.
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7 months ago ::
Oct 29, 2012 - 9:08AM
#10
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Date Joined:
Mar 20, 2003
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Your question might as well be phrased as "if a person won X% of those games played while [some condition] held, they would win Y% of all their games if [that condition] were always true."
That is a non-question, since trivially X = Y. It doesn't even matter if winning depends on that condition.
Your obsession is becoming rather boring, by the way.
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