Does anyone know the formula?

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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.
Best place to start would probably be Elo.

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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.
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 (ugh at this new forum with the ridiculous double login)

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.
Post your initial simple formula you've worked out based on your variables and we can help to tweak it.
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.
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%.
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.
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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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.



It's not a trivial question. Using that phrasing the question is "if a person won X% of those games played with [some condition] held, they would win Y% of all games if [that condition] and [that same condition for their opponent] were always true."

X% and Y% are not the same.

I already know the percentage of games won while not hitting mana issues is 80%, I do not know what proportion of that 80% occurred in games where the opponent had mana issues. Or more specifically I don't know what proportion of that 80% occurred in games where the opponent had mana issues and would have won if they did not have mana issues. While the exact percentage cannot be calculated due to a variety of factors, there should exist a simple formula that comes close.
First we assume that mana issues hit all player equally*.
Therefore your winning percentage for all games with no mana issues, for either player, is equal to you winning percentage when both players mana issues are included..
This is because an equal amount of your games and your opponents games can be discounted due to mana issues.

*this is not strictly true as deck construction, deck play style and player skill all affect what level of problem is actually a significant factor. However including these factors would make this unsolvable. And an equal distribution is a reasonable approximation.

I've bought the cards and made a deck Now how do I win at this?

You would win approximately 50% of the time if there were no mana issues in Magic.


Fortunately, I can be far more helpful than that.  You are asking yourself the wrong question currently.  You don't actually want to know a formula for a hypothetical game that mirrored every aspect of MTG except for one, what you are in fact looking for is your True Skill Level.  You want a number that fills your heart with joy - a number you can fall back on in the face of defeat, knowing the defeat was unjust.  You are looking for something timeless, something applicable to all games, something you know is right and something that will not change due to bad luck.

And I have just the thing.

According to the Overseers of True Skill, your True Skill Level is:  438

Hope that helps.
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.



Ok, I think I get it now. 

You want a formula for something that needs to use a variable that is inherently undefinable (mana issues) since it means something different to each player and each deck and also depends on my opponents deck (if I play someone that has land destruction does that count as mana issues when i can't cast what I want next turn?).

Then, you want this formula to provide a "rough" percentage.

I vote between 0-100%.

Perhaps that is the easiest way to approach it. Every nth game will be decided by mana issues, those will be equally split by both players. If those were not equally split by both players they would instead be representative of the population of games where neither players had mana issues. Well, it does seem like that is leaving some important factors out. I'll have to think on this some more.

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.



Ok, I think I get it now. 

You want a formula for something that needs to use a variable that is inherently undefinable (mana issues) since it means something different to each player and each deck and also depends on my opponents deck (if I play someone that has land destruction does that count as mana issues when i can't cast what I want next turn?).

Then, you want this formula to provide a "rough" percentage.

I vote between 0-100%.




Mana issues are defined as either missing one of your first three land drops, or drawing more lands than spells over the course of the first 17 cards (including starting hands), or the first x cards where the game ends before each player has drawn 17 cards. It can also be assumed that every player is playing 23 spell, 17 land decks.

However, I don't believe that any of this should matter, because I'm not expecting for someone to see this through to the point where they've calculated a percentage, I only want to derive the formula itself. The formula will likely include variables like [percent of games where mana issues occur] and [percentage of games won by mana short players vs non-mana short players] -- variables of that nature. The underlying assumption is that you have collected statistics for player 1 such that you know how they'll perform under various splits (mana issues but no muligan, single muligan and mana issues, etc) and now you are looking at that player playing a generic opponent where neither of them are hitting mana issues. So each game is played as normal, with players making standard muliganing decisions, but at the point either player hits a mana issue the game is stopped and thrown out. Then you look at the remaining non-mana issue games to determine the percentage of games that player 1 won.

I guess I'll take a stab at it later in the day, I was really hoping someone on here would be able to come up with it. I don't think it will need to be a very complicated formula. What is being looked for is the strength of the pull towards the center, in the sense that wins/losses due to mana issues  inflate the number of games won by players with an under-50% winning percentage and deflate the number of games won by a person with an over-50% winning percentage.
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.



Okay, again with the caveats that I don't think this really makes sense to do or is worth doing:

Assuming:
1) Win percentage by player A with no mana issues by that player: x (in your example, x = 80%)
2) Typical win percentage of a deck with mana issues against a deck with no mana issues: y
3) Probability of mana issues: p

I'm going to be using decimal form for percents, so .8 for 80%.

Now we want to figure out in what proportion of player A's games the opponent had mana issues. Call this v for "your silly notion of the Value of the player"

Then we have x = p*(1-y)+(1-p)*v

Here p of the time the opponent has mana issues, making a win easier, i.e. player A will win 1-y of the time. The other 1-p of the time, the opponent has no mana issues and player A wins v of the time.

That is, v = (x - p*(1-y))/(1-p)

Example:
For example, if x = .8 and p = .1 and y = .1 (this is what I pulled out of my hat in my previous post for y), then we get v = (.8 - .1*(.9))/.9 = 71/90, which is roughly .789.

Addendum:
A related quantity to y is "typical win percentage by a deck with mana issues". Let's call that quantity z. Possibly it sounds like you wanted to take that as your given. If so, here's how it's related to y:

z = (1-p)*y + p*.5

Here p of the time both have mana issues, giving a typical win percentage of .5, and (1-p) of the time, only the player supposed to have mana issues has mana issues

That is, y = (z-p/2)/(1-p)

In the example, z=.14 (this is what showed up as B in my first post).

(Edited for a typo swapping y and z.)
Also, now that I understand what you're asking, why not just use the player's overall win percentage (including all games, mana screw or no) instead of this "win percentage assuming mana screw never happens to anyone" for whatever purpose you have in mind?

Dealling with mana issues, mulliganing properly, building your deck properly, and the like are all part of the game. Why attempt to remove this? It's not like you're going to be getting mana screwed much more often than others over a suitably large sample of games (unless you're building your deck or mulliganing poorly).
(unless you're building your deck or mulliganing poorly).

*ding*!

This is why there's no point in this exercise. If you have greater or fewer mana issues than average, THIS IS A FACTOR OF YOUR SKILL. As such, there's absolutely no reason to factor it out. In fact, your end result is going to be far less accurate than just taking actual win percentage. 
The purpose of this exercise is to remove the games won/lost to mana issues. I would like to repeat the exercise for muligans as well. Ultimately I'd like to see how various players do outside the games where they start up or down cards relative to their opponents. As stated earlier, the main effect that I see related to mana issues and muligans is that they push the game win rate for all players closer to 50%. Even if someone was winning close to 100% of the games where they and their opponents started at 7 cards and everyone played out their hands, there would still be games where they either get stuck on two lands, draw more lands than spells, and/or start the game with less than 7 cards due to proper muliganing decisions. And a number of these games would be unwinnable even through proper play due to card disadvantage, lack of early plays or virtual card disadvantage late into the game. Likewise, even a player winning 0% of their games where their opponent starts at 7 cards should win a few games where their opponents start at 5 cards or less. So I'd like to see, at the point where everyone starts at 7 cards, makes their first 3 land drops and draws less lands than spells, how players would do relative to their overall and non-mana issue win rates in the current system.
 
The purpose of this exercise is to remove the games won/lost to mana issues. I would like to repeat the exercise for muligans as well. Ultimately I'd like to see how various players do outside the games where they start up or down cards relative to their opponents. As stated earlier, the main effect that I see related to mana issues and muligans is that they push the game win rate for all players closer to 50%. Even if someone was winning close to 100% of the games where they and their opponents started at 7 cards and everyone played out their hands, there would still be games where they either get stuck on two lands, draw more lands than spells, and/or start the game with less than 7 cards due to proper muliganing decisions. And a number of these games would be unwinnable even through proper play due to card disadvantage, lack of early plays or virtual card disadvantage late into the game. Likewise, even a player winning 0% of their games where their opponent starts at 7 cards should win a few games where their opponents start at 5 cards or less. So I'd like to see, at the point where everyone starts at 7 cards, makes their first 3 land drops and draws less lands than spells, how players would do relative to their overall and non-mana issue win rates in the current system.
 


The point, you've missed it again.

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(unless you're building your deck or mulliganing poorly).

*ding*!

This is why there's no point in this exercise. If you have greater or fewer mana issues than average, THIS IS A FACTOR OF YOUR SKILL. As such, there's absolutely no reason to factor it out. In fact, your end result is going to be far less accurate than just taking actual win percentage. 



Certainly having fewer mana issues than average would be desirable and skill based, as would losing a fewer percentage of games when you did have mana issues and making better muliganing decisions. Unfortunately, there will never be a point where you can use proper muliganing or deckbuilding skills to negate the massive arbitrary disadvantage you get in games just from drawing an initial hand with 0, 1, 6 or 7 lands. Keeping those hands means you are likely to incur mana issue losses, muliganing means you are more likely to hit mana issues with your random 6 card hand than you would with a random 7, and at that point getting a 0, 5 or 6 lander should generally be a double muligan loss, while a 1 land hand will typically end in a mana short loss and a 4 land hand will generally end in a mana flood loss. Just picking up your opening hand and seeing 0, 1, 6 or 7 lands means you are the projected loser unless your opponent has 0, 1, 6 or 7 cards in their starting hand as well.

The point, you've missed it again.



Another classic Bubba. Requires no thought, includes no facts, ironically makes no point. When you need to say nothing in 40 characters or less.
You would win approximately 50% of the time if there were no mana issues in Magic.


Fortunately, I can be far more helpful than that.  You are asking yourself the wrong question currently.  You don't actually want to know a formula for a hypothetical game that mirrored every aspect of MTG except for one, what you are in fact looking for is your True Skill Level.  You want a number that fills your heart with joy - a number you can fall back on in the face of defeat, knowing the defeat was unjust.  You are looking for something timeless, something applicable to all games, something you know is right and something that will not change due to bad luck.

And I have just the thing.

According to the Overseers of True Skill, your True Skill Level is:  438

Hope that helps.



Winner!!

Winter.Wolf (ugh at this new forum with the ridiculous double login)

The purpose of this exercise is to remove the games won/lost to mana issues. I would like to repeat the exercise for muligans as well. Ultimately I'd like to see how various players do outside the games where they start up or down cards relative to their opponents. As stated earlier, the main effect that I see related to mana issues and muligans is that they push the game win rate for all players closer to 50%. Even if someone was winning close to 100% of the games where they and their opponents started at 7 cards and everyone played out their hands, there would still be games where they either get stuck on two lands, draw more lands than spells, and/or start the game with less than 7 cards due to proper muliganing decisions. And a number of these games would be unwinnable even through proper play due to card disadvantage, lack of early plays or virtual card disadvantage late into the game. Likewise, even a player winning 0% of their games where their opponent starts at 7 cards should win a few games where their opponents start at 5 cards or less. So I'd like to see, at the point where everyone starts at 7 cards, makes their first 3 land drops and draws less lands than spells, how players would do relative to their overall and non-mana issue win rates in the current system.
 



This is different from your initial post's stated intention. I think it is a valuable thing to attempt find this data out (though again I suggest strongly that it isn't codifiable. )  Get a group of players to report to your their win/loss data along with whether they were mana screwed/flooded and whether their opponents were (and in either case whether it mattered since sometimes the outcome of a game is decided so quickly that manascrew/flood doesn't factor into it.) Also ask them for data on mulligans. Then get back to us on what you think their true skill was.

Winter.Wolf (ugh at this new forum with the ridiculous double login)

Just picking up your opening hand and seeing 0, 1, 6 or 7 lands means you are the projected loser unless your opponent has 0, 1, 6 or 7 cards in their starting hand as well.

I completely disagree with this statement. This is true if both players are playing the same deck, perhaps. They aren't. Deck construction can nullify the disadvantages of mana-light or heavy hands. Better players tend to take this into consideration more when building their decks. If my hand is 6 land and a Merfolk Looter it isn't a great hand but it is far from "unfavored" depending on deck composition.

Likewise if my hand is 1 land but that 1 card is a Weathered Wayfarer and I'm on the draw, suddenly I'm favored. A lesser player might not recognize the value of those cards and play them. 

And yes, despite your skill, there are games that you will outright lose to mana issues even if you build and play perfectly. But everyone will suffer exactly the same number of these on average and over large samples, so there's no point in considering them. 
Well anyway, my formula, which should work for mana issues, muligans or any measurable factor, is as follows:

O = observed game win rate for player 1 with factor x
p = Likihood that factor x is hit by player 2 [given it has been hit by player 1]
y = Win rate for player 2 if factor x is not hit for them, but hit for player 1
r = Win rate for player 1 if factor x is hit for player 1 and player 2 

O = p * r + (1-p) * (1-y)

So r = (O - (1-p) * (1-y)) / p

Which I think is equivalent to the formula that cten came up with, although the expression of some of the probabilities is inverted. In this case the x factors are keeping your initial 7 card hand, not hitting mana issues and both together. It seems like y would be the most difficult part to get, but you should be able to get an average across all players.
The purpose of this exercise is to remove the games won/lost to mana issues. I would like to repeat the exercise for muligans as well. Ultimately I'd like to see how various players do outside the games where they start up or down cards relative to their opponents. As stated earlier, the main effect that I see related to mana issues and muligans is that they push the game win rate for all players closer to 50%. Even if someone was winning close to 100% of the games where they and their opponents started at 7 cards and everyone played out their hands, there would still be games where they either get stuck on two lands, draw more lands than spells, and/or start the game with less than 7 cards due to proper muliganing decisions. And a number of these games would be unwinnable even through proper play due to card disadvantage, lack of early plays or virtual card disadvantage late into the game. Likewise, even a player winning 0% of their games where their opponent starts at 7 cards should win a few games where their opponents start at 5 cards or less. So I'd like to see, at the point where everyone starts at 7 cards, makes their first 3 land drops and draws less lands than spells, how players would do relative to their overall and non-mana issue win rates in the current system.
 



This is different from your initial post's stated intention. I think it is a valuable thing to attempt find this data out (though again I suggest strongly that it isn't codifiable. )  Get a group of players to report to your their win/loss data along with whether they were mana screwed/flooded and whether their opponents were (and in either case whether it mattered since sometimes the outcome of a game is decided so quickly that manascrew/flood doesn't factor into it.) Also ask them for data on mulligans. Then get back to us on what you think their true skill was.



I would like to attempt this using MtGO data, but if enough players volunteered the information it might work. Based on my own data I would say taking the first muligan roughly cuts your chance to win in half, because of the high number of muliganed hands that become either double muligan hands, mana floods or mana shorts, all of which have win rates near 0% if you hit them after you've muliganed. If you could guarentee a muligan did not lead to one of those three things however, you wouldn't be in bad shape losing the one card, almost certainly better shape than if you hadn't shipped the questionable hand that lead to you muliganing in the first place.
Just picking up your opening hand and seeing 0, 1, 6 or 7 lands means you are the projected loser unless your opponent has 0, 1, 6 or 7 cards in their starting hand as well.

I completely disagree with this statement. This is true if both players are playing the same deck, perhaps. They aren't. Deck construction can nullify the disadvantages of mana-light or heavy hands. Better players tend to take this into consideration more when building their decks. If my hand is 6 land and a Merfolk Looter it isn't a great hand but it is far from "unfavored" depending on deck composition.

Likewise if my hand is 1 land but that 1 card is a Weathered Wayfarer and I'm on the draw, suddenly I'm favored. A lesser player might not recognize the value of those cards and play them. 

And yes, despite your skill, there are games that you will outright lose to mana issues even if you build and play perfectly. But everyone will suffer exactly the same number of these on average and over large samples, so there's no point in considering them. 



I have seen decks whose stength was avoiding variance. One with a minimum of 3 Merfolk Looters immediately comes to mind, but in most formats those decks will be the exception. Regarding the mana issues and muligans as I've defined them most decks will draft exactly 0 cards to influence those percentages one way or the other because that is the number of cards they could draft in the format. The best you can generally do is trade one type of mana issue for another by setting your land count higher or lower.

Also, please stop using the 'there are the same number of unwinnable games suffered on aberage by all players across a large sample so they cancel out' argument. I agree that an equal number of unwinnable games are encountered by each player, but it does not cancel out in terms of win percentages. As you start tacking on an equal number of wins and losses to a person's record, their record starts moving towards a 50% win rate. Which is exactly what I was trying to get at with this formula in the first place. I want to get rid of the arbitrary wins and losses tacked onto every player's record due to mana issues and muligans to find out what their win percentage would be in the absense of those tacked on wins/losses:

"With Magic, I could teach you to play today and promptly lose to you next week. Historically, the top players win 60-65% of their PT matches, and, though the number would obviously be bigger if they were playing at FNMs instead, it certainly wouldn’t approach 100%."
It's not a trivial question. Using that phrasing the question is "if a person won X% of those games played with [some condition] held, they would win Y% of all games if [that condition] and [that same condition for their opponent] were always true."



That is not at all apparent from the way you put it the first time. If that is what you are after, you can stop right away because X can not be used to predict Y at all. There is just no way to correlate the two.

Let's assume for the sake of argument that first of all you that can objectively define "mana issues" (which imho you can't, and so far you haven't) and second of all the impact of such "mana issues" on winning/losing can objectively be quantified for every game (which imho is also not possible). But let's assume for the sake of argument you can.

You need to answer the following questions before you can even begin to start your mythical formula.

Does every player always have the same percentage of mana issues? No. Everyone makes his deck differently, ao you might have 40% mana issues while I only have 10%.

Do mana issues always have the same amount of impact on win/loss chances? No. Even with the exact same opening hand, one game the remainder of your deck is vastly different from another.

Is every player's win percentage-in-the-absence-of-mana-issues equal? No. Every player has a different chance to make mistakes, come up with brilliant plays etc.

Yet you start out by measuring only YOUR win percentage by including only the impact of YOUR mana issues and ignoring those of your opponent. You also ignore all the relative strengths of your opponents, and the relative strengths of the decks you're matched against - as in, you're control, they're beat-down, versus you're control, they're combo (and then we're still assuming every deck is that easily pigeonholed).

Then you want to magically turn that lopsided measurement into a prediction of your win percentage that does include mana issues of your opponent (but again ignores every other factor that comes into it). Recall that not every player's win-percentage-in-the-absence-of-mana-issues is equal. So how are you going to pull that off? You want an absolute win percentage that includes a factor that is not absolute. And somehow you think that will actually yield results...
Free Speech
Free speech is the right to speak your mind without government censorship and without fear of extralegal retaliation like harassment or violence. That’s all! Free speech doesn’t include the right to speak your mind on any forum anywhere. The government may not prevent you from speaking, but private parties, like blog owners or corporations, aren’t required to let you use their property as your platform. Free speech doesn’t include the right to be believed or to be taken seriously. People may mock, ridicule or laugh at what you say, or they may reject it outright. Free speech doesn’t include the right to be listened to. People who don’t desire to hear your opinion can hang up on you, block you on social media, change the channel, close the browser tab. Free speech doesn’t give you the right to bombard people with harassing messages or otherwise force them to pay attention to you against their will. And free speech doesn’t include the right to suffer no consequences whatsoever for your expressed opinions.

The point, you've missed it again.



Another classic Bubba. Requires no thought, includes no facts, ironically makes no point. When you need to say nothing in 40 characters or less.



Well no offense, but you usually say nothing in 4000 chars or more. I know which one I prefer.
Free Speech
Free speech is the right to speak your mind without government censorship and without fear of extralegal retaliation like harassment or violence. That’s all! Free speech doesn’t include the right to speak your mind on any forum anywhere. The government may not prevent you from speaking, but private parties, like blog owners or corporations, aren’t required to let you use their property as your platform. Free speech doesn’t include the right to be believed or to be taken seriously. People may mock, ridicule or laugh at what you say, or they may reject it outright. Free speech doesn’t include the right to be listened to. People who don’t desire to hear your opinion can hang up on you, block you on social media, change the channel, close the browser tab. Free speech doesn’t give you the right to bombard people with harassing messages or otherwise force them to pay attention to you against their will. And free speech doesn’t include the right to suffer no consequences whatsoever for your expressed opinions.
It's not a trivial question. Using that phrasing the question is "if a person won X% of those games played with [some condition] held, they would win Y% of all games if [that condition] and [that same condition for their opponent] were always true."



That is not at all apparent from the way you put it the first time. If that is what you are after, you can stop right away because X can not be used to predict Y at all. There is just no way to correlate the two.

Let's assume for the sake of argument that first of all you that can objectively define "mana issues" (which imho you can't, and so far you haven't) and second of all the impact of such "mana issues" on winning/losing can objectively be quantified for every game (which imho is also not possible). But let's assume for the sake of argument you can.

You need to answer the following questions before you can even begin to start your mythical formula.

Does every player always have the same percentage of mana issues? No. Everyone makes his deck differently, ao you might have 40% mana issues while I only have 10%.

Do mana issues always have the same amount of impact on win/loss chances? No. Even with the exact same opening hand, one game the remainder of your deck is vastly different from another.

Is every player's win percentage-in-the-absence-of-mana-issues equal? No. Every player has a different chance to make mistakes, come up with brilliant plays etc.

Yet you start out by measuring only YOUR win percentage by including only the impact of YOUR mana issues and ignoring those of your opponent. You also ignore all the relative strengths of your opponents, and the relative strengths of the decks you're matched against - as in, you're control, they're beat-down, versus you're control, they're combo (and then we're still assuming every deck is that easily pigeonholed).

Then you want to magically turn that lopsided measurement into a prediction of your win percentage that does include mana issues of your opponent (but again ignores every other factor that comes into it). Recall that not every player's win-percentage-in-the-absence-of-mana-issues is equal. So how are you going to pull that off? You want an absolute win percentage that includes a factor that is not absolute. And somehow you think that will actually yield results...



I've defined having mana issues as missing one of your first 3 land drops, drawing more lands than spells in the first 17 cards (including starting hand), or drawing more lands that spells in the first x cards if the game ends before 17 cards were drawn. Reading is a fundemental skill, this information is in at least one other post.

For these calculations the average liklihood of mana issues and the average win rate under mana issues will be sufficient, because I am looking for the average win rate under a set of conditions, not the win rate against a specific deck or opponent. I'd also like to know this information in the general sense, how much does taking a muligan or having mana issues hurt an average player. How big an advantage would they need to have in the general matchup before they are still the favorite starting down one card.
I've defined having mana issues as missing one of your first 3 land drops, drawing more lands than spells in the first 17 cards (including starting hand), or drawing more lands that spells in the first x cards if the game ends before 17 cards were drawn. Reading is a fundemental skill, this information is in at least one other post.



Try that reading thing yourself before you stoop to insults. I'm not saying you never gave a definition, but that you cannot (and have not so far) OBJECTIVELY define 'mana issues'. In other words, that definition that you imply I ignored, is not objective. By the way, for future reference, this may come as a shock to you but you are not so perfect that everyone who disagrees with you must therefore either misunderstand you or have ignored some of your posts.

Anyway, your so called 'objective' definition is actually quite arbitrary. I know you tried to make it objective, but it just isn't. Think for example about these: "drawing only one color of mana in a two color deck for X turns", or "only drawing extremely high cost spells in the first Y turns". Hopefully these two make it clear to you that the very notion of 'mana issues' depends to a great extent on the exact deck you try to define it for. There are decks where drawing more land than spells in the first 17 cards is perfectly fine, and actually desirable. There are quite formidable decks out there that happily miss one or more land drops. You're free to consider those as exceptions, but don't pretend you're not arbitrarily doing so.

For these calculations the average liklihood of mana issues and the average win rate under mana issues will be sufficient, because I am looking for the average win rate under a set of conditions, not the win rate against a specific deck or opponent.



Yes, I know. You're basically trying REAL hard to ignore (possibly) relevant factors and hoping you can get away with it.

The fact that you're not interested in something doesn't mean it's automatically irrelevant. For example, say I'm looking for my average win rate when it rains. You know, and I know, that it is very unlikely that the weather has any bearing on my win rate. But it's an example of "looking for a win rate under specific conditions".

Now say I'm not so smart and am convinced that the weather DOES influence my win rate. So I'm going to define all sorts of experiments that start out assuming that the weather is a factor. It might even be true (perhaps rain distracts me because I have hydrophobia) but how likely am I to be able to do any useful measurements if I ignore obviously relevant factors such as skill, luck, deck type etc...? Especially if those things have much more influence and will probably drown out the effects of rain on my game?

Do you think that even in this case, if I play enough different opponents, decks etc. etc. it will all cancel out and the influence of the weather will become apparent automatically?

Unfortunately you cannot simply assume things will work out this way. Something else could outshine the thing you're focused on so much that only removing it from the equation will help.

What if I do the above and it turns out that I win 4 times as often when it rains... does this prove rain helpse me win, or does it mean I must have missed some factor?

For this example it's quite obvious, but what if I had taken some condition that might or might not be of influence? Where it isn't so cut and dry? how useful are your results then if you test things as above?

But that IS what you're basically doing. You're saying "yes, I know there might be other factors here that are relevant to a greater or lesser extent. Without going into why, I have decided that THIS factor is the only one that is relevant enough to be interesting to me. I'm not even going to try and figure out if anything else has more bearing, or if I can safely ignore those things, but I'm just going to do so and see what happens."
Free Speech
Free speech is the right to speak your mind without government censorship and without fear of extralegal retaliation like harassment or violence. That’s all! Free speech doesn’t include the right to speak your mind on any forum anywhere. The government may not prevent you from speaking, but private parties, like blog owners or corporations, aren’t required to let you use their property as your platform. Free speech doesn’t include the right to be believed or to be taken seriously. People may mock, ridicule or laugh at what you say, or they may reject it outright. Free speech doesn’t include the right to be listened to. People who don’t desire to hear your opinion can hang up on you, block you on social media, change the channel, close the browser tab. Free speech doesn’t give you the right to bombard people with harassing messages or otherwise force them to pay attention to you against their will. And free speech doesn’t include the right to suffer no consequences whatsoever for your expressed opinions.
I defined mana issues the way that I did because they are very easy to track in that manner and it is an objective criteria that everyone can follow. Certainly there are other types of mana issues, but I am looking solely at the "drew too few lands", "drew too many lands" conditions for the average limited deck. The average limited deck is handicap both by missing its first 3 land drops, as well as drawing more lands than spells in the first 17 cards (or over the course of the game)

If you really did find you won 4 times as often when it rained over a sufficently large sample size that would certainly be significant. Whether or not it was correlated to another more predictive condition. Based on my own notes I know that both mana issues and muligans are hugely significant, and the best single predictor of whether I will win a given game is that I don't hit them. If I keep my starting hand and don't hit mana issues I am winning upwards of 80% of those games. If I hit either mana issues or muligan my starting hand my chance of winning has now dropped to less than half that. And I suspect it's likely this way for everyone. Most people muligan 0, 1, 6 and 7 land hands, most people keep 2, 3 and 4 land hands, and most people play around 17 lands in a 40 card deck. So the probabilities for muliganing their starting hands and the chances that they hit mana issues for each hand will be the same, or at least roughly the same as mine.

This is primarily what I'm trying to get at with my formula, but I would be satisfied with experical results as well. I would like to know the percentage of games whose outcome was determined by mana issues and muligans and how game win rates would change in the absence of those factors. One related set of statistics that I would like to know, which you should be readily available, is the percentage of games a player keeping 7 cards wins vs a player keeping 6 cards, as well as the percentages for 7 vs 5 and 6 vs 5. I know they will all be over 50%, and the 7v5 is likely 90% or higher, but I would like to know the exact values.
But you still just don't get it. I can artifically impact whether my "win percentage if I don't mulligan" - by too aggressively mulliganing any hands that aren't really, really good. If your win percentage when you do not mulligan is very high, this could very well be nothing but an indicator that you're really, really bad at choosing when to mulligan - specifically that you do it many times when you shouldn't. 

I'm not saying that's the case with you personally, but it is certainly possible. You can't measure "win rate of one player keeping 7" vs "win rate of another player keeping 7" because they wouldn't keep the same 7s and you have no reason to believe they would! 
But you still just don't get it. I can artifically impact whether my "win percentage if I don't mulligan" - by too aggressively mulliganing any hands that aren't really, really good. If your win percentage when you do not mulligan is very high, this could very well be nothing but an indicator that you're really, really bad at choosing when to mulligan - specifically that you do it many times when you shouldn't. 

I'm not saying that's the case with you personally, but it is certainly possible. You can't measure "win rate of one player keeping 7" vs "win rate of another player keeping 7" because they wouldn't keep the same 7s and you have no reason to believe they would! 



Again, we are looking at the results of games for people playing under current tournament rules, and then removing those where either person ran into mana issues, or either person was forced to muligan, or both. Ostensibly both players are playing to win games under the standard set of rules, and are making muliganing decisions accordingly. They aren't trying to manipulate their winning percentage under one set of conditions at the expense of another. No one is trying to artificially impact their results.

Also, since I feel it needs to be stated explicitly - I believe that the majority of hands that are muliganed are 'consensus muligans'. That is, I believe the majority of muligans occur because a player has drawn a starting hand of either 0, 1, 6, or 7 lands and has elected to ship it and that the majority of players would agree with that decision.

Or to put it another way, if you took 100 random starting hands from 100 different limited decks, and asked 20 different players with online limited rankings of at least, say 1800, whether they would muligan or keep each starting hand (based on the hand itself and the deck it was being played in). I would expect to see overwhelming consensus among the 20 participants. So much so that for the majority of starting hands I would expect all 20 participants to reach the same conclusion.
I'll give you an example. After the first game againts an opponent you sideboard a one of card that your opponent cannot win againts. You draw your seven cards. 6 lands plus the sideboard card. Do you mulligan? Isn't it correct to mulligan since you had 6 lands? After you win are you considered that you had mana issue but still won?
That is an interesting situation. I've been in a similar one with a 5 land hand that included Stuffy Doll, because I knew my opponent had no good answers for it, but also knew that it wasn't going to come down until turn 5 and if I was near death's door at that point it wasn't going to stop my opponent from attacking like it did game 1.

It's hard to think of a single card that turns a six land hand into a keeper, but if I did it would likely be considered a mana flood win if I did win. Or alternatively a standard win because by the time I got to 17 drawn cards the mana flood status may have been removed from the game. That's actually the reason I modified my mana flood criteria to 'mana flood in the first 17 cards or at the conclusion of the game' because when I had it at only 'mana flood at the conclusion of the game' I had virtually no mana flood wins. The reason is that in most mana flood situations I either hung on long enough to get out of the flood and won, or remained flooded and lost because of it. So there were virtually no mana flood wins recorded only mana flood losses and standard wins.
..."window.parent.tinyMCE.get('post_content').onLoad.dispatch();" contenteditable="true" />It's hard to think of a single card that turns a six land hand into a keeper



Assuming one of the lands is a fetch land, I think Brainstorm might qualify as a keeper in a 6-land hand.  Depends on the deck.
Would you keep a hand with 6 Plains and a CoP: Black vs a mono-black deck? Not trying to be sarcastic. I think I would, but I don't consider myself smart enough to be confident in doing so.
X=((PWAMI - PLWMI)/2)/NOGP


PlayerWinsAbsentManaIssues, PlayerLosesWithManaIssues, NumberOfGamesPlayed, 1vs1 that is why the division by two.

In all seriousness though I doubt you can really make up a formula for that.  There are too many variables you can't account for such as deck sizes, deck strength level, each player's level of experience, each player's experience with that deck, did they lose to other issues such as timing out?

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.

If mana issues were taken out then the oppenent would not have had them either. ;)



*Perhaps this would help.  Build two Identicle "stalking stones" type land decks so Mana should not be an issue as all cards are lands.  Play them against themselves 100 times.

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