Would You Guys Keep This Hand?

[Loggiu]

yes it's very defensive and win with a combo, controlling opponents creatures and with some equip...when the tax end you control or stop the strongest creatures

[Red_Wyrm]

This thread is an absolute mess. It seems like there are two conversations going on at once. I'll see if I can break this down.

But first, there is something we need to get out of the way. When choosing a starting hand, you don't get to see your next three draws. So to settle the argument on whether to keep a hand or not, the decision needs to be independent of what you would have drawn.

Now to break this down.
Scenario 1: Red_Wyrm
Commander: Thraximundar

• Command Tower
• Terramorphic Expanse
• Blood Crypt
• Omniscience
• Nicol Bolas, Planeswalker
• Prince of Thralls
• Grave Titan

Here's my logic for not keeping this hand. With no early turn plays (no mana ramp or card advantage) your opponents will have a huge advantage over you. Even if you can get to the 6 mana to start casting stuff, it's too little, too late. You are starting the game in top-deck mode. Not good.

By looking at your list for Thraximundar (http://deck.tk/7uno54W6) it seems like the goal is to make sure that your opponents don't have any creatures to attack with, and then you win with a big bomb... In that order. If you keep this hand, you're starting with the bomb, and then struggling to find a way to control your opponents' board state. Your first priority should be to set up your boardstate, so you can ready to begin control phase (AKA, start the game with mana ramp and draw engines).
Scenario 2: Loggiu
Commander: Grand Arbiter Augustin IV

• Island
• Island
• Plains
• Patron Wizard
• Godhead of Awe
• Path to Exile
• Jace Beleren

So this hand I would actually keep. You may not have any mana ramp, but you have responses to your opponents (Path to Exile, Patron Wizard) and card advantage (Jace Beleren). I couldn't find your list, but I'm assuming that the goal is to gradually stax your opponents until you can build a combo. This works then. You have enough to be able to stop your opponents in the early game, you can build into Augustin, and then you still have a draw source so you can continue to lay down the stax into the mid and late game.
Now to talk about my favorite thing Deckstats has to offer: the stats!

I would like to see the stats that The Command Zone has (I refuse to dig through YouTube videos looking for it). What was the value of the correlation coefficient (>0.70 is a fairly good correlation), what was their sample size, what were their error margins, and how did they measure which decks did better?

Lands alone are also a poor measurement. Mana sources would be better. I tend to have less lands then most other players (I don't use Cultivate or Kodama's Reach) by my win ratio is abnormally high. The really important factors are what the power level of the decks are, and how skilled of a player you are.

Okay so it requires a while because it is a two part video, both being around an hour or loner as their videos normally are. They go over sample size etc at the beginning, but they don't exactly give all of the data they get. By this I mean if they ran an ANOVA, T-test Chi-Square (Absolutely no reason to run this one with this type of data) or similar, which I assume they did as they hired a statistician to analyze the data, they didn't give us the correlation coefficient, (Which I've never heard of) or a P value to describe if the results were statistically significant or insignificant. The P value is, if I remember stats class correctly, the probability that you will get the same results from a completely random sample. And I think like <.005 is insignificant, and greater than that is significant. They just present the final data. For example: They state having white in your deck leads to your chance to win decreasing by 1% (assuming you start with a 25% chance to win in a 4 player game) and playing red increases it by 3%, and blue green and black were around 8% I think. Hopefully I described the video enough for you to decide if it is worth it to watch, and hopefully I didn't bore you with stats. That class was were I caught up on sleep. Who is going to hold a stats class at 7 in the AM??

So here is the link to part 1:  https://www.youtube.com/watch?v=Iwdb_kPCwNU

It is not just about Sol ring, but they cover that topic.

This is the second video:  https://www.youtube.com/watch?v=ttGjuNXWxpY

Both videos include a lot of DJ and Josh hypothesizing why the data is the way it is. It would probably go quicker if it was so conversationally, but I am digressing, as I often do.

Oh and they cover the price of the decks and their win% too.

[WWolfe]

See, that's another point I thought of Morgantor (and made in the post that did indeed disappear).

While it makes sense that the person with the most resources would win, only counting lands is not a true measurement of available resources. I may only have 6 lands on t8 but I may also have 2 mana rocks, a mana dork, or a land like Cradle or Coffers that taps for more than 1 mana and have more mana at my disposal than someone who has hit a land drop every turn but has little to no other way of making additional mana.

Also, did they give the same weight to a player who went out on t8 who had 6 lands in play as they did the person who won that game on t17 with 13 lands in play? These give a similar % of land drops hit (75 versus 76) but IMO should be weighted differently due to circumstances that happened with in the game that led to the first player going out less than halfway through the game.

[Red_Wyrm]

Also, did they give the same weight to a player who went out on t8 who had 6 lands in play as they did the person who won that game on t17 with 13 lands in play? These give a similar % of land drops hit (75 versus 76) but IMO should be weighted differently due to circumstances that happened with in the game that led to the first player going out less than halfway through the game.

Okay so from my understanding, they hired some data analysis with little-no experience with MTG and told them to rewatch a million EDH games from The Command Zone, Star City Games, and a bunch of other places that record EDH games and look for these certain things that they were curious about. They don't mention mana rocks, and clearly state that the player with the most lands in play has most often won according to their data. But they do also make it apparent that they it is about how much mana you have because more mana=more powerful spells. I assume, much like you guys have guessed, that it doesn't necessarily matter where the mana comes from, so long as it is from something that stays on the table for a while because counting a sol ring that is out for 2 rounds doesn't make much of an impact over the course of a commander game.

So Wwolfe, I cannot answer your question, I do apologize. I would suspect, since they made no mention to the contrary, that they compared everyone's lands on turn x where x is the turn the game ended. So let's say it ends on turn 10. Johnny died on turn 5 with 5 lands out, so on turn 10, he played a total of 5 lands, and I think that is how they did it. It seems to be the easiest. If they did it differently, I feel that is something they would've mentioned.

[Morganator 2.0]

Motherfu-

Why are these videos so long?

So I'll (begrudgingly) watch them, but I'll get a couple things out of the way first.

The correlation coefficient is a measure of how strongly related two things are. It ranges from -1.00 (strong negative correlation) to +1.00 (Strong positive), and 0.00 is no correlation. For example, there is a strong positive correlation between firmicutes (a type of bacteria) in the gut track and obesity, so people who were obese tend to have more firmicutes than someone who is not.

Here's the issue; correlation is not causation. Are firmicutes causing these people to be obese, or does being obese cause you to have more firmicutes? Or is there some third factor (like sugar intake) that is the cause of both? So the correlation measurement is not so good at directionality.

There's also another issue. Lands is the first variable, but what is the second? Are they measuring the turn that the deck won on, or just the win rate of the deck? The other issue is that game length would need to be taken into account, because if not, then a deck winning on turn 4 with 4 lands has a different correlation than a deck winning turn 10 with 10 lands.

So I would have measured this as mana sources per turn versus win rate. This would take mana ramp into account.
Null hypothesis: There is no relation between the win rates of decks and the number of mana sources in a game.
Positive correlation: Decks with higher win rates had more mana sources in a game.
Negative correlation: Decks with higher win rates had less mana sources in a game.

So now I'll watch the videos and see what the result is.

Bringing this back to "Should you keep a hand", I generally like to keep a hand with 3 mana sources, or 2 mana sources and a way of getting a third.

[Red_Wyrm]

Motherfu-

Why are these videos so long?

So I'll (begrudgingly) watch them, but I'll get a couple things out of the way first.

The correlation coefficient is a measure of how strongly related two things are. It ranges from -1.00 (strong negative correlation) to +1.00 (Strong positive), and 0.00 is no correlation. For example, there is a strong positive correlation between firmicutes (a type of bacteria) in the gut track and obesity, so people who were obese tend to have more firmicutes than someone who is not.

Here's the issue; correlation is not causation. Are firmicutes causing these people to be obese, or does being obese cause you to have more firmicutes? Or is there some third factor (like sugar intake) that is the cause of both? So the correlation measurement is not so good at directionality.

There's also another issue. Lands is the first variable, but what is the second? Are they measuring the turn that the deck won on, or just the win rate of the deck? The other issue is that game length would need to be taken into account, because if not, then a deck winning on turn 4 with 4 lands has a different correlation than a deck winning turn 10 with 10 lands.

So I would have measured this as mana sources per turn versus win rate. This would take mana ramp into account.
Null hypothesis: There is no relation between the win rates of decks and the number of mana sources in a game.
Positive correlation: Decks with higher win rates had more mana sources in a game.
Negative correlation: Decks with higher win rates had less mana sources in a game.

So now I'll watch the videos and see what the result is.

Bringing this back to "Should you keep a hand", I generally like to keep a hand with 3 mana sources, or 2 mana sources and a way of getting a third.

Thank you, Morgantor. I thought I was done with stats class, but no. The more you post, the more I wonder what the heck you do in your life. Not just anyone knows stats. And who the heck knows about firmicutes?

Kind of related to the correlation vs causation thing. You know there is a correlation to the amount of chocolate intake a country has and the amount of noble prize winners they produce?

Best of luck enduring the 3 hours of video watching.

You mention keeping 3 mana sources, but that would contradict your statement about not keeping my original hand of 3 mana sources, but I assume this is because of the high CMC cards I had. As many have stated, i was top decking aside from my land drops per turn.

[Morganator 2.0]

As I'm watching the videos, I am writing this post. Keep in mind that I already despise most YouTubers and how YouTube styles itself. I'm not happy about watching for 3 hours, so expect this to be rage-induced.

Exactly How Good is Sol Ring? Commander Gameplay STATS (pt1)

1:00-1:30: Okay, so we got a group of statisticians that don't play Magic, to explain data to Magic players that don't understand stats. We are not off to a good start.
2:00: Gonna just skip the sponsors.
4:35: Sample size n=313. A very good number.
5:10-6:50: Data was taken from YouTubers; Game Knights n~22, MTGMuddstah, Commader Clash, and Commander Versus. From what I gather, cEDH is not taken into account, but the decks used are well tuned.
7:10: "You can go watch the games and find out the same stats". Piss on that.
7:25: "Full data set will be released at the end of the second video. Cool. Skipping ahead to the data set.

https://public.tableau.com/profile/andrew.greene#!/vizhome/CommanderStatistics/Title

So this data set is a mess, and it will take me a while to analyse it myself. So while I'm doing this, are there any other things you guys want me to check for? I've listed the relevant things in the data set below.

Commander name l

AVG CMC of Deck l

Deck cost (USD) l

Lands in deck l

Lands during game l

Who won? l

Color identity

[Morganator 2.0]

Do you know what my favorite thing about Deckstats is? The stats.

Do you know what my most hated thing about The Command Zone is? Their stats.

First off, their data set is super incomplete. There are some instances where the number of lands was just left blank. This doesn't mean that there was no lands (I checked a couple of the videos), it just wasn't recorded. There were two games where mass land destruction was involved (I included those games). I also excluded games where there was no winner, because in all cases we are comparing who won.

But this is still an amazing data set to work with, and I applaud everyone who put this together. It's a big data set, so short of cEDH games, the sample is a good representation of the population.

Question 1: Does having more lands in a game cause you to win?
Null Hypothesis: There is no relation between the number of lands you play and if you won (-0.7>Correlation coefficient<0.7)
Alternate Hypothesis 1: Decks with more lands in play are more likely to win the game (Correlation coefficient>0.7)
Alternate Hypothesis 2: Decks with less lands in play are more likely to win the game (Correlation coefficient<-0.7)

There is an expression among statisticians; If you torture the data enough, you can make it talk. Which is why you want to avoid torturing data, lest you show that green jellybeans cause acne.

Believe me, I tortured this data for a long time. I could not get it to say that the players with more lands in play were more likely to win.

First I just ran the correlation of "Mana producing Lands at end of the Game" versus "Player Won?". So this is comparing across all games (n=304) if the player who won had the most lands. Correlation coefficient= 0.204, so there is no correlation between number of lands in play and who won. But then I did some things I wasn't supposed to (I tortured the data). I started by averaging the number of lands within games, to make a proxy for game length. So if a game had players with 15, 19, 14, and 16 lands, the average was 16, so the game was about 16 turns long. This is unlikely to be the actual game length (keep in mind I'm not supposed to be doing this), but it's a proxy. I then ran the correlation again, this time controlling for game length, to see if players ahead of the mana curve did better. Correlation coefficient= 0.275, so again, no correlation. Finally (really pushing it this time) I did within game correlation. So within each game, did the winning player have the most lands. Correlation coefficient= 0.218, once more no correlation!

Conclusion: I failed to reject the null hypothesis. I can say with confidence that there is no relation between the number of lands you play and if you win.
Interpretation: I think the problem with this analysis is that it only looked at lands. As I said before, mana sources would give a different result. Also, there are a lot of cEDH decks (namely Flash Hulk and Godo) that can easily win with only two lands, but with that early a win, everyone would have 2 lands.
Question 2: Does having Sol Ring or Mana Crypt within your first 3 turns cause you to win more often?
Null Hypothesis: Sol Ring and/or Mana Crypt in your first 3 turns does not have an effect on you winning (-0.7>Correlation coefficient<0.7).
Alternative 1: Players with Sol Ring and/or Mana Crypt in their first 3 turns are more likely to win (Correlation coefficient>0.7).
Alternative 2: Players with Sol Ring and/or Mana Crypt in their first 3 turns are less likely to win (Correlation coefficient<-0.7).

So I should get this out of the way; this null hypothesis sucks. I just can't think of a better way to phrase it. We know that Sol Ring improves the power of your deck, that's why everyone uses it. So this is more measuring the strength of having this early game fast mana.

Running the simple correlation of "If there was a Sol Ring/Mana Crypt" versus "Did that player win?" gives a correlation coefficient of -0.019, so no correlation. But because Sol Ring is such a common card, I frequently saw games where 3 players all had Sol Ring/Mana Crypt, but only one person can win. So this time around, I think it's fair to transform the data. Next I compare "Did the player that won have a Mana Crypt/Sol Ring?" and this is something for a Chi^2 test to handle. A Chi^2 test compares what was expected due to chance (the null hypothesis) compared to what actually happened. The math bit is a little complicated for me to explain, but if you're interested, this was the result.

		Win	Loss	Total
Had a ring	Actual	25	87	112
	Expected	27.91	84.09
No Ring	Actual	278	826	1104
	Expected	275.09	828.91
Total		303	913	1216

So instead of me describing how I got to the p-value (0.505 by the way, so not significant). We can just look at the numbers. All the numbers we expect to get are very close to what we actually got.

Conclusion: I failed to reject the null hypothesis. There is no relation between you winning and if you played a Sol Ring in the first 3 turns.
Interpretation: I think this question was asked the wrong way. What it actually should have been is "Do decks with Sol Ring win more often then those without?" The issue is that budget would have an effect (most of the time people don't use Sol Ring because they just don't have one).
Question 3: Which color is the strongest?

This is the point where I really get mad at the way this data set is organised. I'll be back in a few hours to finish this post off.

[Loggiu]

it's normal...a deck that have a sol ring on 100 cards, it's insignificant...! need to test if a deck with a lot of ramps win instead

[robort]

Morgantor, kudos to you man for going through all that and such. I agree with everyone that the Command Zone were just stats but based apon what? I am going to say incomplete data. Out of the 300+ games there was a winner and a certain percentage of the winners had more lands then the other players. We don't know the other variables which were already pointed out from mana rocks/dorks were also used. Was a combo done and it was over? Did the person who won who had the most lands also have someone else with the same amount of lands?? Did the person with the most lands tutor for his/her lands? Did any of the opponents the were playing against miss any land drops? Were the lands able to produce more than 1 mana? Again to me just to many missed variables to conclude there is indeed that having more lands than your opponents increases your wins

[WWolfe]

Very good read Morgantor! Many props for taking the time to do that.

[Morganator 2.0]

So couple things.

The statistics part has gotten off topic from "should you keep this hand". I meant to make this a new topic already, but I messed up. So I'm going to that tonight, along with the analysis of the best color.

Which gets to my next problem: I don't know how to analysis this.

I'm not incapable, I just don't know how I should go about it. Should I compare the total win rates of each color (grouping together all red decks, all white decks, etc.) Or should I compare each color pair as it's own group (Boros versus Izzet vs mono-black etc.)?

How do you think I should do this?

[Soren841]

I think we should go with what everyone knows.. blue, green, black, red, white  more or less in that order

[WWolfe]

I'd go with color pairings but that opens up 31 potential pairings to track (32 if you include colorless).

[crimsonking]

Hi all,
I hope not to jump into this conversation too late.
The short answer to your question is: "No, I won't keep that hand."
A more articulated answer would be: "It depends..."
It depends on what you're playing. You've already said you're playing Thraximundar, this gives some information about your deck but not all of it.
Since you're not playing green, I suppose you don't have a lot of ramp apart from some mana rock, and from the cards you named I could infer your mana curve is quite high, but these are just suppositions.
For instance, you could be heavy on cheap reanimation spells and be interested in discarding Prince of Thralls to later cast Animate Dead on it and start some recursion chain or whatever.
While the number of lands is a good rule of thumb, and I would normally keep a 3-lands hand, a more accurate criterion would be the amount of plays that hand is actually capable of.
For instance, I will surely keep a hand with only 1 Plains and a Land Tax, or a 2-lands hand with Sensei's Divining Top, no matter what.
Moreover, if my deck is heavy on lands, I would be much eager to mulligan a 2-lands hand because I'm likely to see more lands than that.
Conversely, if my mana base is tight, I would keep even if I'm on the fences, because I could easily draw a 1-land hand instead.