This argument on EV comes down to 2 key issues. Your real win percentage and how "long run" your finances can take you.
#1 Win percentage
At 50-50 you can make more packs playing more 8-4s in the long run.
However, most players are considerably less than 50-50 against the people who know the format inside out and those people expect to go 2-0 and split in the finals. Be honest here.
#2 Long run
Even IF you are 50-50, losing 3 packs + 2 tix at once is tough. If you are not lucky enough to make that one lucky finals every X drafts, you will find yourself dwindled down on resources. If you have a very large pool of resources available, then you really should play 8-4s if you think that you are 50-50. However, most people are happy enough opening $ cards + getting 2 to 3 packs and going into another draft because they can afford the loss of a few tix value per draft instead of losing 14 tix worth at once.
It's actually about stability over risk. In real life, high risk ventures give you higher expected returns in the long run. It's the same thing here.
If going 2 wins = 3 packs, I would gladly take that over 3 wins = 3 packs simply because I think I can make 2 wins and get the 3 packs and I hope not to lose round 1.
If you really cared about purely EV, you would have played constructed instead because drafting in the long run is a $ losing venture.
Yeah, the problem is that the win ratio doesn't hold up in 8-4s. And compared to 4322, my average pack wins is just higher than 2.48 anyways.
On top of that, I just don't have enough capital to handle the swings of 8-4s.
Another interesting tidbit is that I'm like 78% in match one, but only 71% in match 2. I can't remember the match 3 numbers, since I'm at my laptop instead of my desktop, but its around 75% too, but that changes things a lot. I figure its because I face more good decks and players round 2, but in round three, I guess I have a good deck that's passed two rounds, so I win more often.
The problem is that math doesn't account for "Wife says we gotta go..." or "Good players think they need to avoid swiss" or "8-4s are more intimidating" or any of a million other factors.
I love the set-up of this post, it was very easy to follow.
I think for MTGO UB is the better deck to play during the dailies due to UW, Valakut and Goblin being player in heavy numbers (though its much more unforgiving to missplays - which based on our hours of playing happen often enough)
Good luck in grinding for Sept's MOCS I'll be doing the same aimming for 3 byes.
While it sucks I'll be skipping monday's MOCS this month since it goes into my work hours right now money is more important then hobby (which is a shame since I have 1 bye).
Better then a spreadsheet is spreadsheet AND math ^^
If we model it using you winning each round with 75% chance, this is what you get in 4-3-2-2 and 8-4:
Probabilities:
1/4 for losing in round 1
3/16 for winning round 1 and losing in round 2
9/64 for winning round 1 and 2 and losing the final
27/64 for winning all rounds
Which gives 2,48 packs for 4-3-2-2 and 3,94 packs for 8-4 - note that the later is quite a bit more than 3 and hence you could expect to be infinite if you played 8-4 exclusively and the model took everything into account...
If we use the model in the article instead, with you beating 3/4 of all players and losing to 1/4 (note: winning 75% is better than that).
Probabilities:
1/4 for losing in round 1
21/64 for winning round 1 and losing in round 2
4725/16384 for winning round 1 and 2 and losing the final
2187/16384 for winning all rounds
Which gives 2,06 packs for 4-3-2-2, 2,22 packs for 8-4 or 2,53 packs if you split the final in 8-4.
I know the people have decided that music is poor taste for Magic, but its much easier for someone to just mute the video then to for other to go without expereince new ear....ehhh I won't finish that.
Looking forward to the draft video mates, if you manage to also record your picks and choices that would great.
You should talk more in your videos. It sounded like you were trying to be quiet like the rest of the family was asleep or something, but we need some commentary!
I seriously doubt Shocklands will plummet in the short term. There SHOULD be plenty of warning if they start to. Pacts...well they are probably good to stay up for a while anyway (past PT PHILLY.)
It is super-irritating that the payout is not 5-3-2-2, but the "WAHHH 8-4 and SWISS ARE STRICTLY SUPERIOR RETARDS" people are pretty dumb; most especially the guys who studies stats for a living and wants to ignore basic facts.
If I feel like I can win r1 a high % of the time (oh hey I just got two packs not one sucky swiss) and r2 a decent amount fo the time (oh hey, 3 packs for winning two rounds, suck it swiss) but not always final/win the draft, my best EV is 4-3-2-2 even if the AVERAGE EV sucks in those. 8-4 is fine if you're finalling a lot, but not really otherwise. Swiss is fine for uh... getting 12 packs back into the system? Otherwise, not great. 4-3-2-2, while a dumb payout (EVERY PLAYER GETS 1/8 less of a pack on average that's a whole pack you missed on average after 8 drafts!1111) is fine for someone who feels like R2 is an easy target and R3 is doable.
@ people talking about reprints. I mean, I hope so in some capacity, but Wizards has demonstrated throughout their history that they are basically unwilling to print cards based on secondary market and availability issues. Look at Legacy's big offenders. Sure the Reserve List stops reprints of dual lands, but what about cards NOT on the Reserve List. Stuff like Force of Will or Wasteland. Where are those reprints? What about when Tarmogoyf was expensive previously (before tanking after rotating out of Ex)? Why didn't they reprint Ravnica duals in some other set since? Can someone point to an instance where Wizards printed cards to make them more accessible because of market values? If not, I'm not sure where this faith is coming from.
Look, they made a bug hupplah over printing ONE Chain Lightning foil in a $30 (iirc?) premium deck. That card could and should have been in M10 or M11 or M12. It's not broken power wise, so why not just reprint the cursed thing? Simply put, they just aren't interested in reprints on the scale on which most people seem to think the Modern stuff will appear.
Modern events are on the event calendar - the are just listed on the Premier event calendar with TNMO for some reason. I don't know why the put the modern daily events on the premier event calendar, but they did.
It would be really nice to see you update this article with a correction to your math and the modern events added.
Except that your math is wrong. Please see the comment by Reaper9889, which has the correct math.
According to your formula 4-3-2-2 goes:
(2 *.5) + (3 * .125) + (4 *0.0078) = 1.4 packs
That means that you win some packs 1/2 + 1/8 + 1/128 of the time, which is substantially more than half. As you have defined yourself as the 'average' player, it is easy to see that this cannot be true. What happened was that you double-counted your wins. You said that you will win game 1 half of the time, so you put 2*(1/2) in your formula. The problem here is that the 1/8 of the time you win again is PART of that 1/2 of the time, you can't just add them together.
The correct formula is:
2 * (3/8) + 3 * (15/128) + 4 * (1/128) = 1.13.
Using correct formulas you will see that the EVs come out as follows:
Swiss: 1.5
4-3-2-2: 1.13
8-4: .53
I do agree that a simulation will reproduce numbers - just not the numbers you present in the article.
Note also that if you are worse than average [which, lets be honest, half of us are, by definition] the payout becomes even more tilted. Swiss declines the least quickly, and 8-4s quickly become entirely unprofitable. If you suspect that you are not in the top 40% or so, swiss is far and away the best choice from an EV perspective.
I think the reason this is controversial is the 1 pack difference between the 8-4 and swiss drafts and the 4322 drafts. Group A believes the discrepancy is a good reason to avoid 4322 in favor of other forms of draft because WOTC is getting away with giving out 1 less pack. They are insistent that we boycott the 4322s and I think I more or less agree with this in principle. Though in fact I don't have a stake because the last cycle I loved drafting was Alara Block before the mixed packs.
Group B does not care about the discrepancy and just wants to play fast and get the heck out. I see their point even if it does not ever have any impact on my choices. This is similar to the argument about whether players should avoid the pre-release events. Some will because they want to see better value for their money and others won't because they just want to have fun and money is no real object.
The EV question is something Hamtastic was fascinated with and I think it has for many magic players an allure because of the math element. I am decent with calculation but don't particularly care about math when it comes to figuring out odds and what not. But I know a lot of players who really get a kick out of it. And arguing about this kind of thing takes it to the next level.
The main target audience for WotC are the casual players. Swiss are meant for them. It only became an issue when some players started to flame the 1 pack prize difference.
Swiss: For players who are trying to learn how to draft, maximize playtime from the packs, learn how the set works. Sometimes sharks appear for easy QP.
4-3-2-2: For semi competitive players and above. Most online life tilting experience starts from here.
8-4: I want your life. Simple.
In my humble opinion it is not even an issue to spark a heated debate. To each his own preference, choose the type of draft that suits them best and work our way up the ladder. No need to argue which has the highest EV as playing limited is definitely negative EV. The percentages brought up are just an excuse to so call justify claims of which is better but when all are negative EV, what's the point? It is the same as comparing who has the worse job but they still stick to it.
As said by oraymw, he just wants to play. When his objective is met the rest will fall in place as his skill rewards him with cheaper drafts to continue playing. He is still a paying player but the bonus of forking out only 1/5 of the cost more than compensates EV of drafts. How much a player can afford determines how much fun he can have.
Pete stated the math as an oversimplification sample. If it evoked negative reaction, please be kind enough to understand it is not that easy to write an article every week with other responsibilities and we will all overlook on a certain aspect. All we need is a little empathy to make the world a better place.
I suppose that if you are really grinding out 15 or more drafts a week, then this is really going to matter to you. But since I'm the kind of person that sets aside enough time to do one draft twice per week. If I play in a swiss, I guarantee that I will be able to play my three rounds. Since my goal is to play Magic, this works out well for me. If I were to do a 4322, I might lose in the first round. After that, I don't have enough time to do another draft, so I'm just done. The difference is the cost in limited matches played, which is what I'm trying to maximize.
re: Prize Payouts
I think too many people operate under the assumption that they are going to be able to "go infinite" in limited. That is absurd. I have a 75% win ratio in Limited matches on Magic Online, and I haven't gone infinite. Maybe there are mythical people who do "go infinite," but I can tell you that they aren't achieving this status in 4322s.
re: Math
Better than math is for each player to keep a spreadsheet of their results. That is what I do, which is how I've found that I have just barely short of a 75% win ratio. I also keep track of my wins and losses, and how many prizes I get. On top of that, I track how many tix I gain from selling draft spoils. I've found that on average, a draft costs me 2.4 tix. In other words, I essentially get each pack for $0.80. Maybe I'm not infinite, but I can sure afford 5 dollars a week to draft essentially as much as I want. And $0.80 per pack is a heck of a lot better than paying retail.
Clearly something is wrong with prize payouts for middle of the road drafters (myself included), otherwise there wouldn't be this much of a discussion about EV.
On the other hand, being someone who consistently wins the first round only to lose in the second round, I understand the point Mr. Jahn is trying to make here as well.
Swiss is random. A lot of those queues seem to fire with people just trying to rare draft and get value from prize packs, perhaps recouping more packs if they are get "lucky" enough to get good cards both for sale and for draft quality. I occasionally do Swiss, but only when I feel like I have enough time to do all three rounds.
You get the same payout in Swiss if you win two rounds that you would by winning one round of a 4-3-2-2, also. If all you expect to win is one round, based on whatever assessments you make of yourself as a player, then I would use the "time is money" argument and say that you actually net more by going into 4-3-2-2s, even if the EV isn't there.
I am no statistician (although I am going to take some basic statistics classes soon), but isn't EV calculated in a vacuum anyway? Or does everyone just always assume a "null hypothesis" method when calculating this?
I may not seem like I can "count to 12", but I feel that I have gotten more packs back by playing 4-3-2-2s at this point based on where my overall skills are.
Maybe someday I will shark the 8-4s, but until I get a real grasp of drafting in general, it is all Swiss or 4-3-2-2 for me.
If someone were to petition for 5-3-2-2s, I would get behind that cause. I think that is a better approach to this whole situation. Wizards does listen to its customer base if they scream loud enough (See Jace 2/SFM bans or "Modern" as a format for evidence that substantiates my claim).
My sample player in this example has a rating exactly in the middle of the spread. Exactly half the players playing in drafts have higher ratings, and exactly half have lower ratings.
Then let's assume that rating do equate to skill. We can use the six month average rating for each player, to cut down on variance if you prefer.
Now let's build some sort of formula that estimates the likelyhood of winning based on the difference in rating. For example, the chance of winning is 50/50 for equal ratings. For a lower rated player, the change of winning is 50+ (half of the difference in ratings). Do the same thing for the odd of winning verses higher rated players - the chance of winning is 50 minus half the difference in rating. Or use the log of the difference, if you want a curve that tails off. Whatever.
You can also add random factor to represent strength of cards opened - add or subtract a random percentage to represent opening bombs by one player or the other. Just keep it equal.
Now run 500 drafts.
At that point, the percentages and random factors even out, and our sample player will end up, on average, beating the lower ranked players, and losing to the higher ranked players. Or, put another way, our player loses to better players and wins against worse players.
For any simgle game, the random factors matter. However, in calculating long term outcomes over a large number of matches, you have to calculate based only on the factors that stay relatively consistent (or change at a predictable and consistent rate) like player skill.
My article was excessively long even without the more complex math, so i simplified. I should know better.
I'll try explaing this in another way. Let's simplfy the game enough to model. We'll use the d20 roll-playing system. Each player has a skill level, and a game consists of both players rolling a d20 and adding their skill ratings. Further, let's assume players have skill ratings of 3, 6, 9, 12 or 15. My middle-of-the-road player in the above example has a skill of 9. Put him in a draft and choose the skill level of players in each of the other seven slots randomly. Play it out, with each match being best 2 of 3 rolls. Now write some code to do this and run the model 5,000 times. The payout per match will be really close to my estimate.
Good to see that your math supports what I have been saying for years.
Only people who cannot add to 12 would do a 4322 instead of a swiss or 84, and now with math to back it up! Defending 4322 because it takes less time than swiss is fully retarded. If you do not have time to do a draft, then DONT DO ONE!
Modern- The prices are ridiculous due to the hype. This format is the same as extended before they neutered ext, and nobody played it then except for tourneys. Modern is dominated by combo with the average game lasting 5 turns or less. Not a recipe for fun.
There is no magical difference between the first and second rounds -- half the time you will be paired in R1 against a deck of identical quality to the average deck you face in R2. I find it naive that people say they can always get out of the first round of 4322. After all, you have a 1/8 shot of playing the eventual winner in round 1 (and of course a 1/8 shot of being the winner).
I agree that swiss takes forever though, which is why 8-4s are king.
I also strongly object to your methodology. Check out the pro drafts online at other sites. They lose plenty of matches, sometimes due to luck, sometimes due to being outplayed. You say that it doesn't matter what we assume the win% is of a worse player versus a better player, that the same result emerges, but this is demonstrably false: if better players only won 50.000000001% of the time versus worse, the average payout from an 8-4 for anyone of any skill level would nearly mirror swiss. Since it doesn't in your 100-0 win rate, we know it matters.
I would love for Wizards to feed us some data on win% broken down by player/opponent rating. Perhaps the next community cup team can twist some arms!
I feel like a great alternative to 4322s would be just flat, one round 3333s. Of course, people keep playing 4322s so nothing will ever be done about it.
Didn't watch the UZ vids, but I didn't think you misplayed versus the final opponent at all. Hydra would have eventually killed you no matter what. Best to get aggressive to punish him if he doesn't have it.
This argument on EV comes down to 2 key issues. Your real win percentage and how "long run" your finances can take you.
#1 Win percentage
At 50-50 you can make more packs playing more 8-4s in the long run.
However, most players are considerably less than 50-50 against the people who know the format inside out and those people expect to go 2-0 and split in the finals. Be honest here.
#2 Long run
Even IF you are 50-50, losing 3 packs + 2 tix at once is tough. If you are not lucky enough to make that one lucky finals every X drafts, you will find yourself dwindled down on resources. If you have a very large pool of resources available, then you really should play 8-4s if you think that you are 50-50. However, most people are happy enough opening $ cards + getting 2 to 3 packs and going into another draft because they can afford the loss of a few tix value per draft instead of losing 14 tix worth at once.
It's actually about stability over risk. In real life, high risk ventures give you higher expected returns in the long run. It's the same thing here.
If going 2 wins = 3 packs, I would gladly take that over 3 wins = 3 packs simply because I think I can make 2 wins and get the 3 packs and I hope not to lose round 1.
If you really cared about purely EV, you would have played constructed instead because drafting in the long run is a $ losing venture.
Yup =)
Yeah, the problem is that the win ratio doesn't hold up in 8-4s. And compared to 4322, my average pack wins is just higher than 2.48 anyways.
On top of that, I just don't have enough capital to handle the swings of 8-4s.
Another interesting tidbit is that I'm like 78% in match one, but only 71% in match 2. I can't remember the match 3 numbers, since I'm at my laptop instead of my desktop, but its around 75% too, but that changes things a lot. I figure its because I face more good decks and players round 2, but in round three, I guess I have a good deck that's passed two rounds, so I win more often.
The problem is that math doesn't account for "Wife says we gotta go..." or "Good players think they need to avoid swiss" or "8-4s are more intimidating" or any of a million other factors.
I love the set-up of this post, it was very easy to follow.
I think for MTGO UB is the better deck to play during the dailies due to UW, Valakut and Goblin being player in heavy numbers (though its much more unforgiving to missplays - which based on our hours of playing happen often enough)
Good luck in grinding for Sept's MOCS I'll be doing the same aimming for 3 byes.
While it sucks I'll be skipping monday's MOCS this month since it goes into my work hours right now money is more important then hobby (which is a shame since I have 1 bye).
Better then a spreadsheet is spreadsheet AND math ^^
If we model it using you winning each round with 75% chance, this is what you get in 4-3-2-2 and 8-4:
Probabilities:
1/4 for losing in round 1
3/16 for winning round 1 and losing in round 2
9/64 for winning round 1 and 2 and losing the final
27/64 for winning all rounds
Which gives 2,48 packs for 4-3-2-2 and 3,94 packs for 8-4 - note that the later is quite a bit more than 3 and hence you could expect to be infinite if you played 8-4 exclusively and the model took everything into account...
If we use the model in the article instead, with you beating 3/4 of all players and losing to 1/4 (note: winning 75% is better than that).
Probabilities:
1/4 for losing in round 1
21/64 for winning round 1 and losing in round 2
4725/16384 for winning round 1 and 2 and losing the final
2187/16384 for winning all rounds
Which gives 2,06 packs for 4-3-2-2, 2,22 packs for 8-4 or 2,53 packs if you split the final in 8-4.
I know the people have decided that music is poor taste for Magic, but its much easier for someone to just mute the video then to for other to go without expereince new ear....ehhh I won't finish that.
Looking forward to the draft video mates, if you manage to also record your picks and choices that would great.
You should talk more in your videos. It sounded like you were trying to be quiet like the rest of the family was asleep or something, but we need some commentary!
it's been all about luck. If I get lightning helix and mana leaks I'm ok. If I get cancels and fetters, I'm toast
I seriously doubt Shocklands will plummet in the short term. There SHOULD be plenty of warning if they start to. Pacts...well they are probably good to stay up for a while anyway (past PT PHILLY.)
I do agree that if you are pretty bad you should ALWAYS swiss. At the least, 3 rounds per draft will teach you about the format much more efficiently.
It is super-irritating that the payout is not 5-3-2-2, but the "WAHHH 8-4 and SWISS ARE STRICTLY SUPERIOR RETARDS" people are pretty dumb; most especially the guys who studies stats for a living and wants to ignore basic facts.
If I feel like I can win r1 a high % of the time (oh hey I just got two packs not one sucky swiss) and r2 a decent amount fo the time (oh hey, 3 packs for winning two rounds, suck it swiss) but not always final/win the draft, my best EV is 4-3-2-2 even if the AVERAGE EV sucks in those. 8-4 is fine if you're finalling a lot, but not really otherwise. Swiss is fine for uh... getting 12 packs back into the system? Otherwise, not great. 4-3-2-2, while a dumb payout (EVERY PLAYER GETS 1/8 less of a pack on average that's a whole pack you missed on average after 8 drafts!1111) is fine for someone who feels like R2 is an easy target and R3 is doable.
I must admit though, I do flame the one pack difference in modo when there are 2 people in a 4322 queue, and 7 in a swiss
You are becoming one of my favorite commenters. I especially like your appeal for empathy.
I am going to add buddy you when I fire up MTGO tonight.
april_sebastian, right?
@ people talking about reprints. I mean, I hope so in some capacity, but Wizards has demonstrated throughout their history that they are basically unwilling to print cards based on secondary market and availability issues. Look at Legacy's big offenders. Sure the Reserve List stops reprints of dual lands, but what about cards NOT on the Reserve List. Stuff like Force of Will or Wasteland. Where are those reprints? What about when Tarmogoyf was expensive previously (before tanking after rotating out of Ex)? Why didn't they reprint Ravnica duals in some other set since? Can someone point to an instance where Wizards printed cards to make them more accessible because of market values? If not, I'm not sure where this faith is coming from.
Look, they made a bug hupplah over printing ONE Chain Lightning foil in a $30 (iirc?) premium deck. That card could and should have been in M10 or M11 or M12. It's not broken power wise, so why not just reprint the cursed thing? Simply put, they just aren't interested in reprints on the scale on which most people seem to think the Modern stuff will appear.
Modern events are on the event calendar - the are just listed on the Premier event calendar with TNMO for some reason. I don't know why the put the modern daily events on the premier event calendar, but they did.
It would be really nice to see you update this article with a correction to your math and the modern events added.
Except that your math is wrong. Please see the comment by Reaper9889, which has the correct math.
According to your formula 4-3-2-2 goes:
(2 *.5) + (3 * .125) + (4 *0.0078) = 1.4 packs
That means that you win some packs 1/2 + 1/8 + 1/128 of the time, which is substantially more than half. As you have defined yourself as the 'average' player, it is easy to see that this cannot be true. What happened was that you double-counted your wins. You said that you will win game 1 half of the time, so you put 2*(1/2) in your formula. The problem here is that the 1/8 of the time you win again is PART of that 1/2 of the time, you can't just add them together.
The correct formula is:
2 * (3/8) + 3 * (15/128) + 4 * (1/128) = 1.13.
Using correct formulas you will see that the EVs come out as follows:
Swiss: 1.5
4-3-2-2: 1.13
8-4: .53
I do agree that a simulation will reproduce numbers - just not the numbers you present in the article.
Note also that if you are worse than average [which, lets be honest, half of us are, by definition] the payout becomes even more tilted. Swiss declines the least quickly, and 8-4s quickly become entirely unprofitable. If you suspect that you are not in the top 40% or so, swiss is far and away the best choice from an EV perspective.
I think the reason this is controversial is the 1 pack difference between the 8-4 and swiss drafts and the 4322 drafts. Group A believes the discrepancy is a good reason to avoid 4322 in favor of other forms of draft because WOTC is getting away with giving out 1 less pack. They are insistent that we boycott the 4322s and I think I more or less agree with this in principle. Though in fact I don't have a stake because the last cycle I loved drafting was Alara Block before the mixed packs.
Group B does not care about the discrepancy and just wants to play fast and get the heck out. I see their point even if it does not ever have any impact on my choices. This is similar to the argument about whether players should avoid the pre-release events. Some will because they want to see better value for their money and others won't because they just want to have fun and money is no real object.
The EV question is something Hamtastic was fascinated with and I think it has for many magic players an allure because of the math element. I am decent with calculation but don't particularly care about math when it comes to figuring out odds and what not. But I know a lot of players who really get a kick out of it. And arguing about this kind of thing takes it to the next level.
The main target audience for WotC are the casual players. Swiss are meant for them. It only became an issue when some players started to flame the 1 pack prize difference.
Swiss: For players who are trying to learn how to draft, maximize playtime from the packs, learn how the set works. Sometimes sharks appear for easy QP.
4-3-2-2: For semi competitive players and above. Most online life tilting experience starts from here.
8-4: I want your life. Simple.
In my humble opinion it is not even an issue to spark a heated debate. To each his own preference, choose the type of draft that suits them best and work our way up the ladder. No need to argue which has the highest EV as playing limited is definitely negative EV. The percentages brought up are just an excuse to so call justify claims of which is better but when all are negative EV, what's the point? It is the same as comparing who has the worse job but they still stick to it.
As said by oraymw, he just wants to play. When his objective is met the rest will fall in place as his skill rewards him with cheaper drafts to continue playing. He is still a paying player but the bonus of forking out only 1/5 of the cost more than compensates EV of drafts. How much a player can afford determines how much fun he can have.
Pete stated the math as an oversimplification sample. If it evoked negative reaction, please be kind enough to understand it is not that easy to write an article every week with other responsibilities and we will all overlook on a certain aspect. All we need is a little empathy to make the world a better place.
Peace and out. =)
re: Swiss takes too long.
I suppose that if you are really grinding out 15 or more drafts a week, then this is really going to matter to you. But since I'm the kind of person that sets aside enough time to do one draft twice per week. If I play in a swiss, I guarantee that I will be able to play my three rounds. Since my goal is to play Magic, this works out well for me. If I were to do a 4322, I might lose in the first round. After that, I don't have enough time to do another draft, so I'm just done. The difference is the cost in limited matches played, which is what I'm trying to maximize.
re: Prize Payouts
I think too many people operate under the assumption that they are going to be able to "go infinite" in limited. That is absurd. I have a 75% win ratio in Limited matches on Magic Online, and I haven't gone infinite. Maybe there are mythical people who do "go infinite," but I can tell you that they aren't achieving this status in 4322s.
re: Math
Better than math is for each player to keep a spreadsheet of their results. That is what I do, which is how I've found that I have just barely short of a 75% win ratio. I also keep track of my wins and losses, and how many prizes I get. On top of that, I track how many tix I gain from selling draft spoils. I've found that on average, a draft costs me 2.4 tix. In other words, I essentially get each pack for $0.80. Maybe I'm not infinite, but I can sure afford 5 dollars a week to draft essentially as much as I want. And $0.80 per pack is a heck of a lot better than paying retail.
Clearly something is wrong with prize payouts for middle of the road drafters (myself included), otherwise there wouldn't be this much of a discussion about EV.
On the other hand, being someone who consistently wins the first round only to lose in the second round, I understand the point Mr. Jahn is trying to make here as well.
Swiss is random. A lot of those queues seem to fire with people just trying to rare draft and get value from prize packs, perhaps recouping more packs if they are get "lucky" enough to get good cards both for sale and for draft quality. I occasionally do Swiss, but only when I feel like I have enough time to do all three rounds.
You get the same payout in Swiss if you win two rounds that you would by winning one round of a 4-3-2-2, also. If all you expect to win is one round, based on whatever assessments you make of yourself as a player, then I would use the "time is money" argument and say that you actually net more by going into 4-3-2-2s, even if the EV isn't there.
I am no statistician (although I am going to take some basic statistics classes soon), but isn't EV calculated in a vacuum anyway? Or does everyone just always assume a "null hypothesis" method when calculating this?
I may not seem like I can "count to 12", but I feel that I have gotten more packs back by playing 4-3-2-2s at this point based on where my overall skills are.
Maybe someday I will shark the 8-4s, but until I get a real grasp of drafting in general, it is all Swiss or 4-3-2-2 for me.
If someone were to petition for 5-3-2-2s, I would get behind that cause. I think that is a better approach to this whole situation. Wizards does listen to its customer base if they scream loud enough (See Jace 2/SFM bans or "Modern" as a format for evidence that substantiates my claim).
Okay, me try phrasing it this way.
My sample player in this example has a rating exactly in the middle of the spread. Exactly half the players playing in drafts have higher ratings, and exactly half have lower ratings.
Then let's assume that rating do equate to skill. We can use the six month average rating for each player, to cut down on variance if you prefer.
Now let's build some sort of formula that estimates the likelyhood of winning based on the difference in rating. For example, the chance of winning is 50/50 for equal ratings. For a lower rated player, the change of winning is 50+ (half of the difference in ratings). Do the same thing for the odd of winning verses higher rated players - the chance of winning is 50 minus half the difference in rating. Or use the log of the difference, if you want a curve that tails off. Whatever.
You can also add random factor to represent strength of cards opened - add or subtract a random percentage to represent opening bombs by one player or the other. Just keep it equal.
Now run 500 drafts.
At that point, the percentages and random factors even out, and our sample player will end up, on average, beating the lower ranked players, and losing to the higher ranked players. Or, put another way, our player loses to better players and wins against worse players.
For any simgle game, the random factors matter. However, in calculating long term outcomes over a large number of matches, you have to calculate based only on the factors that stay relatively consistent (or change at a predictable and consistent rate) like player skill.
My article was excessively long even without the more complex math, so i simplified. I should know better.
I'll try explaing this in another way. Let's simplfy the game enough to model. We'll use the d20 roll-playing system. Each player has a skill level, and a game consists of both players rolling a d20 and adding their skill ratings. Further, let's assume players have skill ratings of 3, 6, 9, 12 or 15. My middle-of-the-road player in the above example has a skill of 9. Put him in a draft and choose the skill level of players in each of the other seven slots randomly. Play it out, with each match being best 2 of 3 rolls. Now write some code to do this and run the model 5,000 times. The payout per match will be really close to my estimate.
Good to see that your math supports what I have been saying for years.
Only people who cannot add to 12 would do a 4322 instead of a swiss or 84, and now with math to back it up! Defending 4322 because it takes less time than swiss is fully retarded. If you do not have time to do a draft, then DONT DO ONE!
Modern- The prices are ridiculous due to the hype. This format is the same as extended before they neutered ext, and nobody played it then except for tourneys. Modern is dominated by combo with the average game lasting 5 turns or less. Not a recipe for fun.
There is no magical difference between the first and second rounds -- half the time you will be paired in R1 against a deck of identical quality to the average deck you face in R2. I find it naive that people say they can always get out of the first round of 4322. After all, you have a 1/8 shot of playing the eventual winner in round 1 (and of course a 1/8 shot of being the winner).
I agree that swiss takes forever though, which is why 8-4s are king.
I also strongly object to your methodology. Check out the pro drafts online at other sites. They lose plenty of matches, sometimes due to luck, sometimes due to being outplayed. You say that it doesn't matter what we assume the win% is of a worse player versus a better player, that the same result emerges, but this is demonstrably false: if better players only won 50.000000001% of the time versus worse, the average payout from an 8-4 for anyone of any skill level would nearly mirror swiss. Since it doesn't in your 100-0 win rate, we know it matters.
I would love for Wizards to feed us some data on win% broken down by player/opponent rating. Perhaps the next community cup team can twist some arms!
I feel like a great alternative to 4322s would be just flat, one round 3333s. Of course, people keep playing 4322s so nothing will ever be done about it.
Didn't watch the UZ vids, but I didn't think you misplayed versus the final opponent at all. Hydra would have eventually killed you no matter what. Best to get aggressive to punish him if he doesn't have it.