Many people have pointed out that, from a pure expected value standpoint, drafting in the 4322 queues on Magic Online is a misplay because it pays out 11 packs, compared to the 12 packs that the swiss and 84 queues pay out. A common response is that I win more matches in 4322s than I do in 84s and so I’ll end up winning more packs in 4322s and thus they are better value. I’ve heard this response a number of times, but I’ve never actually seen anyone include their win percentages, so I decided that to dig in and find out whether there are win percentages that make 4322s a better choice.
Let’s start out by looking at some data. I don’t draft a great deal online, so I don’t have a nice MtGO dataset of my own. But I do have my real life limited data that we can use to approximate my expected MtGO win rates. I went to the Planeswalker Points website and aggregated all of my limited match records. I grouped these data into three categories – matches in prereleases and release events; matches in PTQs, GPs, and Pro Tours; and all of the rest of my matches. Let’s map these three data categories to swiss, 84, and 4322 queues respectively. This seems like a decent first approximation, although I’d imagine that my win percentage in actual 84s would be better than my PTQ/GP/Pro Tour win percentage. This data includes both sealed and draft data as otherwise I’d have very few data points for the top and bottom categories. So, mapping my results to the queue payouts, here’s how I did:
Queue  Record  Win Percentage  Expected Value 
84  80 wins, 51 losses  61%  2.4 packs/draft 
4322  192 wins, 78 losses  71%  2.29 packs/draft 
Swiss  61 wins, 18 losses  77%  2.32 packs/draft 
As we would expect I have a higher win rate in swiss than I do in 4322s and I have a higher win rate in 4322s than I do in 84s. But even though my win rate is 10% lower at 84s than 4322s, I still have a higher EV in the 84 queue. This is partially due to the structure of the tournament (84s reward higher win percentages more than 4322s), but it is also because there is a pack missing from the prize pool (if it was a 5322 my EV would be 2.65). You’ll notice that I also have a higher EV in swiss than in 4322. When people make the “my win percentage is better in 4322s than 84s” argument they frequently don’t take into account that they probably have an even higher win rate in swiss.
Let’s look at some more data. My friend Daniel Duterte kindly let me publish his MtGO draft numbers from the last year:
Queue  Record  Win Percentage  Expected Value 
84  85 wins, 72 losses  54.1%  1.8 packs/draft 
4322  13 wins, 7 losses  65%  2.0 packs/draft 
Swiss  13 wins, 2 losses  86.7%  2.6 packs/draft 
OK, small sample size on 4322s and swiss queues, but this is an example of how just crushing swiss queues gives you a huge edge on 4322s. The whole “my win percentage is higher in 4322s than 84s” argument is a double edged sword.
One more set of data, Limited Resources listener Vis posted his win percentages in the comments of one of the latest LR podcasts:
Queue  Number of events  Win Percentage  Expected Value 
84  35 events  61.9%  2.48 packs/draft 
4322  127 events  63.35%  1.92 packs/draft 
Swiss  82 events  67.9%  2.04 packs/draft 
Well, we keep having pretty bad EV with 4322s. We’ve got a decent sample size here and see that 4322 is wildly less profitable than 84 when there’s a small difference in win percentages and we’re a solidly winning player. And, again, swiss manages to edge out 4322s, even though the win percentages aren’t as dramatic as they were in Daniel’s case.
So, we’ve got some real world data sets in which 4322s seem to be a losing proposition, in terms of EV opportunity cost. Let’s take a look at the actual EV numbers for particular win rates and see if we can draw some conclusions. Here’s the relevant info:
Win %  84 EV  4322 EV  Swiss EV 
5%  0.01  0.10  0.15 
10%  0.04  0.21  0.30 
15%  0.10  0.33  0.45 
20%  0.19  0.45  0.60 
25%  0.31  0.58  0.75 
30%  0.47  0.72  0.90 
35%  0.66  0.87  1.05 
40%  0.90  1.02  1.20 
45%  1.17  1.19  1.35 
50%  1.50  1.38  1.50 
55%  1.88  1.57  1.65 
60%  2.30  1.78  1.80 
65%  2.79  2.00  1.95 
70%  3.33  2.23  2.10 
75%  3.94  2.48  2.25 
80%  4.61  2.75  2.40 
85%  5.35  3.04  2.55 
90%  6.16  3.34  2.70 
95%  7.04  3.66  2.85 
100%  8.00  4.00  3.00 
That’s useful reference data, but it’s a bit hard to interpret. Let’s visualize this by looking at equivalent win percentages for 84s and swiss compared to the 4322 queue:
4322 Win percentage  Swiss  84 
5%  3%  15% 
10%  7%  21% 
15%  11%  26% 
20%  15%  29% 
25%  19%  32% 
30%  24%  36% 
35%  29%  39% 
40%  34%  42% 
45%  40%  45% 
50%  46%  48% 
55%  52%  51% 
60%  59%  54% 
65%  67%  57% 
70%  74%  59% 
75%  83%  62% 
80%  92%  65% 
85%  N/A  67% 
90%  N/A  70% 
95%  N/A  73% 
100%  N/A  75% 
Here’s how you read this chart: let’s say you have a 40% win percentage in 4322s, so you look at the 40% line under “4322 Win Percentage,” then look at the percentages for swiss and 84, which are 34% and 42%. This means that a 40% win rate in 4322s is equivalent to a 34% win rate in swiss or 42% in 84.
Looking at the chart, it’s pretty obvious that if your win rate is 60% or less in 4322s then you would do better by simply playing swiss queues, since you’ll have the same or better win percentages and a higher EV (actually the breakeven point is at a 61.9% win rate). If you have a greater than 60% win rate in 4322s there needs to be a pretty large difference in your win rates between 4322 and 84 queues AND there has to be a small difference in win rates between 4322 and swiss queues for 4322s to be correct. The win rate differences between 4322s and 84s are so big, however, that this isn’t really plausible. If you win 70% of your 4322 matches then you should be able to win either 60% of your 84 matches or 75% of your swiss matches (or both!).
It turns out that the “I win more matches in 4322s than I do in 84s, so I’ll win more packs by playing 4322s” argument just doesn’t hold any water. First off, you have to consider swiss queues as well, and if you assume that your win rate is higher in 4322s than 84s, you also need to assume that your swiss win percentage will be higher than either of the others. Given that, you now need to be an excellent drafter with a greater than 61.9% win rate for 4322s to possibly be better than swiss queues. And you need to be doing much worse in 84s than you are in 4322s, like 10% worse or more, to not move up to 84s. These circumstances just aren’t going to occur for the vast, vast majority of drafters.
The best way to figure out which queue to play in is to keep track of your results, determine your win percentage, and then figure out which queue offers the best value. If you want to challenge yourself and play against the best, or if you are a very winning player, you should draft 84s. If you’re just want to play some magic, or if you’re still learning and are not yet a strong drafter you should draft in the swiss queue. But please, do not ever draft in 4322 queues – they’re a terrible deal that you always come out behind on.
Cheers,
Joe
Postscript:
For the mathy completionists out there, here are the equations I use to calculate pack EV:

Swiss: EV = 3 * Win%

4322: EV = Win% * (Win % * (4 * Win% + 3 * (1 – Win%)) + 2 * (1 – Win%))

84:: EV = Win% * Win% * (8 * Win% + 4 * (1 – Win%))