We've been looking at the expected values of playing in the three different types of draft queues on MTG Online over the past few days. Here's a graph of the expected return of all three draft types:

Black: Swiss - Red: 8-4 - Blue: 4-3-2-2

As a quick review, if the player base is of equal skill in all three queues, then if your probability $p$ of winning a match is less than .5, your best expected return is in the Swiss queues and in the 8-4 queues otherwise. The 4-3-2-2 queues never provide you with the best expected return. But yet, people still play in them. What are some of the reasons why?

#### Risk

The nature of an 8-4 draft is that it is a riskier proposition than a 4-3-2-2 draft or a Swiss draft. You have to win 2 matches without losing one to win any packs back at all.

Black: Swiss - Red: 8-4 - Blue: 4-3-2-2

Across the board, there is less risk to the player by playing in a 4-3-2-2 draft instead of an 8-4. Even at a 60% win clip, you have a 64% chance of missing the finals of an 8-4 draft vs. a 40% chance of missing the semifinals of a 4-3-2-2. But risk aversion can't be the only factor; playing in Swiss queues is by far the least risky choice of the three. At a 60% win clip, you'd miss out on any packs at all only 6.4% of the time in Swiss queues! What else plays into people playing in 4-3-2-2s?

#### Convenience/Time Commitment

Players don't have infinite time on their hands. Completing a Swiss draft can take over 3 hours for at most 3 packs. In a 4-3-2-2, you can have 2 packs by going 1-1 and be done in around an hour and a half. While it takes the near 3 hours to get paid in an 8-4, you're getting more packs than you possibly could in a Swiss event. And if you're 0-2 in a Swiss event going into that last round scraping by for one pack to make the draft not a total failure? Rough night.

The additional issue is convenience. You log into MTGO and there's 6 people waiting for a 4-3-2-2 to fire and the 8-4 and Swiss queues are empty. You know it's wrong. You know you should cheap auto insurance quotes wait for people to load up the better queue. But there's a draft that about to start right now. You could be sitting there, waiting for that draft to fire for 15 minutes... a half hour... an hour? On top of the time it would take to play out that draft? You're on MTGO to draft, not to durdle around!

People make decisions based on factors other than EV. Opportunity cost is a real thing. The time investment in waiting for the right draft to fire and play out vs. the ability to just play in that 4-3-2-2 right now might sway you to the worse EV.

#### Quality of Opponent

Players in the 4-3-2-2s are typically not as good as those in the 8-4s. Some players may not think they're good enough to compete in the 8-4 queues, others may see the 4-3-2-2s as slump-busters. But how much worse do the 4-3-2-2 players need to be than the 8-4 players before it makes EV sense to play there?

As we showed earlier, you'd have to have approximately a 45.7% chance of winning a match or better before playing an 8-4 made sense instead of a 4-3-2-2, so we can ignore all cases below that threshold. We can also ignore all cases where the expected return on an 8-4 is greater than 4 packs as well, since at that point the only thing that could make you possibly want to go to a 4-3-2-2 queue is risk aversion or opportunity cost. It would have nothing to do with the difference in quality of opponent. So where's that point?

$$4p^3+4p^2=4$$

$$4(p^3+p^2)=4$$

$$p^3+p^2=1$$

Solving an equation of this nature is really ugly, but we can use the graph to give ourselves a best guess-timate of the number for our needs. That estimate is .755. (Interestingly, a player with a just good enough win rate to not ever want to think about anything but 8-4s still will fail to cash over 40% of the time!) Obviously, the better you are against the 8-4 field, the greater the gap needs to be between the player pool of the two queues.

## 8-4 vs. 4-3-2-2

p(8-4) Expected Return Needed p(4-3-2-2) Difference in Difficulty
.46 1.235744 .462 0.43%
.48 1.363968 .497 3.54%
.50 1.5 .533 6.60%
.52 1.644032 .569 9.42%
.54 1.796256 .605 12.04%
.56 1.956864 .641 14.46%
.58 2.126048 .678 16.90%
.60 2.304 .714 19.00%
.62 2.490912 .751 21.13%
.64 2.686976 .788 23.13%
.66 2.892384 .825 25.00%
.68 3.107328 .862 26.76%
.70 3.332 .899 28.43%
.72 3.566592 .936 30.00%
.74 3.811296 .973 31.49%

This table gives you an idea of how much softer the 4-3-2-2 queue would need to be to justify switching from 8-4s to 4-3-2-2s solely for expected return purposes. How much softer can we reasonably expect a 4-3-2-2 to be, though? Without access to player ratings, it's impossible to be certain. Even using results-based analysis on your playgroup's results against the two queues is flawed because presumably, the more you play Magic, the better you should get at the game, right? We can't even really guess and say that 4-3-2-2s are 10% easier or 20% easier. But the table can give you an idea of what win probability you'd need to have to make the jump down and shark the kiddie pool.

So what does this all mean? Is it a fool's errand to play in 4-3-2-2s at all? If it is, why do so many fire off on MTGO? Next, we'll look at the pros and cons of each draft format.