Relative amounts of luck in MTG limited formats?

Question

While I haven't played very much, I've noticed there seems to be slightly more luck in sealed than in draft. In draft, skill can prevail by recognizing bombs/archetypes, observing what colors are available, stealing good cards from your opponents, etc, while in sealed you are just forced to work with what you have; if you are stuck with mediocre rares and no good uncommons that fit with your general color pool, you're probably going to do slightly worse against somebody without these initial disadvantages no matter how skilled you are at deckbuilding.

How much luck is present in the 3 popular limited formats? Which have the most and least luck involved in determining the winner of individual matches and tournaments? In which is it easiest and hardest to win when you are the superior player?

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NOTE: by 3 limited formats, I mean booster draft, 6-pack 40-card sealed, and 4-pack 30 card sealed. Feel free to include information on other limited formats if you like but these were the ones I'm most interested in addressing.

Answer 1

You pretty much answered this question already. While I haven't heard of 4-pack 30 card sealed yet,I would say this is the format that is the most dependent on luck. A single bomb in a 30 card deck has a much larger impact than in a 40 card deck, for 2 reasons:

1) With 4 packs, opponents have a lower chance to equalize a single bomb of yours with at least 2 solid rares of their own, simply because they only get 4 rares instead of 6.

2) Assuming the average game runs for at most 15 turns, you get to see 22 cards of your deck, ignoring cantrips and library/graveyard manipulation: That is ~75% of a 30-card deck, and only ~55% of a 40-card deck. So you have a chance of up to 75% vs. 55% to draw your bomb in a game. Or stated differently, to get your bomb with a 50% chance in any given game, you need to draw only 15 vs. 20 cards, again ignoring library/graveyard shenanigans.

Obviously, this applies to every participant, so it all averages out in the long run, and it comes down to skill again. But in the 4-pack format, I would expect the standard deviation in deck strength to be significantly higher than for 6 packs, or, to answer your question, the luck factor is highest in the 4-pack, 30-card deck sealed format.

Answer 2

I think it's rather self-evident that 6-pack 40-card sealed, has less of a luck component than 4-pack 30 card sealed. As mentioned by @Hackworth, you're much more likely to see a rare bomb in a 30-card pack than a 40-card one.

It's definitely going to be hard to judge, but I wouldn't overestimate the gulf in “luck” between 6-pack sealed and draft. There are some considerations:

• Certainly sealed and draft require slightly different skill sets. A good drafter might not be a good sealed deck builder and vice-versa. Yes, there's a lot of overlap in knowing how to choose good cards and build a deck, but a good drafter will know how to signal and read signals when drafting, and a good sealed deck builder will know how to adjust his deck between games.
• Consider that a sealed deck pool is twice as big as draft. Each player is passing around three packs compared to getting six packs to build a sealed deck. Assuming you're reading signals perfectly, you might be able to get “better” card pool in 2 out of 5 colours from three packs than just a random selection of 5 colours in six packs, but I believe this depends on the sets you're drafting. But, if the number of synergies in commons is large, or the depth of card quality in the set is relatively large, it's conceiveable to be just as likely or more likely to be able to build a competitive deck with any random six packs than it is to draft your best from three.
• Don't underestimate the ability to tune between games. It's far more likely to swap out an entire colour — or even two — in sealed, or to change the entire deck archetype (say from aggro to aggro-control) than it is in draft. So if you realize after the first game you've run into a bad matchup, you might be able to change your deck from paper to rock and beat the scissors you encountered.

In conclusion, all Magic games of course have some element of luck. The effect of luck can be mitigated through skill in deck building, card selection, adaptation between games, and knowing when to mulligan. My intuition and experience leads me to believe that 3 pack drafting might have a very slight edge in mitigating the luck factor, but the difference between that and 6-pack 40-card deck sealed is really hard to judge and might not even be evident.

The very best sealed deck players might be just as good at mitigating the luck as the very best drafters. I've looked for sites with statistics on player win percentages but haven't found any yet…