How many of each land do I need to support a draft tournament?

Question

I am planning on running some booster draft tournaments, and want to make sure I am well supplied. The best case scenario is that each player takes 8 of one color and 8 of another color (assuming a typical 40% land spread). Realistically this doesn't happen, though. Sometimes there's more of one color than another in the draft packs. Some people go mono-color. Some people might be poor players and go with a color they don't have strong cards in (this is very common in red and green) which increases demand for that 'overloaded' color (while decreasing demand for another).

So the 'best all around' would be 4 land per color per person. So for a 10 player draft I should have 40 land of each color.

The 'worst case scenario' (while realistically impossible) would be 17 land of the same color for every person. So a 10 player draft would be 170 land of each color (since I don't know ahead of time which color will get 'overloaded' as such).

In summary, For a magic booster draft of N players, how many of each land should I have available to accommodate a reasonably likely scenario?

Answer 1

A little bored at work, so I coded up a simulation. I assume that each of n participants picks 2 different colors, with slightly higher probabilities for choosing red or green (0.23) than blue/black/white (0.18) to account for the "overloading possibility". I assume each person wants 8 lands of a chosen color. I ran this simulation 10,000 times, and took the 90% quantiles of the number of lands required.

I ran the above code for n=5 up to n=30, which I figured covers your home-drafting range. Fitting linear models to the results (they do look linear, see below), gives

red/green lands = 10.3 + 4.2 * n
blue/black/white lands = 10.4 + 3.5 * n,

which for n = 10 is 52.3 each mountains and forests and 45.4 each of the others. Sounds pretty reasonable (like what @Affe says in the comments and @wpickett says in the answer).

My assumptions are bad in that each player's choices are independent--if 9 of 10 people pick blue, the 10th is still just as likely to pick blue too, but that's conservative, and somewhat makes up for the impossibility (in the model) of someone picking a mono-color.

Red dots are for red/green lands, blue dots are for blue/black/white lands.

Answer 2

In a booster draft, generally a player has about 16-18 lands depending upon their card choices. So for a 10 person draft, you can assume around 160 - 180 lands in use at one time. However, because of the random nature of the cards in the pack you can't assume the distributions of the colors for each player, so you should probably assume that you need at a minimum 180/5 = 36 lands of each type. I wouldn't feel comfortable holding a draft unless I had 50 or so of each color, though.

The next question you need to ask is if you are allowing the participants to keep their land or if they need to give it back. MTG players are kinda forgetful in giving back basic lands, so you should probably consider having as many lands as possible so that you don't run out as you hold multiple tournaments.