Thursday, July 4, 2013

Event Theorycrafting

So you want to make money, huh?

This is probably the right post for you.

This post will cover all sorts of events on MTGO and tell you why they're all bad ideas! (Well, not really.)

For those of you who would otherwise go straight to the bottom, I'll give you the punchline now. If you want to make a net profit out of MTGO, either only do constructed dailies or consistently have winning records. That's all there is to it.

If you want to the crunch, carry on.

Above is a compilation of many events and their payout rates with respect to their total cost. For instance, for every 100 tix you put into playing 4-3-2-2 M13 Drafts, you can expect 63.74 out. Investmentwise, that's a pretty poor pick.

I think what should stand out is that among all these events, which are fairly representative of the breadth of events offered, only two have payout rates above 100% - Momir Basic and Pauper (lines 5 and 6). These are the ones to do if you're new, want to get into an inexpensive format, and want to come out ahead. Momir Basic decks literally cost $10, and Pauper decks can range from 2 tix to perhaps 20 tix.

Now, what makes these events so different from other events?

There are two things to notice.

First, these are daily events. They happen at specific times each day rather than firing once eight people convene, and also have many more than eight people playing at once. Note that not a single non-daily event has payout above 100%.

"But King!", the astute among you say, "not all dailies have payout over 100%!" That is true. If you look at line 10 for the RTR Block Sealed daily, it has a poor 78.71% payout rate. That leads us to the second observation.

Momir Basic and Pauper, unlike RTR Block Sealed, are constructed events, whereas RTR Block Sealed is a limited event. For the former, you bring your own deck, and for the latter, you open boosters and make something of them.

For those of you who don't know, opening boosters by themselves is a very, very bad idea financially.

Limited events are almost just as bad. Constructed events are winners since once you buy into a deck, you're set! (Kind of. You still probably have to keep up with standard and whatnot, but that's the beauty of Pauper and Momir Basic.)

So those are the two qualifiers. Constructed, and daily. Please don't try the two-player constructed queues. Their payouts are absolutely horrid. So horrid that even with a 100% winrate, you're still only getting an 80ish percent payout. (See the last line in the image above.)

EDIT: A helpful reader has pointed out a miscalculation above. The payouts on two-player queues with a 50% winrate is 83.75%, and takes a 60% winrate to break even.

Now, I'm sure some of you will be asking, "King, how can you extrapolate this to all constructed dailies? I'm sure that these two formats for cheapos like you pay alright, but what about for us people with money for standard?"

Well, since the constructed dailies all have the same entry fee and payout structure, it's probably a fair deduction to extend what we know from Momir and Pauper to all constructed dailies.

This, by the way, is what an event's calculation looks like.

Okay. That was the easy part. Ready for the deeper analysis?

Before we get into that, a quick note. If you've been looking closely, you'll see my chart skips from the "C" column to the "M" column. I've omitted several columns in the interest of space. Those columns detail mundane things used to calculate the total entry fee.

Moving on, please note the green column in the image above, labeled "Win", short for win rate. This means that these calculations take into account a 50% win rate. For formats like Momir, where strategy takes the backseat to chance (though, let it not be said there is no strategy involved. That will be a later post.) a 50% winrate is definitely a safe assumption, but among other events where skill (and sometimes one's wallet) takes a much more prominent role, there will be varying winrates. Let's go ahead and take those into account.

Above are two copies of the original chart, this time with 35% and 65% winrates to indicate some variance. There are some very interesting things to note here. First, dailies are very volatile. At a 35% winrate, it is more profitable (rather, you incur fewer losses) to draft than it is to do dailies. On the other hand, if you win 65% of the time, for every 6 tix payin for a daily, you can expect to walk away with 12. There's no question what events you should be doing at that point. What's more interesting is that at the 65% winrate, even some drafts (8-4 drafts) and limited dailies become profitable. It goes to show that, even if you don't pick winning events on average, you can still come out ahead by winning. Winners win.

Note that the two-player constructed events are still very low, even at a 65% winrate. Eight-player redeems itself at the 65% winrate, but only barely.

The last item of note is that the 4-3-2-2 drafts are rather stable. Even with a 30% swing in winrate, they swing proportionally to that. They're still not a good pick unless you're sure you're going to win very often. But seriously - it takes over an 80% winrate in 4-3-2-2 drafts to break even.

I'm sure there's one more burning question on your mind - why do the RTR drafts and the M13 drafts have not only different entry fees, but different payouts? This is where pack prices come into play, and is probably the most tenuous part of my analysis.

These prices haven't been updated in a week or so, but they're still relatively representative. I think RTR has shifted down 10 cents, and the ISD block might have changed. I don't really follow them. That's not the major part of this though, since the difference between their buy/sell prices (what you can reasonably expect to get from bots) will remain about the same. (An important note)

Here's what matters. When prices shift upwards but the gap remains the same, then daily events become more profitable as your entry fee is only in tix and the reward is constant in packs. At the same time, limited events become less profitable as the % of payout relative to entry fee is reduced, assuming a 50-50 winrate. The opposite is true for when prices drop. At some point, you might as well buy packs rather than participate in dailies for all you're getting, (though that is a very low point) but at the same time, the limited scene becomes more appealing. This is also due to the content value relative to the price of the pack.

This is probably the point of contention, the content value of a pack, or what you can reasonably expect to pull if you open a pack straightup. I haven't done the calculations for these, though I will at some point (at which point I will revisit this with fancy graphs and such). This value no doubt varies from pack to pack; DGM might be overvalued relative to GTC and RTR, but I'm fairly certain that the disparity in price of these packs is less due to their inherent value and more due to availability as DGM is by far the easiest pack to get one's hands on following an event.

Some quick analysis on content value. The actual values of these do not affect the earning power of constructed dailies at all since you're not ripping packs for those. Naturally, payouts in the limited scene move upwards if content value is higher than $1, and will drop if content value is lower than $1.

Now, my analysis has two other possible points of contention, and I'll close with those.

First, the disparity in buy-sell prices on booster packs is not accounted for in event payouts. This means that for reinvestors, actual entry fees are somewhere between 0.1 to 1 tix lower than listed, and payouts are subsequently adjusted (the percentage is also dependent on the event's inherent payout) upwards. When I say reinvestors, I mean those who do one event type continuously, like RTR drafts. This can help reduce the cost, but probably not significantly. (You get a free draft every ten to one hundred drafts, so it's really not major.)

Second, not everything is about money! Very true. This post concerned itself with the financial aspect of things, but don't forget, you're (hopefully) in this for fun! If you're not too concerned with the finances, the 66.83% returns on 8-4 M13 drafts should be heartening. Why is that? For the 10.1 tix entry fee, you get 6.683 tix back each time, meaning that after the first draft, you're on average only paying 4.3 tix per draft, a third of the price! That's excellent.

Let's put this into perspective. Going infinite is great. That's the ideal, to never have to pay for Magic again. But even without that, Magic can be very cost efficient. Let's consider the 8-4 M13 draft again, with a 50% winrate. Putting $100 in, we get ~10 drafts initially. But with that, we should get about 66 tix out, which is enough for another six drafts, and so forth. Therefore, we can use an infinite geometric series to calculate that on average, $100 spent will fund (10 / (1 - 0.6683)), or about 30, drafts. That's about $3 a draft, which definitely does not come out to the most expensive hobby out there.

In the end, it still holds. Either to constructed dailies, or win. That's how to make the most out of these events.

Of course, a final caveat. These numbers are all assuming you have the same winrate in each format, which might not be true! People are stronger in different formats, so maybe your 8-4 draft winrate is 75% while your Momir winrate is 40%. Let these dictate what events you play, not necessarily what I say here. Of course, there's also more subtlety in each event you can use to boost your winrates. I'll do my best to shed some light on that in future posts.

But I digress. There will be more talk about how to pay $0 per event. This is just to show you that it's not that bad even if you're not going infinite. It doesn't mean you shouldn't try though!

Have any additional commentary or analysis on something I missed? Please let me know!

Oh yeah, and happy fourth of July everyone!

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