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By: xger, Xger
Jul 27 2015 12:00pm
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Doom is here! It's not that bad! Dailies are over! We'll get used to it! 

...time to analyze the changes...

Quick preface: I've studied lots of mathematics, but I graduated 6 years ago and am a bit rusty, so hopefully everything is correct. If corrections are needed, I will add them in comments. Note, I might put up numbers from mid calculation and thus rounded. When I make calculations I always use the raw numbers, so there might be slight differences if you use my numbers instead of following the formula. This will be a wonky article, but some useful charts at the end if you want to skip the explanation.

The Changes:

I've linked to the changes above, but here is the article again.

Essentially, we have a new currency: the Play Point (PP). It seems clear that Wizards intends 10 play points to be equivalent to 1 ticket or $1. While true to some extent, it's not always true. First, if you have 19 play points, they do nothing. Second, if you go infinite, you might create a huge stock pile of PP's. I've seen several people discuss that, at the huge stockpile stage, the PP's are worthwhile. This is also false (I will discuss later). For now, an overview of the new prices and payouts:

 

There are several ways to calculate the values of these: convert to a ticket estimation, convert to PPs, convert to entry fees, or convert to one entry fee plus profit. Each method has its own issues. Entry fees vary and packs and tickets aren't really that convertible. Each has its perks, and as such, I will present analysis under each.

The Value of One PP:

This is probably the biggest flaw I have seen in other examinations. First, Wizards seems to value 10 PPs as 1 ticket, or 1 PP is 0.1 tickets. The issue many players have is that if you are strong enough to go infinite you just pile up the PPs. There is in place a conversion already, depending on how you look at it:

The key here is that this isn't packs you can sell. These are opened in the event. I know some players hate sealed in either variant. But, at the moment, this is the method to convert PPs into packs. While I personally don't condone it, join the queue just to open the packs for the cards. Of course, this means using PPs for a lottery. But if you are swimming in them, then a lottery is still better than the PPs just sitting there. So, the value of these leftover PPs would be tied to the expected value of whatever set you buy into.

To determine the expected value of a pack there are a number of calculations. Pulling numbers from mtggoldfish (spreadsheet friendly value listings), I start with Dragons of Tarkir. The first note is that only 2 commons are valued above $0.01, both just $0.02. In reality, a current set commons will nearly never sell for even 1 cent. There are bulk buying bots which gives a rough value of about 1000 commons to 1. So a pack gives ~$0.011 in commons. 

Next is uncommons, where again, most are valued at $0.01. For those, a similar calculation to commons yields $0.005 per uncommon. For the other uncommons valued higher than 1 cent you have to take their value and multiply it by the chance of getting it. With 80 uncommons, the chance of getting any particular uncommon is roughly:

1-(79/80)^3=3.7%

Now, this does not truly reflect the odds because of collation and printing mechanism that are mirrored in MTGO. However, that information is not known publicly so the general approximation is best. So, when the chance of particular uncommons is combined with their price we get a value of $0.0133. The uncommon worth half a cent add $0.014 to the value of pack. That brings the total of commons and uncommons to $0.0283. Ah, commons and uncommons.

Next is rares: 53 rares, 28 of which are valued at $0.01. Here, that value is fine as an estimate. Using the same methodology from previous rarities, the value of the rares is ~$0.3881. But, you only get a rare 7 out of 8 packs, the last is a mythic. So, the value of the rares is really .3881*106/121=$0.34. [In large sets the ratio is not 1 in 8 - there are 53 rares printed twice on an 11x11 sheet with one each of the 15 mythics; so 106/121 is more accurate].

Last is mythics, all priced differently, 15 in total. Their average value is $4.7047, but appearing only in 15/121, we have added value of $0.5832.

So, at this point, we have a total value of $0.9506. There is one last adjustment, foils. Foils have replaced a common in the pack in sets for years, so the analysis. So the value of commons is 55/56*0.011+the average value of foils. Calculating foils is its own problem. At a rate of 1 in 56 (assuming that's still valid), foils don't add much. I attempted to reverse engineer the rates for the type and foils and here is the result: the weighted average value of the foils is $0.0749, which then has to be multiplied by the chance of a foil. Meaning $0.00133. So foils are slightly more than a common, and our pack total is $0.96. Good ol' crack packing terribleness. 

A More Realistic Value for PPs

At 43 and a third PPs for a pack, we have a translatable value of $0.02195, so about a fifth of Wizards value. This means for calculation purposes, any PPs beyond the infinite break point can be valued at the above price. Of course that price will vary with the average pack value.

Is the Change Good or Bad?

Here, of course, is the real question. Previously, the profitability of constructions was tied to the value of a pack. As those calculations and charts have been done numerous times, I am not going to repeat them here. However, I will present the new system and a comparison chart. In this chart everything is calculated based pack value of 3, and an opened pack value of 1. If the prizes gave enough for an entry fee, I converted those PP's at the Wizards rate of 10 to 1, since that would rebuy an entry, negating those tickets. After that, I used the above method for a conversion rate. Any PP conversion has the $ in front.

The first note is that the new structure really isn't that dissimilar, value wise. Of course, the similarity is when you can sell packs for 3 and the average opened pack value is 1. So the new dailies are better value if you can win. This is a pretty harsh value decrease for Legacy, Vintage, and Pauper. Of course this is just a snapshot. Here are charts for other values:

Pack worth: 2.75 Opened Pack: 1 on the left; Pack worth 2.5 Opened Pack: 1 on the right

So, as the charts show, as the pack value decreases the better the new system is. This is somewhat paradoxically however, because the new system should increase the value of a pack as there will be considerably less entering the system. Up next, time to look at win rates and EV.

Win Rates and EV Under the New System

First, the 2 mans are in some ways better and some ways worse. If anything, the new 2 mans are consistent. If you win 60% of the time, you average 20 PPs (18 from winning, 2 from losing). So, you have to win 60% of your matches to continually play, and any better is profit (either to use for larger constructed entry fees or converted as outlined above). Previously, the necessary win rate was tied to the pack prices. If the packs were worth 3, you needed a 2/3 win rate. For 60%, the pack price had to be 3 and 1/3 tickets. Of course, the winnings are different and not directly convertible. For most, I imagine that is somewhat of a con. Some will enjoy having fewer steps. In the end, take it for what you will. 

Next, is EV in the 8-mans and dailies. Calculating this is rather tricky, because there are two approaches - continuously play or making a profit. The first means valuing as reentry, the latter meaning paying for reentry and selling anything above. I'll show each with a pack price of 3 for standard and modern dailies.

 

For standard/modern, if you want to turn a profit, and pack prices are at 3, you need a win rate of 64.3%. If you want to continuously play, you need a 58.9% rate. The difference comes from getting 10 cents a PP if you want entry fees. This again highlights the much worse Legacy, Vintage, and Pauper dailies: higher than 70% to turn a profit, 66.5% to keep playing. Here are the same for 8-mans:

As many have pointed out, 8-mans are being altered to be better than the current incarnations. A 60% win rate turns a profit, and a 50% means really cheap 8-mans.


Well, that about covers it. In some ways the changes are for the better, in others they are not. The biggest takeaway in my opinion is that there is a conversion. I honestly doubt Wizards will be okay with people joining just to open and drop. Nevertheless, without another mechanism, players will at some level of PPs go to convert them. If that happens enough, it'll be interesting to see what Wizards does then.

If you have questions about my calculations, leave a comment and I'll discuss them. Feel free to leave a comment even if you don't want to talk about the calculations!

xger

xger21 on MTGO

3 Comments

I came up with different by Tom Scud at Mon, 07/27/2015 - 19:23
Tom Scud's picture

I came up with different numbers than you for win percentages needed to reenter continuously; I came up with about 54% as the breakeven point for the modern/standard dailies (with 3 ticket packs). My formula for calculating EV there was W^4*(6P+36)+4*W^3(1-W)(3P+18) where W is the winning percentage and P is the pack value. Quite possibly it's me who missed something there since I haven't done any formal math classes in a very long time. (I also came up with 56% for the new 8 mans and legacy/pauper/vintage dailies to play continuously).

I think your calculations are by xger at Mon, 07/27/2015 - 22:38
xger's picture

I think your calculations are right. I'm not intimately familar with EV calculations, and forgot the the dailies are swiss, and thus you have to account for going 3-0 then 3-1, 2-0, then 3-1, 1-0 then 3-1, and 0-1 to 3-1. Thanks for pointing this out and sorry all for the error.

As for the first facebook comment - that's an interesting way to look at that, and a bit disheartening.

by Sensei at Tue, 07/28/2015 - 13:19
Sensei's picture

43.33 or 43⅓ is much clearer than 43+1/3PP