Understanding the economy of Perfect Team

[allenciox]

There have been a number of posts about how using AH is the way to go instead of opening packs, or that the cost of packs should be reduced. Also about rampant inflation of prices on AH, etc.

I think there are some fundamental misunderstandings of how the economy of Perfect Team works. Keep in mind that the prices on the Auction House are not set (except for minimums for each of the "tiers"), but that it represents a (mostly) efficient market.

If you were able to consistently earn a positive return from opening packs and listing their contents on the AH, then everyone should be opening packs instead of buying on the AH. Clearly, supply-demand dynamics would quickly restore an equilibrium to those prices --- the Expected Value (EV) of opening a pack would soon be negative (-EV) as it needs to be for the market to function efficiently.

On the other hand, if opening standard packs (my guess is that >95% of packs that are opened are standard packs) were strongly -EV, everyone would stop spending PPs on packs and buy on AH. That would drive up prices on the AH and, once again, restore the equilibrium.

What is that equlibrium point? That is actually somewhat determined by the Vig of listing a card on the AH (i.e. 10%) suggesting that the overall EV of opening a pack and selling all contents will generally stabilize between 90% and 100% of the cost of a pack. I actually have calculated this based on prices and it seems to be right around 96% --- opening a standard pack will, on average, get you back 960 PPs when listed on AH.

As to inflation or deflation, that will not happen over an extended period as long as the quick-sell price of cards and the cost of packs remain constant. There can be "temporary" inflation when a change is introduced (such as collections, and probably tournaments later on), but the market will quickly stabilize. Note that the collections, in particular, generated some temporary inflation due to the "free" packs that they introduced.

So why does it "seem" like inflation is occurring to many people? The reason is that prices of the entire universe of cards will not experience inflation, but certain cards WILL inflate and deflate. So cards that are needed for collections will get inflated prices, while cards NOT in collections will drop in price to compensate.

My estimate is that, at the very beginning of Perfect Team 20, the percentage of teams that were FTP might have been right around 90% --- with 10% of the teams PTP. Over time, the great majority of new teams introduced have been FTP, and the PTP % may be as low as 1 to 2% of teams. As a result of the relatively high PTP % early on, top cards were priced extremely high. The top cards have actually dropped in value considerably since then --- for example, I got perfect Yaz not long ago for 60k, when early on he was well over 100k.

Early on, historical bronzes and historical silvers were quite expensive relative to their quick-sell price, because all the FTP teams were filling up their rosters with those players. Just before collections came out, the great majority of historical bronzes were trading close to their quick-sell price, as these FTP players were no longer buying bronze cards. Most silvers had dropped in price as well, but the top golds and the low diamond cards were showing inflation as those were the cards that the FTP players were gobbling up, as they continued to improve their teams.

So what did collections do? Well, except for the temporary price inflation, it caused cards that were part of important collections to go up a whole lot on the auction house, but cards that were NOT part of collections had to go down in price to compensate. It's just that nobody looks at those cards because they are in low demand; they just see the high prices of the in-demand cards.

The one drawback in the preceding analysis is that new PPs are introduced into the system as a result of achievements; as are new (free) packs from challenge packs, as is additional money invested in PPs. So it is possible that the EV from opening a pack will have been increasing all along (price inflation) --- it is just hard to imagine (based on the previous analysis) that it could go above the price of a pack for an extended period.

This is where the new card introduction can play a role. If the new cards are at a higher tier than their value (as I think many of the All-Star cards are) then it reduces the percentage of gold, diamond, and perfect draws that are really useful cards. There are two other things that can play a role: if the influx of new players is sufficient to offset the gain in PPs (i.e. average PP per team stays relatively constant) then that can keep it balanced. The final thing is the removal of cards from "circulation" which currently happens when a collection is completed --- those cards can no longer be sold. So -EV collections (which most appear to be) can take these PPs essentially "out of circulation".

Thoughts regarding the previous analyses?

[dkgo]

Most of this is all pretty obviously right. The average return of a pack can never be more than it's cost. The one part that sticks out is how you got to the 960 number. Are the drop rates of cards listed somewhere?

[allenciox]

So the 96% comes from opening 250 standard packs and observing the average selling price (-15%) of the bronzes, silvers, golds, and diamond cards that came out of those 250 packs. I also looked at the selling prices of the non-live iron cards that came out. To estimate selling price of perfect cards, I looked at practically the entire universe of perfect cards on the AH over a period of time to estimate the average selling price, assuming that 70% were LIVE cards evenly distributed across all LIVE cards for those 70% and evenly distributed across all non-LIVE perfect cards for the others.

The expected % of each card type is published (right on the pack), so all I had to do was to multiply the average price of each tier by that percentage. The one tricky part is that the percentage of cards that are non-live iron cards is NOT listed anywhere, so I used the percentage that I got across the 250 packs for that percentage.

All of this analysis has been done post-collections, so the 96% could have been lower before collections came out.

The reasons I used -15% instead of -10% is the following:

1. Increasing the number on the AH for a particular card will cause average selling price to drop a bit.
2. There is effort involved in putting a card on AH and pricing it correctly. I assume that someone putting a lot of bronze and silver cards on AH is not going to micro-price it as effectively as somebody putting one or a few cards on.


For cards whose 7-day price was less than 15% above their quick-sell price, I used quick-sell price instead.

[HiDesertAce]

Originally Posted by allenciox

I actually have calculated this based on prices and it seems to be right around 96% --- opening a standard pack will, on average, get you back 960 PPs when listed on AH.

I think the actual average return is between 400 and 500 PP per pack. That has been my average return when i don't hit a big card in a 100 pack run and get LIVE diamonds. But thats based on a minimum of 100 packs being opened.



You get 1 bronze guaranteed in a pack. So the EV is 50 PP. 5 quicksell Iron and 1 quicksell bronze totals 50 PP. You can extrapolate this further with the odds: 1 in 20 silver; 1 in 50 gold; 1 in 150 diamond.



150 cards equals 25 packs.

7.5 silvers (we will round up to 8)

3 gold
1 diamond
25 bronze
113 iron


at quicksell pricing the "average" yields a total of 8990 PP

8 silver = 800 PP
3 gold = 3000 PP
1 diamond = 4000 PP
25 bronze = 625 PP
113 iron = 565 PP


8990 PP total is EV of 359.6 PP per pack based on opening 25 packs. I think that is most people's experience with packs unless they get "lucky"



I stopped ripping packs in large quantities before collections so that number doesn't reflect collections related cards that may sell for a lot more. I found that the amount of time I had to put in to post cards to sell on the AH was not worth it.



The overall market is trending downward and will continue to trend downward UNLESS there is a substantial influx of users at some point. As more packs get ripped there are more big cards that come out. And the pool of ppl willing to pay for those cards has basically remained the same--so the sellers have to lower prices in order to make the sale.

[dkgo]

the actual quicksell ev is super easy to calculate. its 426. a heavy portion is from diamonds and perfects though which take a lot of packs to regress towards the mean

assuming

1/5 bronze
1/20 silver
1/50 gold
1/150 diamond
1/1000 perfect

cant remember 100% if that is correct. also assumed that they are indeed fractions and not like 5:1 for bronze

[Dogberry99]

I disagree with the premise that cards not involved in missions have seen a decrease in price or value. As missions have been introduced, those cards have seen no change.

This is something that I have been in a position to notice. Beyond pursuing various themes (Rangers, names that include colors, Browns before they became a mission, et al), I have been pivoting to focus on potential future collections.

[eldur00]

I must have been ripping packs wrong because my average is a lot closer to 96 PP than 960 PP.

[bailey]

This efficient market theory only works if millions of people are playing the game daily. PT is more like a back of the back room and out in the alley kind of transaction. I have 19 historical perfects on my team. How many packs need to be ripped to get 19 RANDOM historical perfects? How many packs need to be ripped (by everyone) to supply enough Cy Youngs, Walter Johnsons, etc that all the best teams have? If I think about it too long, maybe Mr. Market Maker is Mr. Markus himself, supplier and buyer of last resort to keep prices reasonably stable.

[One Great Matrix]

If you're not caught up in the 1% of the team's in the 'verse on your schedule every month & remember that each member of the 'verse processes..? things differently, you can think of the 'verse as wide open.

Kind of a simple take but not often mentioned.

A couple times I've opened up the universe tab and pictured 15 PT games going on in each honeycomb baseball hexagon.
This helps me step outside my league.

[allenciox]

	Std	Gold	EV/card	EV/std	EV/gold
Iron	3.612	3.612	8.3	30.1	30.1
Bronze	2.000	1.000	38.6	77.2	38.6
Silver	0.250	0.250	364.8	91.2	91.2
Gold	0.100	1.100	1944.4	194.4	2138.8
Diamond	0.033	0.033	11514.0	383.8	383.8
Perfect	0.005	0.005	37100.0	185.5	185.5
Total:				962.3	2868.1

The values that were computed from the 250 packs are in the EV/card column. The way the values were computed was:

For irons, all LIVE cards were set to 5 unless they were close to 60: 59 was valued as 10, 58 valued as 8,57 valued as 6. (This is because of possibility for them to go up to next tier). All non-live irons were valued based on going price on AH -15%

For bronzes, all LIVE cards were valued at 25 unless they were 69 (40),68(35),67(30). All historical bronzes were based on max(AH - 15%,25)

For silvers, all cards based on max(AH - 15%,100)

For golds, all cards based on max(AH - 15%,1000)

For diamonds, all cards based on max(AH - 15%,4000)

I already mentioned how I valued perfect cards --- I only drew one in the 250 decks, so it wasn't realistic to value it on that one's AH value. As mentioned earlier, all of these decks were opened, and their values calculated, after collections were in place.

All other values except that one column are calculated based on known rates.

[Marleigh]

Originally Posted by eldur00

I must have been ripping packs wrong because my average is a lot closer to 96 PP than 960 PP.

Thats because this expected value is based on spending $200 or so on packs, or getting extremely lucky with diamonds/perfects. if i am reading the tables right the EV if you don't hit a gold is under 200. it is basically confirming the fact that the only people who should spend on packs are people who can afford to spend 100s if not 1000s.

[allenciox]

Agreed, Marleigh, that variance is a thing. The last 15 packs I opened did not have a card above bronze --- total return from those 15 packs was about 2000. The great majority of packs you open are going to be of that nature. There are two sides of the variance coin, however. Suppose someone has three teams (or even six, for those that have bought two licenses). They could decide to have each of them open a bunch of packs, and if one of the teams gets lucky, focus on that team for promotion, ignoring the other teams.

I am not saying that everyone should do that, but it is a possibility. All my teams are FTP. Over 200 of those 250 packs were opened on one team (the other packs have generally been challenge mode packs). The reason that FTP team was able to open over 200 packs was that it got some good luck early on --- selling those players gave additional PPs to open more packs.

But note what would happen if packs were +EV. Then the best play for someone would be to open an infinite number of packs in that situation. That's why they can't be +EV.

[Marleigh]

What they do in other modes like this is have different tiers of packs, for instance Ultimate Team has bronze/silver/gold packs in which the maximum pulls you can get are those cards, that removes variance, so maybe the introduction of a pack where you can pull maximum silver with a lower cost would be an idea, it enables people who aren't spending loads to have some fun opening packs, and they can potentially get some cards worth some PP.

I just think that the game isn't sustainable when its targeted so heavily at whales and hope that tournaments aren't.

[Dogberry99]

There are a lot of lower live irons that currently sell for a lot more than 5. Some are because of post-mission speculation, others because they are newly introduced cards. Either way, the current EV model does not account for the large number of cards selling regularly (based on both historic and last 7 averages) for double digits and the smaller amount that are hitting triple digits.

And this doesn't even touch on the current high prices for many live cards at higher tiers...

[QuantaCondor]

Originally Posted by allenciox

On the other hand, if opening standard packs (my guess is that >95% of packs that are opened are standard packs) were strongly -EV, everyone would stop spending PPs on packs and buy on AH. That would drive up prices on the AH and, once again, restore the equilibrium.

Nonsense. PT players are not rational actors, and opening a pack has nonzero utility. That is, the "fun" value of opening a pack has a real value in terms of amount of PP. I don't care how accessible the secondary market is, people who play card games want to open packs because opening packs is fun. The majority of the economy will be dominated by these people, and AH max EV value-oriented types will always be in the overwhelming minority.

[allenciox]

By the way, based on numbers above, I ran a couple of simulations. The first simulated opening one million decks. Even though the mean deck value (on one million decks opened) was 961 in the simulation, 50% of the decks opened were worth 145 or less, and 75% were worth 230 or less. Only about 15% of the decks paid back more than the cost of the deck.

I then ran a simulation of 10000 people opening 100 decks each. The mean result was a return of 96,300 PP (for 100,000 PPs spent on the decks). However, the median return was about 86,300, and about 35% returned more than the 100,000 PP put in.

[QuantaCondor]

Two more misunderstandings in this analysis: listing 1500 cards on the AH at carefully calculated prices has a very significant time utility value. The person who is doing this accumulates a nonstandard amount of EV. Most people will not even bother listing iron or bronze cards, and some wont ever list silvers either. So you can't just assume people will be flooding the AH with their pack contents, most will not be willing to pay the time cost of recouping full auction value.

Further, pack EVs in card games are notoriously skewed due to very expensive pulls. It's hard to get a good sample with even 250 pulls, since even one or two way above average pulls can thtow off your dataset. Hell, you only pulled a single perfect, and a handful of diamonds, how can you claim that to be a representative sample? The error bars are huge.

EDIT: The simulation helps your argument some, but it reveals that the bankroll you need to assure good EV is enormous. Also, this is a teambuilding game, not "who can be the lucky 15% who cashes in for positive EV". EV when it's skewed like this is flawed as a market driver unless you have an absolutely titanic bankroll. And even then, with all the time cost involved, it's still negative EV to open packs. Unless your team is garbage and you're desperate to maximize variance lest your team wallow in obscurity, AH remains the best way to spend spare PP by a long shot.

[dkgo]

250 packs is small potatoes and not going to give you a good sample of all the cards, especially at high levels where the real ROI comes from.

Obviously extrapolating those numbers to 100,000 packs or whatever is going to come out with the same average. I still think that 960 number is super questionable.