Surprise! The worst pack type for the money is....

[allenciox]

historical packs, and it isn't even close. Just for fun, I thought I would figure out average EV (expected value) of each pack type. Below are the results, copied from the spreadsheet: the Expected Value for each card type for each pack type and a total at the bottom.

card-type:	sellval	stdpack	gpldpac	diampac	histpac	P(card)
Iron-live	5	12.64	12.64	12.64	0.00	0.506
Bronze-live	35	49.00	24.50	24.50	0.00	.140
Silver-live	150	26.25	26.25	26.25	0.00	.035
Gold-liv	1040	72.80	800.80	72.80	0.00	.014
Diamond-live	4000	93.33	93.33	2893.33	0.00	.005
perfect-live	20200	70.70	70.70	70.70	0.00	.001
Iron-hist	30	32.51	32.51	32.51	108.35	.217
Bronze-hist	75	45.00	22.50	22.50	75.00	.060
Silver-hist	850	63.75	63.75	63.75	212.50	.015
Gold-hist	2300	69.00	759.00	69.00	2530.00	.006
Diamond-hist	21000	210.00	210.00	6510.00	700.00	.002
Prefect-hist	55000	82.50	82.50	82.50	275.00	.000
		       827.48	2198.48	9880.48	3900.85	1.00
	        cost:	1000	3000	12000	10000	
		return: 82.75%	73.28%	82.34%	39.01%

To explain the table, std packs, gold packs, diamond packs, and historical packs are shown with expected "sell" values for each pack. This is assuming the values in the sellval column for each type. I feel that these should be accurate for live card values after the last update this week (at that point probably everybody will quick-sell all their duplicates iron lives at least).

The numbers at the third-to-last row (827.48, 2198.48, 9880.48, and 3900.85) represent the total of the numbers above them and are the net expected value of each deck type.
The numbers below that are the nominal cost of each deck type (last time diamond decks were offered, they sold at 12k, and historical, when they were offered, sold at 10k).
The last line shows the percentage return estimated for each deck type. Except for historical packs, they are all between 73% return and 83% return. However, historical packs show only a 39% return: They appear to be worth less than twice as much as a gold deck.

To be honest this was a big surprise to me. I think a lot of the reason is the way the FOTF collections have been structured: Most of the collections require the great majority of the silvers to be collected, but require half or less of the gold cards to be collected. As a result, historical golds generally sell for less than twice their quick-sell value, while silvers sell for 6, 10, or even 15 times their quick-sell value in most cases. So the guaranteed card in historical packs aren't worth much more than their trade=in value.

You might quibble with the sell values I give above, but you can run the numbers for different values. I think any realistic values will show the same overall result.

[ScudDawg]

Good stuff.

[getalife1798]

[JPaq14-2]

Originally Posted by allenciox

historical packs, and it isn't even close. Just for fun, I thought I would figure out average EV (expected value) of each pack type. Below are the results, copied from the spreadsheet: the Expected Value for each card type for each pack type and a total at the bottom.

card-type:	sellval	stdpack	gpldpac	diampac	histpac	P(card)
Iron-live	5	12.64	12.64	12.64	0.00	0.506
Bronze-live	35	49.00	24.50	24.50	0.00	.140
Silver-live	150	26.25	26.25	26.25	0.00	.035
Gold-liv	1040	72.80	800.80	72.80	0.00	.014
Diamond-live	4000	93.33	93.33	2893.33	0.00	.005
perfect-live	20200	70.70	70.70	70.70	0.00	.001
Iron-hist	30	32.51	32.51	32.51	108.35	.217
Bronze-hist	75	45.00	22.50	22.50	75.00	.060
Silver-hist	850	63.75	63.75	63.75	212.50	.015
Gold-hist	2300	69.00	759.00	69.00	2530.00	.006
Diamond-hist	21000	210.00	210.00	6510.00	700.00	.002
Prefect-hist	55000	82.50	82.50	82.50	275.00	.000
		       827.48	2198.48	9880.48	3900.85	1.00
	        cost:	1000	3000	12000	10000	
		return: 82.75%	73.28%	82.34%	39.01%

To explain the table, std packs, gold packs, diamond packs, and historical packs are shown with expected "sell" values for each pack. This is assuming the values in the sellval column for each type. I feel that these should be accurate for live card values after the last update this week (at that point probably everybody will quick-sell all their duplicates iron lives at least).

The numbers at the third-to-last row (827.48, 2198.48, 9880.48, and 3900.85) represent the total of the numbers above them and are the net expected value of each deck type.
The numbers below that are the nominal cost of each deck type (last time diamond decks were offered, they sold at 12k, and historical, when they were offered, sold at 10k).
The last line shows the percentage return estimated for each deck type. Except for historical packs, they are all between 73% return and 83% return. However, historical packs show only a 39% return: They appear to be worth less than twice as much as a gold deck.

To be honest this was a big surprise to me. I think a lot of the reason is the way the FOTF collections have been structured: Most of the collections require the great majority of the silvers to be collected, but require half or less of the gold cards to be collected. As a result, historical golds generally sell for less than twice their quick-sell value, while silvers sell for 6, 10, or even 15 times their quick-sell value in most cases. So the guaranteed card in historical packs aren't worth much more than their trade=in value.

You might quibble with the sell values I give above, but you can run the numbers for different values. I think any realistic values will show the same overall result.

Cool! Historical packs are still my favorite, but with this advice I would never buy them (just open them from missions). Thanks!

[dkgo]

Aren't the rarity odds different in historical packs though? According to this you average 3-4 irons and just 1 bronze per historical pack which definitely isn't true. I think I remember when they were introduced the dev team telling us this and that they were also open to adjusting the pull rates in them.

I do agree they are the worst since you generally want to be maximizing your chances at getting a super high value card with as many lottery tickets (standard packs) as possible.

[Grish]

It looks like you listed the price for a Diamond pack at 12K when they actually cost 15K. I do see that you mentioned they were once sold for 12K. I missed that pricing but the last two times they were 15K.

[rudel.dietrich]

I also have to wonder if using PP value is the best way to do this.
I mean, that is the only value system we have so I understand why it is used. But it is hard to put a value on a historical perfect because sooner or later the sell value to you is meaningless because you are going to want those cards on your team.

I wonder if instead of expected value if we looked at % of drop rate per PP if this would come out any different?

The regular card pack is indeed more bites at the apple. But the guaranteed historical cards may even it up?
If the ultimate goal is landing those historical perfects and diamonds I wonder which route is more economical.

It may turn out that your research is actually true. But I wonder if we could run it not as return on value in terms of points, but needed packs to land historical perfects and diamonds.
Or can we even agree that is the end goal to all this?

[allenciox]

Thanks, Grish. Yes, I see that diamond packs are now available and listed at 15k. It imight have been a "special" sale when they were reduced to 12k. it thought it was like gold, where they permanently reduced the cost to 3k from 5k.

That makes diamond EV about 65.9% of cost --- lower than Gold but higher than Historical. And so the numbers decline going from left to right.

Finally, dkgo, now that historical card packs are offered again, I can see the odds are stated on the pack. It shows the odds for silver as being 1:10, which makes it twice as high as other packs (I just assumed it was the same for all the packs --- and for gold, diamond, and perfect, it is). However, it does not say on pack what the probability of drawing a bronze is. But I do seem to recall seeing more bronzes than normal when opening diamond packs, so I increased (in my spreadsheet) the probability for bronze to .35, meaning that about half the cards are iron cards.

Making thse changes does bring up the value of an historical pack to 4139.60 giving it a return of 41.4% --- still significantly lower than other packs, but not "as" low.

[noragar]

In 192 Historical packs, I've gotten 555 Bronze and 292 Iron, so assuming a nice round number, I would guess that Bronze is twice as likely as Iron. It might also be that all the Bronze/Iron are put into one pool and more Bronzes come out because there are more Bronze Historicals than Iron.

For what it's worth, the rest of my pulled distribution is 2 Perfects, 4 Diamonds, 213 Gold, and 86 Silver.

[ronhatch]

Not a surprise at all... you just have to think about the math of it the right way.

You can buy 10 regular packs for the price of 1 historical pack, so IF historical cards dropped at a 10% rate, you'd tend to get 6 historical cards from the 10 regular packs... plus an additional 54 live cards. In other words, the SAME number of historical cards plus 54 additional cards that will also have at least SOME value. (Good luck with the tedium of selling those, though.) With the actual drop rate in regular packs being 30%, obviously the regular packs will net you more historical cards for the same value unless you're extremely unlucky.

(But yes, the historical packs are skewed slightly upwards in value because the irons are less common in them. When you've got a 3x multiplier to make up for, though, it's not going to get you very far. Historical irons in regular packs seem to drop at about a 15% rate, so you're still likely to get more of them in the 10 packs than the 1.)

[dkgo]

A very simple way to think of it is that you are paying 8000 vs 1000 for 5 cards assuming you can sell the gold for 2K. Is a historical diamond/perfect worth 8x as much as a 30/70 split? I doubt its worth 8x as much as just a live

[tbonetim]

Originally Posted by dkgo

A very simple way to think of it is that you are paying 8000 vs 1000 for 5 cards assuming you can sell the gold for 2K. Is a historical diamond/perfect worth 8x as much as a 30/70 split? I doubt its worth 8x as much as just a live

Yep, and at this point most historical gold cards are only worth about a couple thousand points at best now that the FOTF missions are over with. Even before the FOTF missions wrapped up, nearly every historical gold aside from a few that went for maybe 5K were only selling between 1.6 and 2.4K.

The steep price for high chance of small return does keep people from buying tons of those packs and snagging more historical Diamond and Perfect cards so as not to flood the market but I won't be dropping points on them.

[tehsuigi]

Tampa's golds are still going for five digits, and it's frustrating.

[Tinkerman]

Originally Posted by tehsuigi

Tampa's golds are still going for five digits, and it's frustrating.

I haven't pulled a single TB Gold+ from well over 10,000 packs. If that's common, it's no wonder they're expensive...

[Biggio509]

Originally Posted by rudel.dietrich

I also have to wonder if using PP value is the best way to do this.

If you still have face of the franchise missions available this skews things some. The historical packs give a better chance at getting something that applies to one of these. Maybe it is FOF missions but I seem some really ridiculous prices trying to buy even an Iron guy who I need to complete a set. You are paying at least the price of one tier up if you try to buy guys for the FOF missions. Iron guys going at 450. Bronze sometimes over 1k. I can buy a diamond live card for the price of a gold FOF mission card.

[bailey]

Originally Posted by Tinkerman

I haven't pulled a single TB Gold+ from well over 10,000 packs. If that's common, it's no wonder they're expensive...

There are at least 861 historical golds, so even in 10,000 packs that chances of getting a specific one is probably small. Statistically, I wonder how many different ones you should expect to get in 10,000 packs and how many would you need to open to have a 50% chance of getting them all? (For the record, 1 got 1 TB gold in 1800 packs).

[ronhatch]

Originally Posted by Biggio509

If you still have face of the franchise missions available this skews things some. The historical packs give a better chance at getting something that applies to one of these. Maybe it is FOF missions but I seem some really ridiculous prices trying to buy even an Iron guy who I need to complete a set. You are paying at least the price of one tier up if you try to buy guys for the FOF missions. Iron guys going at 450. Bronze sometimes over 1k. I can buy a diamond live card for the price of a gold FOF mission card.

Actually, the historical packs don't give a better chance... unless you specifically need the gold tier. That's exactly what my point was above, you'll get MORE historical cards from standard packs than historical packs because the drop rate is higher than the price ratio.

Grouping together 10 packs at a time, I can see that I got 11, 12, 9, 13, and 11 historical cards in the last 50 packs I opened. Granted, only four of those were gold instead of the five I would have gotten from the equivalent value of historical packs, but since I saw so many more cards my odds of getting a diamond or perfect were much higher. Not that those odds EVER get to anything reasonable, but you need to open a LOT of packs and historical is NOT the way to do that.

[Tinkerman]

Originally Posted by bailey

There are at least 861 historical golds, so even in 10,000 packs that chances of getting a specific one is probably small. Statistically, I wonder how many different ones you should expect to get in 10,000 packs and how many would you need to open to have a 50% chance of getting them all? (For the record, 1 got 1 TB gold in 1800 packs).

I've pulled roughly 450 historical golds, with a good spread across all teams. Not a huge anomaly that I haven't gotten any TB, but it's the most obvious oddity from my pack ripping.