Data-driven collecting: blind bag figures

[Halichoeres]

In addition to dinosaurs, I casually collect Lego products. Right now they're selling minifigures of the characters from The Simpsons. There are 16 in the series and they are sold singly in blind bags. I got to thinking about how many I would need to buy to guarantee that I got the whole set. My intuition was that the probability that each successive blind bag that I opened would yield a new figure was different from the probability of the preceding bag, given that the preceding bag had yielded a new figure. After banging my head against some conditional probability calculations, I consulted Google, and found that this is a well-known, solved problem. It's called the The Coupon Collector's Problem.

If n is the number of objects in a set, then the average number of packages we'll need to open to complete a set is:

n/n+n/(n+1)...+n/1

The solution depends on an important assumption: The likelihood of drawing any particular object is equal to the probability of any other. This is violated if any figure is significantly rarer than the others.

When you apply this to the Lego minifigure set, this yields an astonishing answer: I have to open 55 blind bag packs to get the whole series, which at $3.99 apiece, means I'm spending more than $200.

What about the Jurassic World blind bags? If you are the sort of collector who needs all variants, there are 36 objects, but each blind bag has at least one of the 12 object classes (species in our case). So let's take the Indominus figure and consider it alone. Almost all blind bags have only a single Indominus figure, and there are three known variants, so the formula yields

1+3/2+3 = 5.5

but Walmart gets mad if you try to buy half a 15-pack, so we must round up and buy 6 blind bags. But that's just for the Indominus. Most bags have only a single Allosaurus, so you might not be lucky enough to get all 3 Indominus and all 3 Allosaurus with only 6 bags. That might be okay because aside from the Indominus, you can get most other figures in the 3-packs. But where they really get you is the variance. I said that the AVERAGE number of bags you would have to buy is 5.5, which means that about half the time, you'll come up short! The variance for a random trial like this is given by a similar equation to the one above and rises extremely rapidly. For our example, to have 90 percent confidence that you have a complete set, you need to buy 9 blind bags. That's over $130.

I wanted to calculate this for the Walking with Dinosaurs 3D figures, but I'm not quite sure how because the Pachyrhinosaurus figures are each twice as common as, say, Troodon. I got a complete set with 22 bags, but I suspect I was at the lower end of the distribution (i.e., I got lucky). Of course, I didn't want a full set in the first place, just 5 of the minor characters. So it was particularly wasteful from my perspective.

This is probably the future of collecting. A Safari Ltd. Toob has 8 or 10 figures and you buy it one time and have the complete set. What if they instead sold a single dinosaur miniature in a little bag? How many would you buy if they were the same unit price, about a dollar each? It's ingenious and cynical and guarantees that at least some subset of consumers will spend a fairly foolish amount of money. So as collectors, I think the best defense is not buying blind bags. But if we were the sorts of people with that kind of self-restraint, we probably wouldn't be on this forum.

Our second best defense is trading. If you're buying blind bag figures and you have extras, post them! Someone else might have complementary extras, especially if none of the figures are rarer than others.

[CityRaptor]

Well, you could always grab touch the bags and feel for the shape inside.  Worked quite well for me. Naturally it is a bit of a problem with color variants, but it works for different molds, even if the number of different Pachyrhinosaurs in the WWD bags was a bit of a challenge.

[Halichoeres]

That's true, you can do that sometimes. That's not useful with the JW bags, if you want all the variants. (If you don't care about variants, one bag is sufficient, because it has every sculpt). With Legos that's a little harder because they all have big round heads, although a few very distinctive ones can be detected. I bought my WWD figures online, so I got very lucky indeed.

Speaking of which, I just now thought of a potential solution: double-counting the double-packed figures. It becomes equivalent to an 18-item instantiation of the problem, which would require about 60 tries!

[joossa]

When it comes to trading cards and blind bag figures and I am adamant about getting a full set or getting a particular figure/card, I strongly prefer to buy the set or the single card/figure off Ebay/Amazon, even if it's slightly price-inflated. Not worth the risk to me.

Halichoeres, you demonstrate your point nicely, though and I agree with your first stated defense. The downside is, I think and based off what I have seen, that blind bags really appeal to younger kids who badger their parents into buying them the bags. And it's likely neither of those parties will understand that the company/manufacturer is trying to make money in the way you have stated.

[stargatedalek]

I'm not against it, because most of the time I ed up saving money since I don't need to buy a complete set.

Of course if I'm going to buy the complete set anyway, that is preferred, but many manufacturers offer both. JW did and WWD did (but left out the pterosaur the most important one!)

[Kayakasaurus]

I've never boughten a Lego blind bag without knowing what's in it. I've gotten a LOT of them, and only guessed wrong once, when I first started. It only takes a few seconds to find the hat or accessory, and then you know. I like to buy multiples of the historical figures. I have 10 of the Roman guys lol. I've also found that some seem to be much more common, and others are hard to find; There was one figure in particular that took forever to find.

[Halichoeres]

When it comes to trading cards and blind bag figures and I am adamant about getting a full set or getting a particular figure/card, I strongly prefer to buy the set or the single card/figure off Ebay/Amazon, even if it's slightly price-inflated. Not worth the risk to me.

I actually think that's a smart move. Based on this, I think that most sellers are, if anything, slightly undervaluing complete sets--unless they're buying in such extraordinary numbers that they can complete many sets.

I'm not against it, because most of the time I ed up saving money since I don't need to buy a complete set.

Of course if I'm going to buy the complete set anyway, that is preferred, but many manufacturers offer both. JW did and WWD did (but left out the pterosaur the most important one!)

Do you mean the 3-packs?

I've never boughten a Lego blind bag without knowing what's in it. I've gotten a LOT of them, and only guessed wrong once, when I first started. It only takes a few seconds to find the hat or accessory, and then you know. I like to buy multiples of the historical figures. I have 10 of the Roman guys lol. I've also found that some seem to be much more common, and others are hard to find; There was one figure in particular that took forever to find.

That surprises me! You must have very nimble fingers. I guess I have to revise my thesis: our best (realistic) defense is your sense of touch! I think what I need to do is put my unfortunate doubles back into their bags and train my fingers.

Another unfortunate thing I've noticed is that some random toy lines are packed in boxes, which would probably render dexterity moot.

[Kayakasaurus]

Maybe my fingers are nimble  I enjoy doing it. It probably looks a little funny when a 17 yr old is feeling through every bag in the toy section. However, when I go to the Lego store I feel right at home with all the other Lego enthusiasts  (nerds)

[Halichoeres]

Maybe my fingers are nimble  I enjoy doing it. It probably looks a little funny when a 17 yr old is feeling through every bag in the toy section. However, when I go to the Lego store I feel right at home with all the other Lego enthusiasts  (nerds)

I assure you it looks even funnier when it's a 33-year old...

[stargatedalek]

We never actually got the 3-packs or blind bags, we got toobs like safari toobs. Each had half of the figures but they wanted to have that one Pachyrhinosaurus twice so the poor Quetzalcoatlus got left out. I don't know if it was a Canadian thing or a Toys R Us thing.

[Halichoeres]

We never actually got the 3-packs or blind bags, we got toobs like safari toobs. Each had half of the figures but they wanted to have that one Pachyrhinosaurus twice so the poor Quetzalcoatlus got left out. I don't know if it was a Canadian thing or a Toys R Us thing.

Huh! I've never seen those. That would be the way to go (except the pterosaur).