MMO blogger dives into the theoretical math behind lockboxes

MMO blogger Serrenity, whom many of you will recognize from his clever comments here on MOP too, has a compelling blog post on his personal site today diving deep into the lockbox debate. But far from merely offering another exhortation to stop buying lockboxes, he’s doing some complicated napkin math (and by napkin math, I mean python scripting) to try to understand why publishers are so fixated on selling them.

Since studios are generally not in the business of handing out detailed sales figures and drop rates, Serrenity is forced to calculate potential revenue based on publicly gathered data, which he admits upfront result in rough estimates. “This information is purely extrapolated and used for demonstrative purposes,” he warns.

Using Guild Wars 2’s wiki data on drop rates for the bank access token, he finds that the revenue from selling lockboxes vs. selling that item directly increases 14-fold – almost 1500% higher. And that’s just a minor, relatively undesirable item with a relatively high drop rate; admittedly, nobody’s going to go ham buying lockboxes just for that (we hope, anyway). Plugging rarer, desirable drops that would cost much more upfront (like weapon skins) into his formula sees the estimated revenue soar as high as 12500%. That is not a typo.

Granted, his calculations cannot take into account the fact that it’s fairly unlikely that most people would spend $1200 in lockboxes trying to get a sword, so that isn’t guaranteed money for a game at all. What we’d really need are better stats on gambling-minded whales vs. non-whales to see how much more money whales generate vs. the rest of us who nope right out of anything with a .1% drop rate. Any studios wanna pony up? Other than, you know, Star Citizen?

“It’s not hard to see that lockboxes theoretically generate orders of magnitude more revenue than direct sales,” Serrenity concludes. “From a business perspective, locking desirable items behind chance mechanics just makes good sense. But at this point, trading real money for a chance at a valuable object makes lockboxes seems a little bit more like gambling than video games.”

Source: level-42
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Anthony Clark

It’s gambling plain, and simple.
The courts missed it.

I leave games that add these, and don’t buy them if they do have them.

More people need to boycott if any change is to be seen.

dixa
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dixa

It needs to be recognized as gambling and subject to the same regulations

Too easy for a 12 year old to buy a steam wallet card at a grocery store with their allowance and blow it all on lockboxes.

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Sally Bowls

I don’t understand this. At all.

Are there [m]any people who would buy a lockbox key in order to get an Instant Bank Access???

Definition: the expected value of a discrete random variable is the probability-weighted average of all possible values. In other words, each possible value the random variable can assume is multiplied by its probability of occurring, and the resulting products are summed to produce the expected value.

Isn’t the value of the lockbox the “expected value” of the lockbox, the sum of the product of the value times the probability of the item. So lockbox that costs 84 gem has an expected value, in gems, of (.182+25)+(.265*24)+(.201*180) …. I didn’t bother to look up all the prices to see if the EV of the lockbox is greater than the cost. ( I greatly preferred SWTOR’s system where you could sell the contents. You could buy the lcokbox for credits and sell the contents for credits; most times for less than the purchase price but the rares meant it tended to average out a net profit.)

How is looking at one of less valuable of two+ dozen items in a box in any way informative as to the value of the box?

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Serrenity

It was really just a data point I picked honestly, because it was first in the list on the GW2 wiki and had a higher drop rate. I don’t think anyone is buying ‘all teh bank’ access tokens via lockboxes. That’d be silly.

You make a good point about expected value (which is … interesting to say the least — I have part 2 going up today talking about the legality of all of this, and value is pivotal). I made the broad, general assumption that the actual value of the lock-box is going to normalize out to slightly below the expected value because that’s what keeps people coming back–if the actual value met or exceed the expected value – people wouldn’t buy as many lock-boxes. If the actual value trends too far below the expected value, people won’t buy as many lock-boxes because they can’t maintain the fantasy that it *can* be worth it.

Keeping in mind that this kind of math is looking at populations and averages — not individuals.

FWIW, this is the full output from my calc on a rare skin, with a .1 drop-rate

Rare Armor Skin:
800 gems / skin, .1% drop

Direct Sales
Per Item Cost: $10.00
Total Direct Purchase Revenue: $10.00
# Items Acquired: 1

Lockbox Sales
Per Item Cost: $1,253.72
Lock Boxes Purchased: 1007
Total Lockbox Purchase Revenue: $1,253.72
# Items Acquired: 1
# Losses: 1006
Standard Dev: 28.5861067885

Theoretical Revenue increase of 12,527.2%

Again, I know my math is flawed because there are too many variables that I don’t know about but I wanted something to give an idea. I might refactor the script to calculate the expected value based on the data in the GW2 wiki.

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Schmidt.Capela

The math is off because it doesn’t consider the value of the unwanted items the player got. For most lockbox-like deals the average value of what comes in a box is slightly more than the value of the lockbox itself.

Though, of course, just the fact the player was forced to get a large number of unwanted items in order to acquire something he or she desired is already one heck of an ethical issue.

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Serrenity

Right. Because its pretty much impossible to quantify that ‘unwanted’ factor and the probability associated with it. the only thing I could reasonably calculate was revenue that would be attributed in the attempt to get a single item … or to reach a certain number of items in the game world. The better metric is probably the cost per item — which in the rare skin scenario was $10 in direct sales, and I think $1,300 for lock-box with a .01 drop rate.

But even still, the calc is still, by necessity, incomplete.

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Schmidt.Capela

Yeah, it can’t be calculated because it’s subjective, as it depends on whether the player is interested in, or even has a use for, more of the items that can come from the lockbox. If the player is actually interested in any and everything that can come from the lockbox, purchasing them might even be a good idea.

One such example is LoL’s mystery gift. It’s a bit convoluted because players can only purchase those as a gift for someone else, but it’s basically a lockbox that costs 490rp and is guaranteed to contain a skin worth at least 520rp that the receiving player doesn’t yet have; for anyone that wants to have all skins it’s actually a very good deal, people here often pay other players real money for them to give a mystery gift back.

For the most part, though, even “fair” lockboxes are basically a scam meant to make players purchase a lot of things they don’t want or need in order to get the one thing they want.

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thirtymil

What would be interesting (for me, anyway) is to see how the curve drops off as the price goes up. I’m pretty sure if auto manufacturers hid their cars behind a lockbox-type scheme it’d be a massive profit-denting failure (“Oh, you wanted the family estate with luxury extras… shame, you got the 1 litre hatchback. Another go?”). Games are only really getting away with it because, much like the lottery, the cost per transaction is small.

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Jeffery Witman

They have been small costs, relatively, but that’s changing quickly. The MICROtransactions of the past are giving way to much larger cash shop prices and lock boxes are following the trend. The more they see lockbox potentials at over $1000 revenue for a simple item, skin, or service token, the more they will push the cost to its limit (and probably well beyond that limit, too).

They’re not really doing anything new here. It’s just a fancy looking slot machine, except you’ll never actually get any money back.

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thirtymil

Yep, agreed. That’s why I’d like to see what happens as price increases – I mean, some of the limited ESO houses are £80+ – how long before someone puts three of those in a lockbox and asks you to hope you get the one you want?

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Utakata

So the tl,dr of this story is that game companies move their inventory much better in a spectacular fashion through lockboxes than posting it up on their cash shop? That seems entirely profitable in the disingenuous to the “T”. /bleh

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John Bagnoli

Excellent read. Fix the 3rd sentence in the second paragraph.

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Serrenity

Thanks – the downfall of self-editing :D

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NeoWolf

It’s less about its profitability and more about its morality. As I said in the article the other day there are ways of making money and then there are ways of making money.

For example I could make a heap of money growing and selling drugs..but I don’t, because it is morally and legally wrong.
Money cannot and should not be the only defining factor for a person, a business, a compnay or indeed a nation.. there simply needs to be more consideration and concerns for others than how much we can make off them a middle ground if you will.

Lockboxes are a reprehensible money making methodology and everyone..even those who buy them would prefer it if a less douchey method of making money while providing us desireable content existed.

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Serrenity

Oh for me it has a HUGE moral component, but I’m trying to approach from a demonstrable point of view. It’s easy to point to a 15,000% increase in profit and say “that feels greedy” than it is to point at the practice and say “that’s immoral.”

I also don’t consider the two statements mutually exclusive.

styopa
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styopa

So…how do you feel about states selling lottery tickets?

I fail to see how that’s ANY different than lootboxes.

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Serrenity

Heavily regulated? 6 in 49 model has published probabilities, money generated benefits the states / people in the state instead of lining Booby Kotick’s pockets?

styopa
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styopa

Regulated?
http://www.pennlive.com/watchdog/2017/09/defying_the_odds_part_1.html
IL’s most frequent winners are 3 people from WI.
They’ve each won $600+ precisely 120 times.
Their total winnings (each) are exactly the same at $45,981.

And fwiw the money generated from lootboxes ALSO benefits the state in higher tax revenues from that business….just less directly. One could also assert that it employs people as well.

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Utakata

So are casinos. And yes you can lose your shirt there as well if folks are that wreckless.

However, lotteries or casinos are not lockboxes. Where one drops money onto a chance for digital items that can only be used in the game those items are procured. So they are not even remotely close that way.

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NeoWolf

Exactly, here in the UK (and im sure elesewhere) the national lottery gives 40% of all money generated to national or charitable causes that help or improve peoples lives.. I doubt there are many MMO developing studios who can make that claim :)

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Utakata

Err…

whYfFDU.gif
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Schmidt.Capela

Where I live, the government actually got into the lottery business to undermine organized crime. One of the main sources of income for organized crime was illegal gambling, so the federal government created a nation-wide lottery (or three) with a larger prize pool than any criminal organization could provide, making it more attractive to the common person.

Gambling is a governamental monopoly here, BTW; the private exploration of games of chance was banned over seven decades ago, thus there are no (legal) casinos, betting houses, slot machines, etc. If you want a legal outlet for gambling here your only option is one of the official lotteries, and those cut down the amount of gambling someone can do because there’s at least a full day between two drawings.

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Stropp

Personally, I think that states selling lotteries is state sanctioned exploitation. A way to tax the gullible.

A friend did the calculations a few years ago and figured out that if a person who spent $10 on lotto, instead put it into a superannuation style account (I think that’s 401K for USians) after about 40 years they’d end up with more than the average highest winning prize. (Bear in mind that is in Australia and when he worked it out the top payouts were only 1 or 2 million. These days they’re in the 20 – 50 range I think. Hardly close to the huge US payouts.)

The point being, if someone was diligent they’d have a almost certain chance of retiring wealthy as opposed to a tiny chance of winning the lotto. Of course, getting people to be diligent with their savings is an entirely separate matter.

dixa
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dixa

A 12 year old can’t buy a lotto ticket.

A 12 year old could buy a scratcher from the machine but would not be able to redeem any winnings, their parents or guardian would have to which would alert the hopeful non-degenerate parent that their 12 year old is gambling

A 12 year old can buy a steam wallet card or an Xbox or PlayStation card at a grocery store for cash, gamble on lockboxes and the parents wouldn’t know unless/until the kid developed an addiction to the gambling and started doing something perhaps illegal to gain more money to buy more cards to buy more lockboxes.

It is gambling just like state lotteries, and it needs to be regulated the same way.

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Serrenity

Thanks for the Feature Bree :-) I was thinking we spend so much time on here arguing without specifics, I was thinking “what would specifics look like?” so I figured I would write a script to calculate it. I’m hoping to make it a little bit more robust then throw it up online to let people plug in their own values to see theoretical revenues.

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Schlag Sweetleaf

$

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rafael12104

Awsome. Lol. The zoom in is perfect. Lol!