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Wednesday, August 24, 2016
Raph called it
In 2007 Raph Koster posted on his blog that there is a universal curve of player numbers over time which all open big virtual worlds follow. This week Bloomberg posted a chart showing Pokemon Go user numbers, and not only are these already declining, but they are declining in the slow fashion that Raph's universal curve suggests.
The reason I tried Pokemon go last month for about 3 days before deleting it for being boring was not that I am a Pokemon fan (sorry, I can't even name all 150 basic Pokemon), but because I recognized Pokemon Go as an "open world MMORPG". Just that the open world was a 1:1 copy of the real world, and thus sometimes has curious access restrictions. It does have the MMORPG network effect, becoming more interesting when more people play it, so it following the MMORPG user number curve is no surprise to me at all.
Note that while the general *shape* of the curve is universal, the time from start to peak isn't. World of Warcraft took a long time to peak (although one needs to mention that the WoW curve is the overlap of the curve of the base game with the curve of the expansions, which prolong longevity), while Pokemon Go peaked after two weeks. For me that "time to peak" is a general measure of how long the game can hold the interest of the players. For very simple games like Pokemon Go the time is rather short. But even for a complex MMORPG the time to peak can be as short as a month, if the game uses a lots of mechanics and features from previous games and is thus perceived by the players as not being all that new.
Blizzard stopped this year of reporting World of Warcraft subscriber numbers. But they are easy enough to predict. In a week or two the subscriptions will be back up to over 10 million, although less high than at the release of Warlords of Draenor. And a bit later the next phase of decline will set in, bringing WoW a year after Legion to less subscribers than a year after WoD. Because somewhere hidden below the quarter to quarter changes from each expansion is Raph's universal curve.
The reason I tried Pokemon go last month for about 3 days before deleting it for being boring was not that I am a Pokemon fan (sorry, I can't even name all 150 basic Pokemon), but because I recognized Pokemon Go as an "open world MMORPG". Just that the open world was a 1:1 copy of the real world, and thus sometimes has curious access restrictions. It does have the MMORPG network effect, becoming more interesting when more people play it, so it following the MMORPG user number curve is no surprise to me at all.
Note that while the general *shape* of the curve is universal, the time from start to peak isn't. World of Warcraft took a long time to peak (although one needs to mention that the WoW curve is the overlap of the curve of the base game with the curve of the expansions, which prolong longevity), while Pokemon Go peaked after two weeks. For me that "time to peak" is a general measure of how long the game can hold the interest of the players. For very simple games like Pokemon Go the time is rather short. But even for a complex MMORPG the time to peak can be as short as a month, if the game uses a lots of mechanics and features from previous games and is thus perceived by the players as not being all that new.
Blizzard stopped this year of reporting World of Warcraft subscriber numbers. But they are easy enough to predict. In a week or two the subscriptions will be back up to over 10 million, although less high than at the release of Warlords of Draenor. And a bit later the next phase of decline will set in, bringing WoW a year after Legion to less subscribers than a year after WoD. Because somewhere hidden below the quarter to quarter changes from each expansion is Raph's universal curve.
- posted by Tobold @ 1:10 PM Permanent Link
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You posted about Raph's blog at the time, I see. You're linked in the comment thread, which is an interesting read in itself.
My question is why should we care? It appears this is largely a description of a general trend common to many (most?) product types. That it also applies to MMOs is not particularly surprising or instructive.
One thing that does interest me, though, is whether MMOs are subject to the kind of post-launch spikes in customer interest that affect other consumer/leisure products. For example, it's not unusual for a book to do very poorly at the time it's first published, perhaps even to go out of print, and then re-appear to much greater interest and success five, ten, twenty, a hundred years later. Similarly, we're all familiar with the concept of a "sleeper hit" in Movies or Music. Is there any reason that couldn't happen to an MMO?
My question is why should we care? It appears this is largely a description of a general trend common to many (most?) product types. That it also applies to MMOs is not particularly surprising or instructive.
One thing that does interest me, though, is whether MMOs are subject to the kind of post-launch spikes in customer interest that affect other consumer/leisure products. For example, it's not unusual for a book to do very poorly at the time it's first published, perhaps even to go out of print, and then re-appear to much greater interest and success five, ten, twenty, a hundred years later. Similarly, we're all familiar with the concept of a "sleeper hit" in Movies or Music. Is there any reason that couldn't happen to an MMO?
I'm not even convinced that WoW will hit 10 million subs, and if they do they won't mention it. At least not anymore.
World of Warcraft subscriber numbers decline because Blizzard does not spend enough money on developing new content. And the excuse is always: They are working on the next expansion :)
Besides, I've noticed recently that the WOW team does not care much for veteran players. Getting new players to buy the game, subscribe and quit after some time must be easier.
And I agree that subscriber numbers will not go up to 10 million at Legion launch because Warlords of Draenor burned too much credit. I don't believe any promises the developers make claiming that this expansion will be different or that more content will be available or anything along those lines.
Still the game will be fun to play in Legion. New quests at least :)
Besides, I've noticed recently that the WOW team does not care much for veteran players. Getting new players to buy the game, subscribe and quit after some time must be easier.
And I agree that subscriber numbers will not go up to 10 million at Legion launch because Warlords of Draenor burned too much credit. I don't believe any promises the developers make claiming that this expansion will be different or that more content will be available or anything along those lines.
Still the game will be fun to play in Legion. New quests at least :)
You have argued this before, essentially by saying all curves of all kinds are the same regardless of they look like. World of Warcraft only "follows the curve" because no matter what its curve looked like, you would make the same claim. This, of course, makes the discussion entirely useless as you can not draw any conclusions from something that is the case no matter what.
The more rational analysis of nearly all MMORPGs is that they show a huge spike at the very beginning, and then taper off from then on. WoW and EVE did not do anything like this, they are very very different.
The more rational analysis of nearly all MMORPGs is that they show a huge spike at the very beginning, and then taper off from then on. WoW and EVE did not do anything like this, they are very very different.
@AlexF
Besides, I've noticed recently that the WOW team does not care much for veteran players.
What a weird thing to say. Do you actually believe this? I will never understand the motivations players ascribe to developers. "They don't care about X" is almost never true of any developer. I don't know why you think otherwise but...developers, shockingly, want people to enjoy their game. There are lots of reasons for why games may not be enjoyable to any given person but "not caring" is generally not one.
Besides, I've noticed recently that the WOW team does not care much for veteran players.
What a weird thing to say. Do you actually believe this? I will never understand the motivations players ascribe to developers. "They don't care about X" is almost never true of any developer. I don't know why you think otherwise but...developers, shockingly, want people to enjoy their game. There are lots of reasons for why games may not be enjoyable to any given person but "not caring" is generally not one.
I say that because threads on official forums with titles like "QQQ! Wanna sweetie" with short and sometimes rude statements inside get blue posts for answers but thoughtful, constructive threads are very often ignored. That's why. Not something I've conjured out of the blue.
I think the technology isn't there yet for computer games to suddenly spike after decades. Even films find it hard to compete with modern production values - not all viewers are fussy (I'll happily watch an old black and white movie), but many are. Whereas with books, the language may be a little antique a few decades after it's written - and it's even possible that 'problematic' cultural mores from a few decades past will upset excessively sensitive readers - but there are no real technological developments getting in the way.
I say that because threads on official forums with titles like "QQQ! Wanna sweetie" with short and sometimes rude statements inside get blue posts for answers
Huh? "Blue posts" are not from developers but from customer relationship managers. Developers usually don't have the right to say anything on official forums. And even the people allowed to write blue posts can't talk about everything they know, so they are more likely to be bored and reply to less serious posts than to actually discuss issues.
If you conclude that this is bad customer service and communication policy, I would agree. But concluding that the devs don't care is just plain wrong.
WoW and EVE did not do anything like this, they are very very different.
If you smooth out the curves for WoW and EVE to eliminate the effect of expansions, they both fit to Raph's model. You know that EVE is in decline for some years, do you? Or are you one of the people who is in denial about that because the reality doesn't fit your world view?
Huh? "Blue posts" are not from developers but from customer relationship managers. Developers usually don't have the right to say anything on official forums. And even the people allowed to write blue posts can't talk about everything they know, so they are more likely to be bored and reply to less serious posts than to actually discuss issues.
If you conclude that this is bad customer service and communication policy, I would agree. But concluding that the devs don't care is just plain wrong.
WoW and EVE did not do anything like this, they are very very different.
If you smooth out the curves for WoW and EVE to eliminate the effect of expansions, they both fit to Raph's model. You know that EVE is in decline for some years, do you? Or are you one of the people who is in denial about that because the reality doesn't fit your world view?
"Or are you one of the people who is in denial about that because the reality doesn't fit your world view?"
No, I am not, which is where we differ.
The curves are clearly very different, unless you are making the argument that "all curves are the same." I challenge you to name any product of any kind in any industry throughout all of history that you could not make the same claim that it "follows this curve." If you continue to follow your "ignore all difference and say it's the same anyway" logic, you will not be able to find one.
There are two key differences that I have been unable to communicate to you (and honestly, you have intentionally ignored because they "don't fit your world view"). The first is where the peak is. Peaking almost immediately is VERY different from peaking in the middle. A distribution that is roughly even on both sides of the peak has very important implications statistically and predictively. You cannot say it is "pretty much the same, only in a different place." You might as well say, "it's pretty much a square, it just has 6 corners instead of 4." That makes it not a square, and this makes it not the same curve.
The other key difference you try so hard to ignore is the pattern of falloff. Koster's curve calls for the falloff to taper off. Meaning, if in a given 3 month period, a game loses 100k subscribers, Koster's curve would predict that roughly 50k would be lost in the next 3 month period. If instead the game lost 200k subscribers, that would be contrary to what the curve would have predicted. Both WoW and EVE have NOT followed the pattern prescribed in Koster's curve. Both have accelerated their falloff, which is the exact opposite of what the curve would predict. Removing the bump from expansions, you would still see a significant event following WoD where the pattern changed. For EVE, their decline has accelerated since the last expansion. Again, Koster's curve did not predict these events because it does not fit in their case.
It really feels like I can't convince you that planes can fly. You simply say, "look, they reach the ground eventually, so they fall exactly the same as everything else! There's no flying!" No, that is ridiculous, and no more ridiculous than your current claims.
No, I am not, which is where we differ.
The curves are clearly very different, unless you are making the argument that "all curves are the same." I challenge you to name any product of any kind in any industry throughout all of history that you could not make the same claim that it "follows this curve." If you continue to follow your "ignore all difference and say it's the same anyway" logic, you will not be able to find one.
There are two key differences that I have been unable to communicate to you (and honestly, you have intentionally ignored because they "don't fit your world view"). The first is where the peak is. Peaking almost immediately is VERY different from peaking in the middle. A distribution that is roughly even on both sides of the peak has very important implications statistically and predictively. You cannot say it is "pretty much the same, only in a different place." You might as well say, "it's pretty much a square, it just has 6 corners instead of 4." That makes it not a square, and this makes it not the same curve.
The other key difference you try so hard to ignore is the pattern of falloff. Koster's curve calls for the falloff to taper off. Meaning, if in a given 3 month period, a game loses 100k subscribers, Koster's curve would predict that roughly 50k would be lost in the next 3 month period. If instead the game lost 200k subscribers, that would be contrary to what the curve would have predicted. Both WoW and EVE have NOT followed the pattern prescribed in Koster's curve. Both have accelerated their falloff, which is the exact opposite of what the curve would predict. Removing the bump from expansions, you would still see a significant event following WoD where the pattern changed. For EVE, their decline has accelerated since the last expansion. Again, Koster's curve did not predict these events because it does not fit in their case.
It really feels like I can't convince you that planes can fly. You simply say, "look, they reach the ground eventually, so they fall exactly the same as everything else! There's no flying!" No, that is ridiculous, and no more ridiculous than your current claims.
The "WoW lost 30% of its subscribers in the last quarter" is part of the expansion blip. Quick gain of millions of subscribers, most of which are gone after 3 months, leading the curve back to the underlying basic shape. Which is why WoW still has more than half of the subscribers it had at its peak which was years ago. How can that be a "rapid fall" if there are still millions of people playing even at the end of an expansion?
Note that the "WoW lost X% of subscribers" news happen so often and so regularly, that by now WoW has lost well over 200% of its subscribers.
Note that the "WoW lost X% of subscribers" news happen so often and so regularly, that by now WoW has lost well over 200% of its subscribers.
Quick gain of millions of subscribers, most of which are gone after 3 months, leading the curve back to the underlying basic shape"
It did not do this. You are incorrect. The rate at which they lost subscribers was significantly greater nine months to one year after the expansion than it was three months after the expansion. What's more, Koster's curve would have predicted that the far greatest decline in subscribers should have been shortly after Cataclysm (right after peak), some subscribers lost during Pandaria, and few subscribers lost in WoD. It did not do this, because WoW's pattern does not fit the curve at all. The rates of decline are very important, Tobold, because they ARE the pattern.
This, of course, is aside from where the peak was being contrary to where Koster's curve would have predicted. Saying "the peak is the same, just in a different place" is a totally nonsensical statement. Being in a different place makes it a different curve.
I am still waiting for that product of any kind which does not, in your view, fit this curve. If you cannot come up with one, saying something fits the curve is a totally useless statement.
It did not do this. You are incorrect. The rate at which they lost subscribers was significantly greater nine months to one year after the expansion than it was three months after the expansion. What's more, Koster's curve would have predicted that the far greatest decline in subscribers should have been shortly after Cataclysm (right after peak), some subscribers lost during Pandaria, and few subscribers lost in WoD. It did not do this, because WoW's pattern does not fit the curve at all. The rates of decline are very important, Tobold, because they ARE the pattern.
This, of course, is aside from where the peak was being contrary to where Koster's curve would have predicted. Saying "the peak is the same, just in a different place" is a totally nonsensical statement. Being in a different place makes it a different curve.
I am still waiting for that product of any kind which does not, in your view, fit this curve. If you cannot come up with one, saying something fits the curve is a totally useless statement.
Okay, let's try a different angle. Let me give you some concrete examples of why I say your "interpretation" is useless.
Let's say MMORPG X comes out and released their numbers, and after 3 months they have 2 million subscribers. What would you predict would happen in the next 3 months? I think nearly everyone would predict the subscriber numbers would go down, by a lot. But if you truly believe WoW fits the curve the same as any other, you must say you don't know. You know that eventually it will have a peak, but as far as you are concerned that peak could be anywhere. So for now, it could go up, it could go down.
Eventually, every product of every kind will reach their peak. But if you can only point to that peak after it has reached it and started to go down, you have not identified any pattern. You are simply describing the data after it comes in.
Now let's say MMORPG X releases their numbers a year after launch, and they are down to 300k subscribers. When would you guess they lost most of those subscribers? After 3 months? Right at the end? Evenly divided between quarters? Again, if you claim WoW and EVE fit the curve as well as any other game, you don't know.
This is how any rational MMORPG would use Koster's curve. They plan for a huge spike right at the beginning, followed by a large dropoff in subscribers that will taper off before reaching somewhat of an equilibrium. The examples of WoW and EVE are exceptions which developers would be foolish to expect.
Let's say MMORPG X comes out and released their numbers, and after 3 months they have 2 million subscribers. What would you predict would happen in the next 3 months? I think nearly everyone would predict the subscriber numbers would go down, by a lot. But if you truly believe WoW fits the curve the same as any other, you must say you don't know. You know that eventually it will have a peak, but as far as you are concerned that peak could be anywhere. So for now, it could go up, it could go down.
Eventually, every product of every kind will reach their peak. But if you can only point to that peak after it has reached it and started to go down, you have not identified any pattern. You are simply describing the data after it comes in.
Now let's say MMORPG X releases their numbers a year after launch, and they are down to 300k subscribers. When would you guess they lost most of those subscribers? After 3 months? Right at the end? Evenly divided between quarters? Again, if you claim WoW and EVE fit the curve as well as any other game, you don't know.
This is how any rational MMORPG would use Koster's curve. They plan for a huge spike right at the beginning, followed by a large dropoff in subscribers that will taper off before reaching somewhat of an equilibrium. The examples of WoW and EVE are exceptions which developers would be foolish to expect.
Well, give it another look yourself. Ralph doesn't say "the peak can be anywhere," he explains the peaks are very sudden (as I have been saying ad nauseam), but there can be lots of different peaks stacking on top of each other. He predicts those peaks would continue to stack. There is no "revert to the original curve," only the result of all the stacks. Which is why it doesn't predict the sudden drops in both WoW and EVE. I know you see what you want with WoW, but EVE losing 1/3 of their players directly after an expansion is very much NOT predicted.
Ralph doesn't say "the peak can be anywhere," he explains the peaks are very sudden (as I have been saying ad nauseam), but there can be lots of different peaks stacking on top of each other.
*I* don't say the peaks can be anywhere. And Raph doesn't say that the peaks *have to* be very sudden. What Raph is saying that while many natural phenomena follow a Gaussian distribution which is symmetrical, online multiplayer games follow a curve in which the rise to the peak is about 2 to 4 times faster than the fall. If a game took 1 month to go up from 100k subscribers to peak at 200k subscribers, it'll take 2 to 4 months to fall from the peak back to 100k subscribers. But that is if, and only if, the game doesn't add a lot of content in an expansion, in which case you get, as you say, curves stacked upon each other.
EVE losing 1/3 of their players directly after an expansion is very much NOT predicted
That wasn't predicted because it didn't happen. EVE doesn't report players, it reports "accounts". The expansion that nerfed multi-boxing lost EVE 1/3 of their *accounts*, not their players. If we had a curve that would actually show players, it would be a lot closer to Raph's prediction.
Raph's curve rising fast and falling slow is due to network effects. Word of mouth spreads to attract people to play with each other, and then "but my friends are still playing" makes it harder to quit the game. It doesn't make it hard for a player to decide to stop multi-boxing and concentrate on a single account in the future.
*I* don't say the peaks can be anywhere. And Raph doesn't say that the peaks *have to* be very sudden. What Raph is saying that while many natural phenomena follow a Gaussian distribution which is symmetrical, online multiplayer games follow a curve in which the rise to the peak is about 2 to 4 times faster than the fall. If a game took 1 month to go up from 100k subscribers to peak at 200k subscribers, it'll take 2 to 4 months to fall from the peak back to 100k subscribers. But that is if, and only if, the game doesn't add a lot of content in an expansion, in which case you get, as you say, curves stacked upon each other.
EVE losing 1/3 of their players directly after an expansion is very much NOT predicted
That wasn't predicted because it didn't happen. EVE doesn't report players, it reports "accounts". The expansion that nerfed multi-boxing lost EVE 1/3 of their *accounts*, not their players. If we had a curve that would actually show players, it would be a lot closer to Raph's prediction.
Raph's curve rising fast and falling slow is due to network effects. Word of mouth spreads to attract people to play with each other, and then "but my friends are still playing" makes it harder to quit the game. It doesn't make it hard for a player to decide to stop multi-boxing and concentrate on a single account in the future.
I think the general shape is often there, but it's also true that any curve can be decomposed into the sum of smaller curves of any particular shape. Any maths enthusiasts up for demonstrating that a 'long-tailed pseudo Gaussian' with additive sub-peaks corresponding to major releases nevertheless fits the published subscriber curves better than chance? My guess would be that it's doable.
"The expansion that nerfed multi-boxing lost EVE 1/3 of their *accounts*, not their players."
We are talking about different expansions. That was another expansion. The one which just came out also caused a 1/3 drop in players and did nothing with multi-boxing, so you can't blame multiple accounts this time. Actual players quit. Ralph was just flat wrong here.
That doesn't mean the curve is inaccurate overall. I happen to think this curve is very accurate in most situations. But every curve has outliers. I just think it is crazy that you won't admit there is even a single outlier for this one.
You keep using the world "predict" only when describing things after they happened. Three months after the launch of WoW, based on Ralph's curve, what are you predicting? You can't just watch the exact opposite happen and then say, "oh, yeah, it ALSO totally predicted that too!"
We can debate about whether it can still DESCRIBE the pattern, but it certainly failed to predict it in this case.
We are talking about different expansions. That was another expansion. The one which just came out also caused a 1/3 drop in players and did nothing with multi-boxing, so you can't blame multiple accounts this time. Actual players quit. Ralph was just flat wrong here.
That doesn't mean the curve is inaccurate overall. I happen to think this curve is very accurate in most situations. But every curve has outliers. I just think it is crazy that you won't admit there is even a single outlier for this one.
You keep using the world "predict" only when describing things after they happened. Three months after the launch of WoW, based on Ralph's curve, what are you predicting? You can't just watch the exact opposite happen and then say, "oh, yeah, it ALSO totally predicted that too!"
We can debate about whether it can still DESCRIBE the pattern, but it certainly failed to predict it in this case.
Ralphs curve looks suspiciously like the time time trace 'breakthrough curve' created by an underlying Gaussian dispersion process. This equation describes the proliferation of many substances in the world. You only need to know three parameters: A, B, and D for this simplified form:
subs = A*exp(-B^2/(4*D*t))/(sqrt(4*pi*D*t))
t is time, the independent variable.
the underlying partial differential equations are linear, so superposition (the summation of multiple curves) is a legal way to form a solution.
a decent derivation can be found here https://ceprofs.civil.tamu.edu/ssocolofsky/cven489/downloads/book/ch2.pdf
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subs = A*exp(-B^2/(4*D*t))/(sqrt(4*pi*D*t))
t is time, the independent variable.
the underlying partial differential equations are linear, so superposition (the summation of multiple curves) is a legal way to form a solution.
a decent derivation can be found here https://ceprofs.civil.tamu.edu/ssocolofsky/cven489/downloads/book/ch2.pdf
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