Given how long your post is, it's difficult to remember all things you touched on, but here are a few things that bother me in your analysis.
1. The way you determine the impact of key software on hardware sales. You look only at the surface (month 1 and 2), but don't consider a stacked effect because that one is invisible with your methodology. Software sells hardware, and the continued consistent release of new interesting software boosts the baseline any given console can have. You acknowledge that a lot of consumers buy old key software along with their initial purchase of the hardware, but don't make the connection that the old software still drives hardware sales despite regular appearances in NPD's monthly top 20 software list. A prolonged bump on hardware sales doesn't show up in the data like an immediate bump with a visible spike, but it should be clear nonetheless that old games still move hardware when they keep charting high in the list of best-selling software.
Software sells hardware, but not in the way you think. Having a good library is essential for the health of a system, but we're talking about sales growth here, and simply having a good lineup in a given year does not mean sales will grow. The PS4 managed to have remarkably flat sales in the U.S. For the entire Q1-Q3 period for its first four years, PS4 sales had a relatively narrow range of about 2.2M to 2.5M. The same period in 2018 got up to 2.7M thanks to just three games (more on this in a second). Overall, this is the flattest generation to date. Overall, this has been the "flattest" generation ever for PS & Xbox in the U.S., with probably the least pronounced peaks of any system ever. If strong lineups and growing libraries of quality content are supposed to enhance baseline sales, then why was the PS4 so flat over time?
Now, individual games can and sometimes do have a measurable impact on sales, but that's rare for the U.S. (again, mainly because NPD's monthly tracking can mask the effects of modest system-sellers), and when they do have an effect it's in the form of an obvious spike in their release month, with the rare residual effect in the following month, and never in the form of an increased baseline over many months. 2018 saw total sales across Q1-Q3 go up about 200k from 2017. Why? Because of the combined effects of God of War and Spider-Man, which cause a clear bump in sales in their release months of April and September. Take those two months out of the equation, and 2018 is very slightly down from 2017 for the Q1-Q3 period. And even with those games, we're talking 8% growth for the Q1-Q3 period.
You know what does have a tendency to cause significant sales growth for a period of many months? Price cuts and hardware revisions. The PS2 didn't see any upwards trend in sales in the U.S. prior to May 2002, but when it was cut from $300 to $200 that month, it experienced a period of significant growth over the following 12 months, with its best level of sales by far. The PS3 was languishing with a terrible baseline in 2007 until it finally got a price reduction to $400, and it wouldn't experience any further growth until the release of the Slim, which was near-concurrent with the price cut to $300 the month prior. And those are just two examples.
As for your objections to my methodology of estimating the impacts of individual games on hardware sales, well, I invite you to come up with something better. I think my method is sound. Take my example of Destiny. The PS4 had a remarkably stable baseline that averaged just under 50k units per week from April through August of 2014. Destiny is released and suddenly sales jump up to nearly 108k/week, more than double the baseline that had existed over the previous five months, and October averaged 74k/week. It's reasonable to assume that, since there were no other stimulative factors at play besides Destiny, the PS4's baseline would have remained at or slightly below 50k/week. There is no reason to think it would have been significantly above or below that, so had Destiny not been a thing it's likely the PS4 would have sold 425-450k for the September-October. It instead sold 835k. That pegs the amount of surplus hardware Destiny sold at around 385-410k units.
While it's not an exact science, and when dealing with other complications like price cuts it becomes less reliable, this method can give us an idea of the typical effects of individual games on hardware sales. And there's never been a single case in any point in the past 20 years where we see a single game A) clearly pushing well over a million surplus hardware units and B) causing a marked improvement in baseline sales.
2. The way you use the PS4 and XB1 to determine the magnitude of the COVID bump. You wrote a novel and got to the point that the PS4's June and July sales were still higher than they should have normally been, then concluded it has to be COVID that is responsible for those numbers. But The Last of Us Part II and Ghost of Tsushima released during those months along with a bundles. Surely, that's something you should consider because any time a big title releases for a console, it is accompanied by increased advertising for said console and advertisement works, hence why companies keep paying for it. More awareness of a product raises the chances to sell said product. There's no good reason to sit there and act as if Sony's first party games and marketing had no positive impact on PS4 sales.
The first TLOU game wasn't a system-seller. Uncharted 4 looks to have caused at best a very minor increase in the month it was released. Naughty Dog games in general appear to have negligible impacts on hardware sales in the U.S. Ghost of Tsushima? When was the last time you saw a Sucker Punch title cause a big spike in hardware sales?
Also, why was August so big? Don't say "Madden," because we've never seen it push tens of thousands of surplus units before. There has been only four times August has ever been up substantially from July for either Xbox or PlayStation, and it was because of other reasons: the release of the Xbox One S in 2013, the 360's first price cut in 2007, and the PS3 getting reduced to $300 in 2009 and to $250 in 2011. Popular as the annualized football game series may be, Madden's impact on hardware sales is practically nil.
Again, not every major software title is a big enough system-seller to have any noticeable impact on hardware sales.
You want to know what a real late-life system-seller was? Grand Theft Auto V. You couldn't ask for a bigger game than that. And while it caused a relatively big month-over-month jump for the PS3, that produced only a tiny YoY increase because of the big YoY drop in previous months. GTAV also gave the 360 a modest month-over-month boost (the following month was even bigger for the 360 because of reduced-price holiday bundles issued that October). Yet total PS3+360 sales in September 2013 were only about the same as combined PS4+XBO sales from this past May, and only about 27% higher than combined PS4+XBO sales from August, and that's with the XBO being supply constrained.
Prior to March, the PS4 & XBO were doing considerably worse than the 360 & PS3 were at the same point ahead of the start of this generation, but now they're doing considerably better than the PS3 & 360:
In fact, it we match up just the PS4 & 360 (the top conventional systems of their eras), we see essentially the same thing:
When we "reverse align" to the months their successors were released, combined PS4 & XBO sales had been consistently behind combined PS3 & XBO sales since June 2018, but that's no longer the case. The PS4 has, for the past several years at least, clearly been performing nowhere near the level of the 360 in the U.S. prior to this past March, but now it's suddenly doing better than the 360 in the final months before their respective replacements were released.
Clearly, something else is going on here besides just TLOU2 and Ghost of Tsushima, games from series/publishers that aren't known for being/making huge system-sellers. Why would the PS4 & XBO be doing substantially worse than their last-gen counterparts in their twilight months, then suddenly have a huge turnaround following a big spike in early to mid spring that was obviously caused by COVID? The only plausible explanation for this "last minute second wind" is that the pandemic & stimulus are having a strong residual effect keeping the baseline much higher than it otherwise would have been. Had there been no pandemic, the PS4 & XBO would have had a far worse 2020, even over the summer months.
3. The video game industry is dominated by big budget games targeted at males. This is very important to remember, because it means sales trends have high consistency. However, on the flipside it means that the typical analytical models won't work as well when you are dealing with a game that bucks the trend. Animal Crossing has an enormous female audience and is therefore able to sell to a part of the population that isn't the typical console gamer. Switch had all the typical big guns in Super Mario, Mario Kart, Zelda, Pokémon and Super Smash Bros., but the tipping point to finally buy the hardware is Animal Crossing for many females. Your entire analysis hinges on there not being anything special about Animal Crossing, hence why it is inexplicable to you how AC could be such a big incentive to purchase Switch hardware. But there is a factor you have not considered at all.
New Leaf had a majority female audience, too. It didn't cause a massive explosion of 3DS sales far beyond anything else on the system (maybe 100k or so surplus units in the U.S., and a 90k jump from the week prior to its release in Japan, and that's with a limited edition New Leaf-themed XL to aid it). So AC has more females buy it than most games? So what? Fewer males buy it relative to other popular games. It balances out. Just because AC is popular with females doesn't mean New Horizons is somehow uniquely capable of pushing upwards of 2 million surplus hardware units in the U.S. when the best confirmed record system-seller moved around 400k surplus units.
Lastly, a related point that has nothing to do with COVID, but your original assumption that Switch had probably peaked in 2019. I'll use this as a means to explain why your approach to analyses goes off course in some instances. You based your assumption on sales trends of previous Nintendo consoles and all of the recorded ones in NPD history (so Nintendo 64 onwards, because there was no NPD before 1995) showed that it's only down after year 3, except for the DS. I know it's easy to disregard the DS as an anomaly in a dataset like that, but if you had thought about why the DS was different, you could have figured that Switch would follow the DS. The DS was different because it had more robust third party support than any other recorded Nintendo console, so the consistent arrival of new interesting releases kept sales high. This is how it works for all consoles, hence why the PS Vita flopped so hard in comparison to all other PS consoles.
All Nintendo handhelds have had strong third-party support. The DS was no different. It drew in a non-trivial amount of casuals to be sure, but third-party games writ large were not popular enough to explain the DS's success. The best-sellers list on every Nintendo handheld was utterly dominated by first-party titles, just as the best-sellers list on their home consoles has been dominated by first-party games ever since the N64. The number of DS titles that sold more than 2M copies worldwide can literally fit in your hand, with the case, and that's on an install base of over 150M. Only five third-party games on the Switch have passed 1M copies, and only two of those (Octopath Traveler and Minecraft) have passed that milestone by any comfortable amount. People aren't lining up to buy Nintendo systems for third-party games. They buy Nintendo systems to play Nintendo games.
Most of the rest of your point was addressed earlier.
Meanwhile from the last Nintendo reporting...
The number of consumers who started playing on Nintendo Switch because of this
game continued to increase during the first quarter, from April to June 2020. Of all
systems in the Nintendo Switch family that were played for the first time during
this period, over half were used to play Animal Crossing: New Horizons on the first
I saw that posted in the July thread and ignored it because it didn't say what the poster thought it said (plus he was a new user who went AWOL two weeks ago, so there's no telling if he'd even see my replay). But since this is the second time it's been brought up, I'll deal with it.
It's very intriguing information, but I don't believe that it's the silver bullet argument that proves that AC was the primary driver behind the increase in Switch sales seen over the April-July period. It definitely does prove that AC is a popular game. And more importantly it proves that a lot of new Switch owners also bought a copy of AC to go with it. But note that it does not actually mention anything about AC causing significant YoY hardware growth. Having a good attach rate for new sales is not the same as actually increasing hardware sales beyond what they would be otherwise. There's also a difference between buying a game with a system, and buying the system for the game. Lots of games have phenomenal attach rates early in their runs (Halo 3's was 52% in the U.S. at the end of 2007), but that doesn't mean that they were responsible for most of the hardware units sold at the time.
Also, not only does that attach rate not necessarily imply AC was responsible for the sales growth, think of the implications of that "over half." If we assume that most or all of those people wouldn't have otherwise bought a Switch if it wasn't for AC, it would result in hardware numbers that are way too low. While that "over half" figures is worldwide and thus we don't have region-specific figures, let's assume it's the same everywhere, and let's assume "over half" means, say, 55%.
According to Famitsu, during the period of Week 14 to Week 26 the Switch sold 811,890 units. If 55% of all new Switch owners in that time span bought a copy of AC as their first title to go with the system, that amounts to over 446k people. If we assume that none of those 446k people would have bought a Switch had it not been for Animal Crossing, that means Q2 sales in Japan would have only been 365k. Considering that the Switch sold 514,675 units in the same period in 2019, that would mean the Switch would have been way down YoY had it not been for AC. In fact, it would be considerably worse than Q2 2017, where the Switch sold 474,812 units. Obviously, nobody would be able to reasonably argue that the Switch would have sold that little had AC not been a thing. While we can't say for sure what the Switch would have sold in Japan had AC not been a factor, given that it was still up YoY early this year prior to AC's release, it stands to reason that it was still feeling the effects of the Lite, which did produce a big increase in sales, and it likely would still be feeling at least some residual effects of the Lite boost. It's interesting that the Switch's weekly average for the entire period from Week 14 on up to the most recent week was about 86.5k units (though that was enhanced a bit by a strong showing for Obon), about the same as the average for both the period of Weeks 2-6 and a bit higher than for the month of October 2019. This lends further credence to the Lite having a strong residual effect. While Q2 might have been down a little bit from where it actually was in Japan without AC, it probably wouldn't have been by much.
The numbers for the U.S. fare a bit better. The Switch sold around 1.85M in Q2 in the U.S. If 55% of all those new Switch owners in that time span bought a copy of AC as their first title to go with the system, that amounts to just over 1M people. If we assume that none of those 1M people would have bought a Switch had it not been for Animal Crossing, that means Q2 sales in U.S. would have only been about 830k. That is slightly up from Q2 2019 (by just under 8%), but there's reason to think the Switch would be up far more than that. 830k spread out across the whole 13-week span averages out to about 64k/week. That's worse than Sept. & Oct. 2019 and Jan. & Feb. 2020, which would indicate that, if we assume that 55% wouldn't have bought a Switch had AC not been a thing, the Switch would have started to stall out after Q1 and already be back to YoY drops. Now, had there been absolutely nothing in the first half of 2020 to stimulate sales, I do think this would have been plausible. We possibly would have seen the Switch at best slightly up YoY, and more likely at least slightly down.
But AC wasn't the only stimulative factor. We know the pandemic and the stimulus had an effect on console sales in the U.S. I've already gone into extensive detail explaining this.
Given these facts, there is good reason to think that had AC not been a thing, the Switch would still be up considerably in Q2 in the U.S., and in Japan it'd be flat at worst. If we assume that over half of all new Switch owners in Q2 in the U.S. wouldn't have bought one had it not been for AC, then we'd also have to assume that the pandemic and stimulus had minimal impact on Switch sales, and that is something not supported by the available evidence.
While half of all new Switch owners in Q2 may have bought AC as their first game to go with it, that's because it just happened to be the hot new title. But had AC not been a thing, all or nearly all of them would have likely still bought a Switch regardless, and they would have simply picked up some other game to go with it. Just because a huge share of people bought AC to go along with their Switches, that doesn't necessarily mean AC was actually responsible for the observed YoY sales growth in that quarter.
TL;DR: Having strong attach rate doesn't necessarily mean a game is capable of causing record sales growth.