Saying "there are too many variables so you can't prove me wrong" is just lazy. It's also a gross underestimation of my willingness to waste my time.

There are certainly many variables affecting game sales: marketing, word of mouth, install base, market appeal, and more. We can control for those pretty easily! Let's look at the same game in the same market -- this eliminates almost all variables. If we look at the US alone, the install base of the PS4 and XBO are very close, and we can control for this even further.

Obviously my contention is that the PS4 has had several more major releases this year than the XBO and therefore according to you (and others) it has a 'variable' which would bring sales of all of its games down by an indeterminate amount. My own theory is that this makes the PS4 a healthy platform and it will either have no measurable effect on game sales or it will in fact benefit them.

We'll focus on the major multiplatform games released so far this year: Ghost Recon Wildlands, Resident Evil VII, For Honor, Mass Effect Andromeda, and Hitman, as well as a few smaller games, let's say Yooka-Laylee, Sniper Elite 4, and Telltale's The Walking Dead. Conventional wisdom would suggest that these smaller games would be more easily lost in the shuffle on PS4, so your unknown variable would benefit them on XBO.

Immediately we can observe that the PS4 version of every one of the eight games I named has outsold its XBO counterpart every single week this year, with very few exceptions (a couple of later weeks of For Honor, a few essential ties in the triple-digit range for the smaller games). From this we can conclude that your mystery variable is at least too weak to overcome the 10% install base difference.

But we can bypass the install base entirely by looking at tie ratio. The percentage of total platform userbase who bought each game in the US --

REVII PS4: 2.57%
REVII XBO: 1.61%

Wildlands PS4: 2.57%
Wildlands XBO: 2.58%

For Honor PS4: 2.09%
For Honor XBO: 1.76%

Andromeda PS4: 1.90%
Andromeda XBO: 1.72%

Hitman PS4: 0.62%
Hitman XBO: 0.46%

Trust me that the other three continue this trend. An easier way to illustrate this would be to simply point out that despite only a 10% difference in install base, the PS4 has sold more than 15% more software than the XBO this year. The release of major exclusives like MLB The Show, Persona 5, Horizon, Kingdom Hearts, Nioh, and Nier Automata had no observable impact on sales of other software. If I was to conclude a trend from the figures I've measured, I'd decide that the frequent pace of releases has cultivated a healthy platform that is more beneficial to smaller releases.

I'm sure that if Nintendo flooded the Switch with major first-party exclusives week after week they would eventually hit some kind of breaking point, causing their games to start stepping on each others' sales, especially since supply constraints are a factor. But I'm not convinced that Zelda would have suffered if Mario Kart had released a few weeks earlier.

Zelda can benefit from both pure popularity and a small library. The two aren't mutually exclusive, in-fact they likley compound each other.

(...) for all we know Zelda might have had even better sales with different variables, but ultimately library is still a reverent factor.

I have demonstrated thoroughly that a small library relative to the PS4 has not benefitted XBO releases one bit. The relationship between the two is actually the opposite of what you suggest.

The other half of this demonstration -- that the PS4's large library and frequent releases have not been detrimental to sales of individual PS4 games -- is more important. It ties into my original point that Zelda was the best-selling game this week because people want to play Zelda, and not because the PS4 has too many games or whatever. But that wasn't directed at you.

I wonder what the excuses will be when ARMS, Splatoon 2, Xenoblade 2, Mario Odyssey, Fire Emblem Warriors, etc are all out and Zelda is still going strong.

No, you've only shown that other variables have been more significant in the limited time-frame viewed. But fine, data-ahoy: 

No, you've only shown that other variables have been more significant in the limited time-frame viewed. But fine, data-ahoy: 

The above shows the relationship between the number of games in a console's library (at least as far as VGC have sales tracked in some capacity), and what percentage of that library is bought by the average owner of the system. I've included all Sony, MS, and Nintendo home consoles from gen 5, 6, 7, and 8. The graph implies:

1) A very strong correlation between the size of a console's library, and the average sales of each game. The more games you have, the more games your customers need to ignore. 11 to 12 games per person seems to be some kind of limit so far.

2) More games result in people buying more on average, however that average rises considerably slower than that of the library's overall size (at the extreme ends, the PS2 having 1300%~ more games than the WiiU only results in a 64%~ increase in purchases).

3) The correlation is not 100% strict, with some consoles even falling slightly out of the curve. I'd say this is expected, given the plethora of other variables we know should be involved in some capacity.

Despite how compelling this graph is as evidence for my point, I've avoided bringing it up until now because i think its use is limited in the context of the point I've actually been trying to make. Even accounting for our inability to control for several potential variables (e.g. "How significant an effect does popular systems getting spammed by low-quality titles have?" or "Does the rise of digital strengthen or weaken the correlation?" or "How significant an effect do core players have versus more casual ones?", etc etc), it won't consistently predict specific events. However, this trend being relatively consistent at the macro level does imply it's always a possibility for the elements that make it up. Hence I've focused on saying library size can have an effect even on individual titles, rather than it must. The smaller the scale, the more relevant other factors like popularity become.

Looking back to Zelda: I don't believe it's selling because of a limited library (the evidence actually points to Zelda selling the Switch), however i do think the Switch having released with a larger library could have made it sell less, or could have limited the sales of the games releasing with it (especially because, as you noted, supply constraints could compound the issue). How much larger? It's hard to say, we don't really have enough data. The breaking point is almost certainly lower than in the graph (given we're dealing with months rather than years to decades), but that's all i feel confident in saying.

I hope this all explains my point satisfactorily, because i think I've found the limits to "How much time will i spend on one reply in an internet discussion with a psyduck?" If you notice an input errors in the graph, let me know and i'll adjust it. I double checked it all, but it's almost 4am so i might have missed something.

Other variables? I reduced the situation to as few variables as possible. Your chart has dramatically increased the number of variables! No longer are we looking at the same games released at the same time or even in the same generation. Systems that sell well attract a ton of smaller titles specifically because those games can find success selling to a tiny fraction of a large user base. This is the nature of niche exclusives and shovelware!

I'll delve into all this info later, but right off the bat it seems like a sloppy interpretation of data. That's why I was comparing like-for-like. Hell, this kind of reading might actually 'punish' the PS4 for having exclusives like Gravity Rush 2 just because a minuscule percentage of its owners will buy such games. And I know that's first-party, but the platform attracts more exclusives like that by having a large user base.