Of course how the game is accessed is crucial to player numbers. A game at one point being free on a service of millions is going to have more people download it than it would ever have gotten by not being free on said service. This isn't a hard concept to grasp.
No one has denied that concept, so I have no idea why you are stating the blidingly obvious.
The question you are still yet to answer is why its a problem when doing comparisons between titles?
You keep saying its not a fair comparison, yet have still to explain why that matter if what is being looked at is the simple number of players for a title. Once again, how the player access the title is immaterial. The simple point is how many played it.
DC is a perfect example. With no PS+ help, 2 million sold. With PS+, 10 million+ players.
You are still conflating sales and players. You are also still working on he assumption that what appeared on PS+ was the full title, it wasn't. It was a demo with 14 cars, one location and the main Tour mode missing. It was a demo, we have no idea how many of those demo's from PS+ then converted into sales, or how much DLC was sold as a result of it.
You seem to misunderstand the entire conversation, as I never had a problem with accepting DC has more players than GTS.
Then why do you keep complaining that comparisons between the two in terms of player numbers are unfair? Why have you incorrectly claimed that DC was F2P? Why have you incorrectly claimed that DC was released as a full title on PS+?
You have made repeated false claims about what was a demo for DC that was on PS+ for three months, so yes you do seem to have a problem with this (or at the very least with the truth).
Said services allow you to access hundreds of the games, and MP so cost is vastly reduced, especially over time.
Newly released games do not launch on PS+ because they make money via software sales.
And that invalidates the player numbers in what way?
Neither of this detracts from the clear evidence that being free on services results in games getting massive influx of players, that would be impossible if they had never been on the service.
And that invalidates the player numbers in what way?
And all this links to the popularity of a title. Sales are the best metric (unless you are F2P), however unless a game does notably well publishers don't flaunt such data.
Once again missing the irony that PD have stopped putting out sales numbers for GT.
That said, we are not discussing sales numbers, we are discussing player numbers, and when it comes to player numbers, how the player accessed the title is an utter irrelevance, and you are yet to offer a valid reason (beyond complaining that its not fair) why player numbers should be invalidated for titles aside from GTS.
The only logic seems to be that you don't like it if a player doesn't directly purchase a title, and seem to be arguing that those players shouldn't count, however that forgets that we have an unknown number of players who came to GTS via console bundles (which would be without paying directly for it), it also forgets that PS+ (and the like) are not free. These services are chargeable, and as such access to the title is only available while you keep subscribing, as such its a continues payment to play rather than a one off, but its still paying for the product.
The argument that its not fair simply doesn't hold up, no matter which way you cut it, which is exactly what a large number of people have been explaining to you for over a month now.