Sony claim that the shooter crowd are turning to the PS4 this gen, let's do a bit of math and find out how true that is.

Without getting to complex I will compare this and last gen. Comparing PS3 to 360 and PS4 to XB1. I will use this simple formula to give us a percentage.

(100/A)*B=C     A = Install Base    B= Software sales    C= percentage of install that bought the game

I will only use a month of sofware sales, using total sales for early games like COD4 shows the total sales surpass in consoles install base on day of initial release.

PS3 vs 360

Cod4: Modern Warfare 5th Nov 07

Sales 1M: PS3 - 0.92M    360 - 2.05M
Install base: PS3 - 5.76M    360 - 12.86
% of Intstall base: PS3 - 16%    360 - 15.9%

Tom Clancy's Rainbow Six: Vegas 2   18th Mar 08

Sales 1M: PS3 - 0.39M    360 - 1.09M
Install base: PS3 - 11.15M    360 - 17.29
% of Intstall base: PS3 - 3.5%    360 - 6.3%

Cod: Modern Warfare 2   10th Nov 09

Sales 1M: PS3 - 4.57M    360 - 6.65M
Install base: PS3 - 27.24M    360 - 33.3M
% of Intstall base: PS3 - 16.8%    360 - 20%

Cod: Black Ops    9th Nov 2010

Sales 1M: PS3 - 6.36M    360 - 7.98M
Install base: PS3 - 41.71M    360 - 45.13M
% of Intstall base: PS3 - 15.2%    360 - 17.7%

Battlefield 3 25th Oct 2011

Sales 1M: PS3 - 2.94M    360 - 3.55M
Install base: PS3 - 55.2M    360 - 57.99M
% of Intstall base: PS3 - 5.3%    360 - 6.1%

Far Cry 3  30th Nov 2012

Sales 1M: PS3 - 1.17M    360 - 1.24M
Install base: PS3 - 70.21M    360 - 72.77M
% of Intstall base: PS3 - 1.7%    360 - 1.7%

PS4 vs XB1

Cod: Ghosts 15th Nov 2013

Sales 1M: PS4 - 1.6M    XB1 - 1.37M (Data taken 4th of Jan)
Install base: PS4 - 4.43M    XB1 - 3.08M (Install base 4th Jan to allow launch to settle)
% of Intstall base: PS4 - 36.1%    XB1 - 44.4%

Cod: AW    4th Nov 2014

Sales 1M: PS4 - 3.75M    XB1 - 2.5M
Install base: PS4 - 13.42M    XB1 - 7M
% of Intstall base: PS4 - 27.9%    XB1 - 35.7%

Far Cry 4   18th Nov 2014

Sales 1M: PS4 - 1.8M    XB1 - 0.65M
Install base: PS4 - 13.81M    XB1 - 7.35M
% of Intstall base: PS4 - 13%    XB1 - 8.8%

Battlefield Hardline    17th March 2015

Sales 1M: PS4 - 1.27M    XB1 - 0.79M
Install base: PS4 - 21M    XB1 - 11.95M
% of Intstall base: PS4 - 6%    XB1 - 6.6%

So at the moment it looks like that PS4 might of taken a bigger volume of shooter fans than XB1 due to superior install base but not really increased the percentage of shooter fans when compared to the Xbox One.

Help me increase the data to get a better picture. What shooting games should I add?

Arguably, yes, but not by a huge margin, simply by a "the percentage of people that both switched from 360 to ps4 and never bought an Xbox one" and "buy annual release fps titles"

Which is going to be small regardless.

The sales difference is mainly down to install base difference, but you can't calculate a genre base from total install base because the reason for buying is unique to each user.

For example ps4 could be at 40m and Xbox one at 20, but if only 5 mill fps fans existed on both platforms, the percentages would be 25% and 12.5% respectively.

It also doesn't account for late adopters still sticking with their last gen consoles while they decide their next move.

It probably has taken a few but I don't think it will be a noticeable number or big by any means.

Plus, like you said, the install base of each console has quite a gap so it makes sense if the game sells more on PS4, but not meaning that it took fans away from the Xbox One or anything like that. 

Probably yes. If nothing more than there are more PS4 owners than XBONE.

I certainly am not a good model to base stats on, but I only have an XBONE because of Halo 5 with zero plans of buying any other FPS for my XBONE. The only other FPS I have is Destiny and I got it on my PS4. I'm not even sure I'm happy about Halo 5 as it seems to lack something I have not been able to put my finger on, maybe ill figure it out as time goes on.

Halo i believe is the only reason to go with xbox, If you are a hot halo fan. Otherwise you get a PS4, even for shooters, as they look and perform batter on PS4.

I mean, logically one would assume that to some extent, fans of any genre would have moved from Xbox to PS4, right? That'ssorta what drives the difference in installbase I presume...

I think looking at it that way is complicating the thought process, it's more that the ps4 is simply the go to console this generation.

It's pretty simple really. Attach rates. Just look at the games and their attach rates. If Xbox One has a higher attach rate for shooters, then it's still the go-to for that genre regardless of what the overall numbers are for each console.

The reason I use my Xbox One instead of my PS4 for shooter is because of the controller. My hands need those offset analog sticks. 

Wasn't there already a thread like this that had in depth discussions as well as data being thrown in the process?.