Please spend time understanding how to file tax returns with expense deductions before attempting any further form of this idea.
There's absolutely no way you can get LAF to work on hundreds of NHL players unless you controlled every aspect of their entire life a Tamagotchi. There's no way that anyone would agree to this. Maybe you could do this in the lower leagues at best, but even then, I think many may just refuse the idea. It's insanely invasive of someone's privacy.
That's not including the fact you've now introduced a far more complex bit of chaos when it comes to taxation. You'll need to understand stuff like taxable benefits, allowances, deductions, federal, state and provincial tax credits that not all players qualify for. It's a moving target every time you introduce a new factor.
Any basic idea attempting to address a "tax difference" is going to be ridiculously difficult to design to be fair and meet the intended solution, let alone implement.
Let me just say that I think any attempt to create a completely fair and perfectly balanced is patently absurd. That was not my goal here. My goal was to create a system that could reduce impact that things like taxes and cost of living could have on player decisions of where to play. I have no idea where you get the idea that I am trying to control
You need to look at every player.
Look at signing bonuses for instance.
Matthews pays very little tax, compared to Marner, or compared to rest of league for that matter.
Since each player files taxes, in so many different jurisdictions, it’s becomes a nightmare.
Then you have trades etc
If you're not looking to create a perfect solution but rather an approximate one, you do not need to look at every player.
I discussed signing bonuses in my original post.
When I discussed how I envisioned LAFs being calculated, I specifically mentioned that it included the various jock taxes for where a team would play.
Trades would work like this.
Let's say we have a player on Toronto who has a $7M cap hit and is making $5M in contract dollars for the current season with no signing bonus. Partway through the season, Toronto trades him to Tampa with no retention. While he was in Toronto, he would be paid biweekly based on $5.25M real dollars (because of Toronto's LAF of +5%). In Tampa, he would be paid biweekly based on $4.75M real dollars (because of Tampa Bay's LAF of -5%).
Now, let's say the Leafs retained 50% on the player. What they would be paying him from that point on, would be based on half of what the Tampa value of his contract is. So, basically, both Toronto and Tampa would be paying him biweekly based on $2.375M ($2.5M at Tampa's LAF). If Tampa then moved the player to Edmonton in the offseason, the amount paid for Toronto's 50% of his contract would then be based on Edmonton's LAF.
Note that nothing in here changes anything regarding the cap. The player continues to have a $7M cap hit although it could be split between Toronto/Tampa Bay or Toronto/Edmonton, but that's just standard retention. The only thing that changes is the real dollars the player receives in each of the cities.