Idea balancing weapon tiers

I strongly believe the beginner weapons should be buffed significantly or the later weapons should be nerfed significantly -- that is to say, the power gap between the starting and ending weapon tier is too pronounced. New players are presented with a selection of relatively weak weaponry. While a skilled player can definitely use these weapons to defeat a player with a more powerful weapon, a new player will not have that same skill advantage and will therefore encounter a wall of sorts when they try to progress.

I think the guns unlocked through playtime should not be significantly more powerful than the weapons available at the beginning of the game. A new player with little to no skill is already matched pretty unfairly against a veteran player, but if they have a chance to win in such a matchup, they'll have incentive to continue playing and improve their skill level; players are happy when they defeat a higher level opponent, and they'll work to increase the odds of winning against such an opponent. However, the imbalance introduced by the skilled player's use of, for example, the AK-47 would essentially make the matchup unwinnable to the unskilled player. Thus, that player has no incentive to continue playing war -- they've reached a point where they perceive progression as an insurmountable skill and/or weapon power barrier.

Another way to think about it is this: suppose you have a set W of all weapons in the game and a set P produced by applying a function

Code:

weapon -> weapon's damage

over W. We can then write a function

Code:

weapon damage a, weapon damage b -> (b / maximum skill) - (a / minimum skill)

where "maximum skill" is the maximum possible player skill level and "minimum skill" is the minimum. This function represents the maximum potential difference in weapon power, normalized by skill level, between two weapons in the set P. Thus, the maximum maximum potential difference Q (i.e. the difference between a new player using the weakest weapon and the top-rank war player using the strongest weapon) can be determined by applying this function to the minimum and maximum elements of P. The primary focus of weapon balancing should be to make sure Q is high enough such that players have a motivating force that compels them to continue playing the game, but low enough such that the advantage held by old players isn't overwhelming to the point where new players find the game unplayable. Right now, I believe Q is a little too high for comfort.

This video gives a good visual explanation of this kind of balancing:

This idea occurred to me when I saw that "which gun is best?!?!?" thread. I took a glance and thought to myself, "this is a question that should not have a definitive, objective answer." If such a "best" gun existed, it would represent a total upset of balance, so it's alarming that the answers to that question are a relatively small subset of all the available weapons. You could even say the size of this subset represents `cardinality(P) - Q` for the set of all weapon powers P, speaking in terms of the model developed above. Therefore the tininess of this subset as it is represents a too-high Q.

tldr; play-to-win is just as bad as pay-to-win because new players are screwed.