The Ki61 is on Gavagai's chart between the Spitfire 14 and the Bf 109K and on Lusche's chart between the Ki-84 and the P39Q.
What someone should do is make a formula based on gun hitting power, muzzle velocity, RoF, and mounting placement, and compare all of the aircraft. I imagine it would take a while to create a formula that churns out practical data though. I'll leave that up to someone with a longer attention span than myself.
For the most part this has been done. "cartridge power" is Mr Williams analysis based on shell weight and muzzle veloctity (thus kinetic energy), and explosive filling (=chemical energy). "Gun power" is simply cartridge power times ROF.
In other words: It's the amount of destructive energy leaving the muzzle within one second.
For a planes firepower value I simply added the firepower for all the guns.
No kind of judgement had been made by me.
Unfortunately I see no way to factor in gun placement in any reasonable way.
This is a whole hell of a lot more accurate. I'll never understand why one airframe is a mystery to some of the "chit hot sticks" in this game. It shoots 20mm's faster than any other plane and the MG's are almost equivalent to .50 cals.
But some would put forth misleading information and foist it off as something else.
Please notice that computing the firepower was done by going strictly by hard data on the weapons.
But if some of that data Mr. Williams provided is misleading or plain wrong, it should be no problem to point it out and correct it.
http://www.quarry.nildram.co.uk/WW2guneffect.htm