I began working on my own Excel sheets, building up a database and then trying out various iterations of my own formula. I found it pretty easy to create a system that would generate good results for your typical fighter of the period…but very hard to keep outliers from breaking the system. I spent a lot of time tinkering with the weights assigned to different values. No good. Fix one problem, and another would appear in its place.

What I realized the system needed was a way to account for diminishing returns. If I have a biplane with a 250mph top speed and 2 rifle-caliber guns, but a 10,000 mile range, do I have the best fighter of World War II? Obviously not, but if there's no factor that diminishes the value of range past a certain point, there's nothing stopping the system from telling me that my intercontinental biplane is better than a jet. Firepower is another case where this applies. Having four 20mm cannons on a fighter is a lot better than having one 20mm cannon. Four times better? Close enough. How about a fighter with sixteen 20mm cannons versus that fighter with four of them. Is that also four times better? Not really - those four 20mm cannons are already enough to shred almost any plane the fighter is going to come across, so most of the firepower from the extra twelve will just be redundant.

So mathematically, what will allow us to get the effect we want? Fractional exponents. Your standard square root is too blunt of a tool to work with. We need something that flattens the results more subtly. What happens when we take some data and raise it to the power of 0.95?

- 10: 8.91 (89%)

50: 41.12 (82%)

100: 79.43 (79%)

150: 116.76 (78%)

200: 153.45 (77%)

250: 189.69 (76%)

- 10: 7.08 (71%)

50: 27.81 (56%)

100: 50.12 (50%)

150: 70.74 (47%)

200: 90.34 (45%)

250: 109.21 (44%)

Without further ado, here is the current equation I'm working with. In simplified form:

RATING = SPEED FACTOR + ALTITUDE FACTOR + RANGE FACTOR + AGILITY FACTOR + POWER FACTOR + ROLL FACTOR + DURABILITY FACTOR + GUN FACTOR + BOMB FACTOR - CREW PENALTY - ENGINE PENALTY - NORMING VALUE.

SPEED FACTOR is top speed of the aircraft in km/h, 1 point per 1 km/h. As with all other data in this project, I looked up each aircraft in a wide variety of sources. Since different sources often list different values for the same aircraft, the value I put into my database would be an average of each of the different figures I was able to find.

ALTITUDE FACTOR is the service ceiling of the aircraft in meters, divided by 100.

RANGE FACTOR is range of the plane in km, divided by 25, with the result raised to the power of 0.95. The range figure plugged into this equation is an average of combat radius with ferry range, and if found, combat range with drop tanks.

AGILITY FACTOR is derived from the wing loading in kg/sq meter. The equation is written as (50/((Average Weight/Wing Area)/1000))^0.8, with the average weight figure being the average of the plane's empty and normal loaded weights. The weird division going on produces a positive value that grows higher if the wing loading is lighter.

POWER FACTOR is our proxy for climb rate, calculated as 1000 times engine power (in kW) divided by average weight, with the result raised to the power of 0.85. The value for engine power averages the normal output of the engine with the maximum output possible using things like boost or WEP.

ROLL FACTOR is top speed of the aircraft of in km/h divided by its wingspan in meters. This is a pretty rough and sloppy way to approximate, but while the result is often questionable when comparing two specific aircraft, in general it tends to sort the slow rollers low and the fast rollers high.

DURABILITY FACTOR is empty weight in kg divided by the sum of the plane's length and height in meters, with the result divided by two. This one is another sloppy approximation. Due to the constraints of my own free time, and the desire to make a system that could be applied to less thoroughly documented aircraft, I have not yet tried to incorporate values for armor, bulletproof canopies, self-sealing tanks, etc. Using length plus height as a proxy for overall aircraft size seems questionable, but it worked better than multiplying them (the height figure is unreliable as a measure of fuselage diameter since it is generally the height with the landing gear down and often includes the tail). While the inputs are lazy and arbitrary, in practice the results tend to be satisfactory. The famously durable P-47, for example, scores significantly higher than the famously fragile G4M Betty bomber.

GUN FACTOR is the Offensive Armament value multiplied by two and raised to the power of 0.95, added to the Defensive Armament value ^ 0.95. Offensive armament consists of all fixed and forward firing guns; defensive armament of all turreted weapons. The actual values are placeholders for now, because I have not yet had the time to finish a rating system for different aircraft guns that I am fully satisfied with. For the time being, a 20mm cannon is 20 points, a .50 cal is 12.7 points, etc. Obviously, this is a shortcoming to be addressed by later updates, but actually, in the grand scheme of things, it doesn't seem to make too big a difference in most cases.

BOMB FACTOR is the sum of the normal payload in kg, divided by 10, and the maximum payload, divided by 20. For all fighter-bomber aircraft, the normal payload is entered as 0, to reflect its use in a pure fighter mission. Maximum possible bomb load is valued only half as much as regular bomb load, since a plane will only be carrying that maximum load on a small fraction of its missions.

CREW PENALTY is a deduction of 10 points for every additional crewman beyond a single pilot. More bodies equals more weight and a small penalty on performance.

ENGINE PENALTY is a deduction of 25 points for every additional engine beyond the first one. This accounts for the additional drag that comes with multiple engines. There are a few exceptions to the rule, like the Do 335, with its tandem configuration, or the Avro Manchester and He 177, with their twinned engines, but the Manchester and He 177 had so many shortcomings, and the Do 335 has such outstanding performance anyway, that I felt comfortable leaving the penalty in place for them to keep things simple.

NORMING VALUE is a deduction of 650 applied to all aircraft. All these planes have at least a couple hundred km/h of speed, a few hundred kW of power, a few thousand meters of altitude, etc. This value accounts for all of those things; subtracting it thus accentuates the actual differences between them.

In Excelese, the formula thus looks like this: RATING=SPD+(RNG/25)^0.95+CLG/100+(50/((AVERAGE(EMW,LDW)/WNG)/1000))^0.8+((1000*PWR/AVERAGE(EMW,LDW))^0.85+SPD/SPN+(EMW/(LNG+HGT)/2)+(OFF*2)^0.95+DEF^0.95+BOM/10+MAX/20)-10*(CRW-1)-25*(ENG-1))-650. Hopefully those abbreviations are all straightforward to understand. But enough of the gibberish already. What do the results it spits out actually look like? I'm going to take a few samples next where I break down how many points are actually coming from each different factor so you can get a sense of how much weight each of them is given.

Let's start with a classic rivalry, the P-47D Thunderbolt versus the P-51D Mustang, the two best USAAF fighters. The P-47D comes out ahead by a small but not insignificant margin, 854.8 to 827.5 (if we wanted to, we could divide all results by 10 to have the ratings scale from around 10 to 100; for now they scale more from around 100 to 1000).

P-47D Thunderbolt [854.8]

- SPD: 702.0 | RNG: 48.4 | ALT: 128.0

AGL: 86.8 | PWR: 129.2 | ROL: 56.4

DUR: 150.3 | GUN: 155.8 | BOM: 56.8

- SPD: 707.0 | RNG: 89.4 | ALT: 127.6

AGL: 90.5 | PWR: 129.9 | ROL: 62.7

DUR: 124.7 | GUN: 118.5 | BOM: 45.4

- ALT: +0.4

DUR: +25.6

GUN: +37.3

BOM: +11.4

- SPD: +5.0

RNG: +41.0

AGL: +3.7

ROL: +6.3

PWR: +0.7

Spitfire Mk IX [721.7]

- SPD: 663.0 | RNG: 22.0 | ALT: 122.3

AGL: 117.0 | PWR: 170.4 | ROL: 66.9

DUR: 87.6 | GUN: 102.5 | BOM: 22.7

- SPD: 658.0 | RNG: 35.7 | ALT: 107.7

AGL: 81.5 | PWR: 144.8 | ROL: 62.6

DUR: 121.1 | GUN: 162.2 | BOM: 25.0

- SPD: +5.0

ALT: +14.6

AGL: +35.5

ROL: +4.3

PWR: +25.6

- RNG: +13.7

DUR: +33.5

GUN: +59.7

BOM: +2.3

F6F-5 Hellcat [729.1]

- SPD: 611.6 | RNG: 50.3 | ALT: 113.7

AGL: 98.7 | PWR: 131.1 | ROL: 46.8

DUR: 147.2 | GUN: 118.5 | BOM: 45.4

- SPD: 565.0 | RNG: 70.0 | ALT: 117.4

AGL: 137.8 | PWR: 144.5 | ROL: 51.4

DUR: 70.4 | GUN: 87.6 | BOM: 6.0

- SPD: +46.6

DUR: +76.8

GUN: +30.9

BOM: +39.4

- RNG: +19.7

ALT: +3.7

AGL: +39.1

PWR: +13.4

ROL: +4.6

A6M2 [563.6]

- SPD: 532.0 | RNG: 79.0 | ALT: 100.0

AGL: 153.1 | PWR: 139.6 | ROL: 44.3

DUR: 72.0 | GUN: 87.6 | BOM: 6.0

- SPD: 512.3 | RNG: 50.2 | ALT: 111.9

AGL: 117.3 | PWR: 122.2 | ROL: 44.2

DUR: 106.8 | GUN: 118.5 | BOM: 4.5

- SPD: +19.7

RNG: +28.8

AGL: +35.8

PWR: +17.4

ROL: +0.1

BOM: +1.5

- ALT: +11.9

DUR: +34.8

GUN: +30.9

There are still some cases here and there where I'm not quite satisfied with the system's results, but in general, I think it produces better results than the one the old aircraft ranking library used. Take for instance, the example I started with: the Beaufighter that beat the Spiteful and the Meteor. In the new system, that is not at all the case - the Beaufighter Mk X is rated at 705.9, while the Spiteful ranks at 904.0 and the Meteor at 1017.5 - not even close, just as it should be.

I'm not going to be able to upload the full Excel worksheet for the time being, because reasons. But I can copy over my values and give you score tables like the ones the old library had. I'm eager to hear your feedback, both on the results as they are, and how the system could be improved, or perhaps integrated with the old system, which I know covered some factors that mine overlooks.