There has been a question of what penetration criteria is being used. There are three penetration criteria types for US penetration. The most common for the US during WWII that firing tables were made for was the Naval Ballistic Limit. After WWII the protection criterion became the prevalent method. Here is an depiction of all three.
1. Terminal velocity limit where a plate is defeated is defined in one of several ways. The Navy criterion which demands that at least half the weight of the projectile shall pass through the plate. Note this is also described as "A complete penetration occurs when the entire projectile or the major portion of the projectile passes completely through the armor." (The 'major portion" being at least half the mass.) Note - this results in the criteria (V50) being a 50% chance of 50+% of the mass passing through the armor. [ formula of V50 criteria] [BL(N) V50 calc program (.exe/zip)]
The Army criterion which requires only that light shall show through the hole in the plate when the shot is removed.
The Protective criterion which requires that some fragment shall perforate a weak screen placed a short distance behind the target plate.
Shells tested were either chosen at random or as the German did the best
The US firing tables are in the TM 9 1907 manual. I haven't seen these online. Photocopies can be ordered from Military Info Publishing. Some examples of firing tables from TM 9 1907
Click to enlarge Click to enlarge
3. There are two criteria of WWII Soviet penetration levels. A penetration is counted when at least 75% of the shell mass has passed through the armor. From this definition then a Certified Penetration (CP) is when 80% of the hits are penetrations. Another type of criteria is an Initial Penetration (IP) where only 20% of the hits result in penetration. A few years back I went over the penetrations listed on the Russian Battlefield site and found that the difference between the CP and IP penetrations were from 11-15% for 0° and 12-18% for 30°.
4. The Germans figured their penetration differently. Most German projectiles were APHE shells and contained a bursting charge. To qualify as a successful penetration the projectile was required to penetrate the plate in a condition fit to burst and not to deform in any manner which would prevent detonation. Depending on the shell size a series of consecutive penetrations must be made to qualify the limit velocity that which the armor is penetrated. Below are some crucial factors in determining the limit velocity for German shells. Unlike the other army's tests the series of test shot must begin counting successes again if one shell should fail to penetrate. Source: German Steel Armour Piercing Projectiles and Theory of Penetration by British Intelligence Objectives Sub-committee i.e. the BIOS report. The result of this criteria is that shells with large voids for bursting charges tended to level off penetrations against heavy armor while those with small or no burster tended to have similar penetration values to Allied tests. The Germans may have done some normalizing from test to document. Though not always. I haven't pinned down the number yet. It varies between 243 and 289 BHN, Which is a pretty wide range.
5. March 1944 British Tank School Definition of CV. British penetration was based on The Critical Velocity (CV) - an average velocity at which a 50% projectile success rate occurs. A projectile success being an impact velocity at which at least 20% of the projectile (or the less subjective "significant proportion of the projectile nose") passes completely through the plate (as a "free missile".). A projectile "failure" is any impact velocity which does not meet the definition of projectile "success". This may have changed during the course of the war.
The pre war criteria used for the 2-pdr was that there be a 80% chance of 'success'.
Later for the 6-pdr they did some proof testing vs. armor of specific thickness. (For the projectile to pass this proof of shot test, 66% of the shot (66% by weight) had to pass completely through the plate at the specified impact velocity.)
The Ordnance Board starting May 25, 1943 (revised Dec. 13,1944, then later Dec. 7,1945 ) produced graphs of German KwK 40 penetration labeling them as C.V. 50. Meaning 50% probability of being a perforation. This may have been in co-operation with the US as this data shows up in tables thought to be from Aberdeen. Apparently not. If using the British Mar. 1944 definition of success it would make the German data and US data a little harder to compare.