The determination of military accomplishments in the Military Realm is comprehensive and involves multiple aspects.
One is the recording artifacts carried by the army units, such as Mirage Pearls which can record who killed which enemy. Soldiers submit them to the non-commissioned officers, who then submit them to the officers, and so on, in a hierarchical reporting process.
Second is the Yin God Statue, also known as the Yisuan Star Lord, which accompanies the army. During combat, the Yisuan Star Lord in the Marching Hall will lead a group of wandering spirits around the battlefield to calculate everyone's military merits.
Third is direct monitoring by the Military Realm, such as during the Cloud City period when the Military Realm could directly observe every action taken and tally the kills directly.
These three are the main statistical methods.
The speed of calculation is also very fast, with results typically available on the same day.