High Imperial Roman army vs Late Roman army

[Frank]

... Warren Treadgold estimates the two Praesental armies and the Scolae as 45,500 troops, and that's including the new units Theodosius raised. The Illyrian field army was under western control at the time, and we last see it fortifying Succi Pass at the end of the campaign of 377. The Thracian field army had been defeated at Ad Salices, and enough units were needed to garrison important cities that it's likely out of the action. The Saracen allies aren't particularly numerous, if they arrived in time.

Thank you for these explanations. I was aware, that the thracian field army was already defeated, but not, that the illyrian field army was not on the battlefield. So obviously they were with Gratian on his campaign against the Alemanns?

What I don't understand is the conflict in Heathers book between the numbers he assumes about the roman army in total and at Adrianopel. Ancient and modern historians estimate 400.000-600.000 soldiers for the roman army pre-Adrianopel. I trend to believe in the smaller 400.000. But Heather claims 600.000. This means authorized (normal) strength not real strength. Authors also assume, that around half of them were limitanei and the army was divided almost equally between East and West.

Now take Heathers 600.000 men. That means 150.000 for the eastern field armies. Divided into 5 field armies (Thracia, Orient, Egypt and 2 presental, plus the smaller scholae) means 30.000 per army. We know that some armies like in Egypt were smaller, so others have to be bigger. So 2 presental armies should be more than 60.000 men in Heathers 600K-model. If we assume a total number of 400.000, 2 presental armies are more than 40.000 men. If just 20.000 men are available at Adrianopel, then these units had just half strength. Or more than the assumed 50% of all roman soldiers were limitanei. Or the west has significantly more soldiers than the East.

However, Heathers huge army of overall 600.000 men and his small field armies of 2 x 10.000 men at Adrianopel does not match. If Heather is right about his 20.000 men at Adrianopel, then something is wrong with the shiny and glorious empire without any major decay, he describes in the first chapter of his book. If an army of 300.000 men looses 20.000 men, so what? The numbers do not match!