In all likelyhood, their strength wasn't as low as 40,000. Hence why Jackson's divisions AAG counted 1,684 on the 16th, but Starke was able to report ca. 1,500 in his brigade alone the next morning.
The straggling seems to have happened when Lee tried to reconcentrate at Sharpsburg by forced marches. A large number of men fell out on the march, and were catching up.
DH Hill is interesting. He tried to lowball his strength down to 3,000. Yet his commanders recorded their strength in action as follows:
- Ripley: 1,349
- Rodes: 3rd, 6th and 12th Alabama had around 800. There is no information on the 5th or 26th Alabama, but if average then the brigade would be around 1,300-1,400
- Colquitt: the 4 GA regiments totalled around 1,500 in action. The strength of the 13th Alabama is unknown, but they were a strong regiment (612 men on 2nd September). The brigade thus had around 1,900-2,000 in action
- Garland: the 5th NC alone reported 625 in action, not surprising as they received hundreds of recruits less than a month earlier and marched out of Richmond ca. 900 strong. The strength of the other regiments is not known, but the brigade likely had close to 2,000
- GB Anderson: 1,174
Using only those regiments who reported their strength on the field gets you north of 5,400 on the field. Add the unknowns and DH Hill's division had 7,500-8,000 infantry effectives on the field. More than double his claimed 3,000.