Confederate Straggling in Maryland and Lee's strength at Antietam

I'm interested in just how badly the Confederate Army straggled in Maryland. Using the 22nd September field returns (ref), the casualties in the campaign (from Harsh's Sounding the Shallows, supplemented by the OR's to add in South Mountain casualties) and the estimated strength 2nd September as reported in Harsh.

Longstreet's Command

• DR Jones straggles heavily. Of his 8,615 man division only 4,403 are with him on 22nd September and 1,435 are casualties, leaving 2,777 stragglers (32%).

• Hood's and Evan's "divisions" have 4,834 on 2nd September, but only 3,403 on the 22nd, with 1,109 casualties. Therefore they do not straggle badly and have only lost 322 (7%),

Jackson's Command

• Jackson's own division enters the campaign with 5,650 and has 3,494 on the 22nd, after losing 648. Thus they straggle heavily with 1,508 (27%) disappearing. In his report Jackson seems to try and cover up the straggling by moving these into the killed and wounded, exaggerating how hard his division fought (sustaining more casualties than Jackson reported with the colors on the 17th).

• Ewell's division (under Lawton then Early) entered the campaign with 6,383, lost 1,338 and had 4,066 left on the 22nd, implying 979 stragglers (15%)

• The Light Division enter the campaign with 8,570, lost 417 but only have 5,468 on the 22nd, losing 2,685 stragglers (31%)
  

The other divisions

• DH Hill did not suffer badly from straggling, of his 9,764 on 2nd September, 5,821 are with him and 3,241 as casualties for a balance of 732 (7%) straggling.

• Walker did not suffer badly either. Of his 5,159 he still had 3,871, despite losing 1,120 at Antietam for a difference of 168 (3%).

• McLaws suffers terribly. Of 7,652, he only has 4,018 remaining, after 1,119 casualties. 2,515 men (33%) have straggled out of the ranks

• Anderson's huge division of 11,294 straggles badly. He has only 6,298 remaining on the 22nd after 1,278 casualties. 3,718 men (33%) have taken leave from him.

There is a general pattern. The formations which executed the more arduous marches had the stragglers. The general implication is that ca. 15,404 men were lost to Lee for the battle of Antietam.

If we take the 22nd September morning state, add back in the Confederate casualties for Antietam, and remove Thomas's brigade (absent the field) we arrive at a figure of roughly 50,000. Adding in the cavalry and half the artillery reserve we have roughly 55,000. This is probably close to the strength of Lee's army on the field on the 17th.