History hasn't been very kind to Joe Hooker. He's ridiculed for various made up reasons to do with the Battle of Chancellorsville. This is an assessment of the effective combat strength of his army against Lee's during Chancellorsville.
The main source of Federal strength is the return in the OR (ref) and for the Confederates I'm using Allen and Hotchkiss's work (ref). This makes the standard Lost Cause aggregate present against "muskets" apples-oranges interpretation. I will use their "musket" figure, but strip the Federal figure down to the direct comparative number. This will be based on the enlisted only PFDE figure, which is still a slight overstatement since "muskets" excludes Sergeants and the like. Sgts are estimated at 8% of Federal numbers, so I am using 92% of PFDE (enlisted), which is as stripped down as I can get. I will round to the nearest 100.
The strengths (infantry only) of the Federal Corps are thus roughly:
Hooker's main body
2nd Corps (-): 9,000 (Gibbon's division, detached)
3rd Corps: 15,200
5th Corps: 12,900
11th Corps: 10,600
12th Corps: 11,200
Total "muskets": 58,900
Left at Fredericksburg were:
1st Corps: 13,500
6th Corps: 19,500
Gibbon's Division, 2nd Corps: 4,300
Total "muskets": 37,300
Lee's main body of 43,100 muskets and 2,700 sabres* (45,800 total) opposed Hooker's main body, whilst Early's division of 7,400 muskets held the fortifications.
In light of this we must note that Hooker's main body did not have an overwhelming advantage in numbers as some would maintain. Given Federal dispositions he has close to parity at the actual point of contact.
At Fredericksburg without 1st Corps (sent to the main body when Lee gives them a bloody nose on the 1st), Sedgwick has 23,800 against Early's 7,400, and grinds through, but Lee is able to turn on him with the main body stopped.
All this goes a long way to explain the battle. Hooker's 96,200 muskets do seriously outnumber Lee's 53,200 muskets (and sabres), but they're too widely dispersed. Lee gets a result by defeating the two Federal forces in detail.
* The Federal cavalry are staging a raid and the bulk of the Confederate cavalry are also elsewhere.