How did the confederates win the battle of Fredericksburg despite being outnumbered?

Being outnumbered was a constant factor for the Confederates,at almost every battle and not unique to this battle. At Fredericksburg the Union disadvantages were first logistical in nature. The Union army had to construct a pontoon bridge(under fire from the Confederates) to cross the Rappahannock River just to be able to launch attacks. The Confederate Army was very well prepared and well placed with regard to the infantry and the artillery batteries.This ground was mostly higher(Marye's Heights) than that closer to the river,so the Union troops were very exposed when they got across the river. By contrast,the Confederates were protected by the ground they held and by their being"dug-in." The Union artillery could not get close enough to have maximum effect against the Southern army. In a "nutshell" the battle came down to the advantage of having the strong Defensive position,to just wait for the Union attacks and mow-down the soldiers. Gen.Burnside ordered repeated attacks against this very strong position without success. The Generals under his command eventually refused to carry-out the order for more such attacks.