I'll try to support this a few different ways. I believe I can provide evidence supporting that Easy Company was extraordinarily athletically sound, that it was a preferred assault company, that it was led by daring and effective officers and NCOs, and that its men had a strong tendency to be given commendations and promoted.

Easy Company was in the 2nd Battalion of the 506th Parachute infantry Regiment of the 101st Airborne Division. When formed, 101st Airbourne was the Army's most extensively trained air assault division to date. The 506th PIR was one of it's premier infantry outfits. The 2nd Battalion stood out, and held(holds?) a marching record.

Col Sink, the 506th's commander, read about a feat of premier Japanese troops, marching 100 miles in 72 hours; a world record. Sink ordered his 2nd Battalion, the most physically fit, to march to Atlanta, while the other two companies took the train. It was 118 miles in back country, unpaved muddy roads, and in wind, cold, and snow. They completed it in 75 hours. Of the 586 men and officers, only 12 did not complete the march. The 3rd platoon of Easy was the only unit in which every man walked every step and completed the march unassisted.

Part of parachute school was physical training. The 506th thoroughly embarrassed the school instructors, running backwards during runs, doing 1 armed pushups, and asking for races after hours of exercises. It took 2 days before it was decided the battalion would skip the physical training entirely.

Easy Company in particular was in fantastic shape and discipline, even among the exceptional companies around them. Their first CO, Sobel, was a disciplinarian and whip-cracker. More than anything, he pushed them to be as fit and regulatory as could be. Punishments for small things by individuals were inflicted upon platoons or their company, often 3 miles up and 3 miles down a mountain. While other companies took 72 hours off for the weekend, Sobel would find reasons why his company was not permitted to enjoy these vacations, they would remain at Camp in classrooms, in the fields, or on marches.

That's a bit about physical fitness. The Officers:

Sobel was replaced with 1st Lt Meehan, who was shot down on D-Day. He was replaced by well respected Lt Richard Winters.

Winters was an athletic phenom amoung athletic phenoms. He excelled in all the sports he played, and won the Junior Olympics competition at training camp. Just before the D-Day Jump, a fellow officer wanted to blow some steam off with sparring. He bothered the reluctant Winters until he agreed to wrestle. Winters took him down immediately and broke two of the poor man's vertebrae. Furthermore, Winters was respected and well-liked by the men and NCOs, who at one point essentially attempted mutiny following Winter's re-assignment out of the Company under Sobel. Winters was well read militarily, and would spend nearly all of his free time studying or physically training.

On D-Day, after assuming de-facto command of the company, Winters was tasked to assault a German position near a manor. It was approximately 60 well positioned, well entrenched, and well equipped Germans against a total of 23 American paratroopers. The Paratroopers accomplished their mission, disabling 4 big German 105mms. Winters lost 2 men, 1 dead and 2 wounded, the Americans had 6 total casualties. The Germans lost about 20, and 12 were taken prisoner. This skirmish has been taught and re-enacted at West Point as textbook execution of assault on a fixed position by a weaker force. A few hours before this attack, Winters, along with all other members of the regiment, were green.

Incomplete; To be continued

Sources incomplete: Band of Brothers by Stephen E. Ambrose http://brecourtmanor.net/

The accounts of David Webster, as published on his website and in his memiors