I was watching the documentary "We Stand Alone Together". I was wondering, how significant would the losses have been if paratroopers hadn't have landed?
how significant would the losses have been if paratroopers hadn't have landed?
That question is better suited to /r/historicalwhatif.
As to the importance of paratroopers for D-Day, they provided a critical contribution in a number of areas. Specifically, paratroopers--and I will include glider troops here as well--contributed in the following ways.
German counterattacks were frustrated by veritable swarms of paratroopers that seemed to be hiding behind every tree, house, and hedgerow in Normandy. Hans Von Luck comments on this in his memoir, and this is detailed in nearly every history of the battle. Basically the paratroopers snarled all movement of troops for the first 12 hours and frustrated movement after that. On the subject of confusion, the fact that the paratroopers were scattered that night instead of being concentrated as planned actually worked in the Allies' favor at times. While the troopers lost some fighting power by being dispersed, the very fact that there were small bands scattered to the four winds meant that they were impossible to pin down. The Germans also had to deal with dummy paratroopers which further muddled the intelligence situation. Further still, the Germans had to attempt to figure out if this was a raid, an invasion, or the invasion--a non trivial task.
The paratroopers also seized a number of towns that served as crossroads, facilitating Allied movement and frustrating German units. Also, they took control over the few routes inland from the beaches. These two actions in tandem allowed troops to move rapidly inland once they had overcome the initial beach defenses, rather than having to fight the Germans the whole way. The destruction of artillery that could have attacked the beaches was made famous by the Brécourt Manor Assault and the Rangers attacking Pointe du Hoc. In both cases, elite Allied infantry attacked large numbers of German troops to disable or destroy German artillery positions, and were successful in both assaults. These contributions were critical. The final unplanned use of the paratroopers as elite infantry in the days after D-Day allowed the Allies to continue to grind inland against stiff German resistance.
So without the paratroopers on D-Day Allied losses would be higher. Speculation as to how much higher is best left for other forums. As always, followup questions by OP and others are encouraged.
For further reading, Stephen Ambrose is an easy read if not academically rigorous (Pegasus Bridge, Band of Brothers). I haven't gotten Beevor's account of the battle, but Ryan's The Longest Day is a classic. The 1962 film by the same name is based on Ryan's work and features a stellar cast as well as a bit of movie magic.