This is coolbert:
"Why Waterloo still fascinates us" by Andrew Roberts
"Indeed, without the Prussians, Wellington would not have fought the battle -- and probably could not have won it if he had."
NOT SO FAST Mr. Roberts.
As was the subject of a Military Thoughts blog entry from a long time ago now we subject the Waterloo battlefield to the calculations and analysis as might have been done by Trevor Dupuy using his Quantitative Judgment Model. QJM!
That English/German/Dutch/Belgian coalition army commanded by Wellington numbering about 69,000 troops. The French army as commanded by Napoleon about 72,000 men. These figures generally accepted as correct.
Multiply that number of coalition troops using the QJM equation:
69,000 X 1.3 X 1.1 = 99,000.
1.3 that value for a military force assuming a hasty defensive posture. 1.1 that value the advantage gained by the defender as per the terrain of the Low Countries.
That army of the French under Napoleon consisting of about 72,000 troops having NO CHANCE to defeat the coalition army unless their combat effectiveness value [CEV] = 1.4. Meaning that the French soldiers as a collective on the battlefield would have had to be forty percent [%] more effective in combat than the troops as commanded by Wellington.
Given that: Wellington fought strictly a defensive battle [he did], Napoleon and the French had NO CHANCE of winning at Waterloo regardless of whether the Prussian had arrived on the scene or not.
NAPOLEON DID DETAIL A SEGMENT OF HIS ARMY [THE YOUNG GUARD] AS RESERVES IN ANTICIPATION OF THE PRUSSIAN ARRIVAL ON THE BATTLEFIELD. THESE RESERVES INITIALLY HORS DE COMBAT BUT COMMITTED TO COMBAT AND OCCUPIED FROM THE AFTERNOON OF THE BATTLE ONWARDS.
That Prussian force however arriving in a piece-meal fashion and NOT as a concerted and concentrated force.
It is reasonable to ask if the QJM method of calculation and analysis for combat as fought during the black powder warfare Napoleonic Era is a valid technique. In the opinion of Dupuy QJM legitimate at least from the time of the American Civil War onward!
As to Waterloo, you the devoted reader to the blog must decide for yourself.