Historians never like to answer 'what if ' questions, be better perhaps to phrase the question a little differently.

Such as 'Did the rain the night before the battle of Waterloo affect its outcome?'

The answer to which is, it might have yes.

A wet battlefield is a muddy one, one in which infantry and cavalry get bogged down, cannonballs don't bounce, and the artillery becomes almost impossible to manoeuvre.

Because of the rain Napoleon didn't begin the battle early in the morning, waiting instead for the ground to dry out a bit. The battle probably began in earnest at around about 11 o'clock.

The main drawback of waiting was that it gave the Prussian army, (which had been defeated at Ligny two days before, but not routed as Napoleon had believed) led by Marshall Blucher, more time to march to Wellington's aid. Although the distance between Wavre (where most of the Prussian army had retreated in good order to) and Waterloo was only about 23km, the route took torturous country roads, slowing the Prussian advance. The Prussians did not arrive in force until about 17:30, and broke Napoleon's flank, at about the same time the Old Guard retreated from the ridge occupied by the main force of British infantry.

If Napoleon hadn't had to wait for the ground to dry, the Prussians may never have made it in time, they might not have broken his flank, and Wellington might have been defeated instead.

Still, the Anglo-Allied army, on the ridge of Mont St Jean, received the advance of the French Imperial Guard, the undefeated backbone of Napoleon's army, and sent them into retreat. A retreat that signalled the collapse of morale amongst the French army, upon retreat of the Guard, Wellington reportedly stood high on his horse's stirrups, waved his hat in the air to signal the general advance.

The battle of Waterloo is one of those bits of history that was the result of a vast amount of fortunate coincidences (from the Anglo point of view). For instance, Wellington would never have attempted to fight Napoleon at Waterloo if Blucher had not agreed to march on the French flank. If the force, led by Grouchy that Napoleon had tasked with harrying the Prussian army had been faster it could have defeated the Prussians, ensuring they never reached Waterloo. If the Allies had chosen to advance, instead of retreating after their victory at the battle of Quatre Bras, they would have been cut off and surrounded.

The point is, its very difficult for a historian to identify one single thing that was utterly pivotal to any historical event, as every event is the result of hundreds of strands of circumstance and chance, each of which is entirely dependent on the other.

There is a wealth of books and articles on the battle of Waterloo, Andrew Roberts 'Waterloo: June 18, 1815: The Battle For Modern Europe' is a pretty excellent and relatively short account. I'd also strongly recommend Bernard Cornwell's historical account, 'Waterloo: The History of Four Days, Three Armies and Three Battles'. Although primarily a historical fiction writer, Waterloo by Bernard Cornwell is a history book, excellently researched, and compellingly written - albeit with a bit more drama than you might expect to find in a history book.