Grouchy's rigid thinking is why he didn't march to the sound of the guns

I have thought this over for weeks now and have made a few conclusions. I'll start by saying the defeat at Waterloo was a manpower issue than anything else. With the Prussians arriving its at best a tactical stalemate and at worse a full on defeat for any commander fighting with conventional warfare. So given the numbers its Wellington+Blucher (etc)'s to lose rather than it is Napoleons to win. Blucher was defeated but could recover as the French had to be basically perfect.

Basically Napoleon has an unrigid mind, as in hes able to think beyond just numbers and rather see the bigger picture while dividing his army into chunks in his head to achieve the objective. For example dividing his force, defeat in detail, making the enemy send in its infantry reserves then breaking their center forcing a retreat or full on crusing their army. Given the technology of the time this mind is suited to this era of warfare.

However Grouchy had a more rigid mind, as in he was only focused on "persuing the Prussians", he didn't think beyond this. He thought too 1 dimensionally (rigid) instead of in an unrigid way. Hes basically the type of commander to play it by the book, but not be able to adapt on the spot. Due to this he didn't march to the sound of the guns given rigid minds don't like taking tactical risks (risks are unrigid).

In a sense splitting up your army is unrigid, so the Prussians copying Napoleons unrigid tactics split their army up and marched to Waterloo while their rear gaurd stayed at Wavre to pin down Grouchy.

Napoleon splitting up his army to delay the Prussians was a good idea, its just that Grouchy was the wrong guy for the job. Grouchy would have been better suited to Trench warfare or something. Tell me what you think!