Stanley was pretty slippery and never wanted to commit if he didn't have to. The History of England podcast is quite good and is into the Tudor period now, goes over the Wars of the Roses pretty well. I've listened for a long time now and have a better understanding of the Wars of the Roses. However, I wish I remembered more from it, but it's so much information, and the Wars of the Roses has always been one of those conflicts that is hard for me to keep straight due to the ever changing political landscape.
I say that Stanley might have had as much impact on who would be King by his inaction, as Warwick had with his action. The War of the Roses went from about 1440 to 1485, and Stanley's troops didn't show at Blore Heath in 1450, didn't join Henry VI at Northhampton in 1460, didn't involve himself with Edward IV's Towton campaign in 1462, and didn't join Warwick in the 1470. And it can be said that Richard wouldn't have been King if Stanley had been mortally wounded in June of 1483, and there after Richard spared Lady Stanley from her actions, awarded a knightship to Stanley and his brothers with offices in the north, all reasons to presume Stanley's support when Henry Tudor arrived from France in 1485.
Regarding the politics of the era, in reading Bicheno's books, there is quite a bit of discussion involving the influence of the French. As an example and with the Bosworth campaign, various accounts of historians follow the Tudor narrative of the French playing a minor role in Henry VII's effort, and yet the French commanders present were one that later became a marshal of France, and the other was commander of French Royal Guard, and so their contingents accompanying Henry into England had to not only be significant, but also paid for by France, and armed and drilled in the continental fashion of military fighting of the time.
And back to Stanley, Henry marched into Stanley's territory where one of Stanley's men acted as a co-ordinator with Henry while Stanley stayed away, and when the campaign moved into high gear, Stanley marched parallel to Henry while reporting to Richard that he was blocking Henry's march, yet in actuality seems to have been screening it. And this was followed up by Stanley reporting to Richard that Henry's Vanguard had taken a certain route, which caused Richard to move his army in a way that placed him in a spot where numerical superiority was neutralized by location, and if this was Stanley's intention, quite the deception could already have been in motion, particularly if one takes into account where the French vanguard of Henry ended up on the battlefield followed by the rest of Henry's troops. And then before the battle even started, it appears Stanley backed up his position while his brother moved his own forces more in line with how the rest of Henry's moved onto the field. Meanwhile, Percy troops and artillery, the latter as shown through where artillery shot has been archaeologically discovered to have fallen, stayed in a position to cover Stanley while Richard led his forces down into the valley to confront Henry the contender and his French allies.
I had read Bicheno's first volume of the two book series, and was quite pleased with the detail and interpretations based on such, even sensing that so much after Towton and in the second book was somewhat anti-climatic, even the Warwick side switching. Then in reading the Bosworth ending, my ride through the two volumes became quite the enjoyable experience.