Jack Did Strangle Danny; Here's the Proof

As it is always a work in process, I have noticed another implication about Stanley Kubrick's The Shining. Now, I watch this film kind of often now; and believe I have an idea for a moment that occurs in the film.

Do you remember when Jack was throwing the tennis ball at the wall and down the hall? From that, we can certainly imply that it is Jack's ball and it belongs to no one else, right?

Now, later in the flick when Danny is playing with his toys on the rugs; the tennis ball comes rolling toward him and Danny gets up and walks down the hall to room 237, which is open.

Now, a few minutes later we find Jack screaming and Wendy finds that Danny has been strangled (not dead, though) and his sweater torn. She then accuses Jack of doing it following his dream of killing her and their son. Now, he goes and talks to Lloyd the bartender and Wendy shows up to tell him a woman in the hotel did it.

Even when he sees the woman in the room, he comes back and tells Wendy that Danny must've done it to himself.

Now, here's where my idea kicks in.

The marks on Danny's neck and his ripped sweater would be too much for a boy his age to do. He simply couldn't, you see? So, with that; Danny is not responsible for self-harm.

Secondly, the notion of ghosts being real are deliberately played down to being all the nature of cabin fever, right? I think even though Jack is going crazy, he is still sane enough to realise the ghosts aren't real and that's why he tells Wendy there was no woman in room 237 even though he saw one. We never see her again, because she wasn't real and Jack knew it.

Going back to the tennis ball, I believe that Jack was waiting in room 237 for Danny, and so he threw the ball toward him to get his attention and once in the room, he tried to strangle him. Waking up from a 'trance' he realised what he did, told Danny to tell Wendy it was a woman, and he went back to the Colorado Lounge to pretty he was asleep.

Just a very rough idea in process, but it seems plausible, right?