I don't know how the film makers are going to answer the question. Here is how Sir Arthur Conan Doyle had Holmes answer it in The Adventure of the Empty House (in The Return of Sherlock Holmes) [BTW Don't British libraries have the Sherlock Holmes books? The man is one of the worlds famous fictional cultural icons.]
"This is indeed like the old days. We shall have time for a mouthful of dinner before we need go. Well, then, about that chasm. I had no serious difficulty in getting out of it, for the very simple reason that I never was in it."
"You never were in it?"
"No, Watson, I never was in it. My note to you was absolutely genuine. I had little doubt that I had come to the end of my career when I perceived the somewhat sinister figure of the late Professor Moriarty standing upon the narrow pathway which led to safety. I read an inexorable purpose in his grey eyes. I exchanged some remarks with him, therefore, and obtained his courteous permission to write the short note which you afterwards received. I left it with my cigarette-box and my stick and I walked along the pathway, Moriarty still at my heels. When I reached the end I stood at bay. He drew no weapon, but he rushed at me and threw his long arms around me. He knew that his own game was up, and was only anxious to revenge himself upon me. We tottered together upon the brink of the fall. I have some knowledge, however, of baritsu, or the Japanese system of wrestling, which has more than once been very useful to me. I slipped through his grip, and he with a horrible scream kicked madly for a few seconds and clawed the air with both his hands. But for all his efforts he could not get his balance, and over he went. With my face over the brink I saw him fall for a long way. Then he struck a rock, bounded off, and splashed into the water."