Later, I pleaded guilty by letter and also explained some mitigating circumstances (which were true btw), and explained my positive plans for the future, and profusely apologised for what I had done.
Thing is, I was being completely honest with myself and everyone else. I was genuinely shocked and remorseful at how I had behaved (or misbehaved).
I was ordered to appear in Court and I explained again that I had compensated the victim (and family) the same day the crime had been committed, and again stated how sorry I was, and how I would never behave that way again. I was 'admonished'. An admonishment is a declaration of guilt (I'd pleaded guilty anyway), but no further punishment was handed down other than the 'admonishment'.
Moral of the story is (apart from not getting too drunk and get into trouble), is do your utmost to make ammends as soon as you possibly can - but it MUST be genuine and the Court MUST see that your remorse is genuine.
To this day I am still genuinely very sorry for doing what I did, but very grateful at taking the good advice I got, and even more so that I apologised as soon as I could, and that the extremely nice people affected by my act recognised my sincerity and accepted my apology, and the court giving me what was essentially a 'second chance'. I've never abused that second chance.
Make ammends. But do it because it is the right thing to do. Don't do it in the hope you'll get a lighter sentence.