See I'm not talking about when you enter a turn correctly I'm talking about when you realize your to hot in the middle. At THAT point I go to the inside.
It also depends on what you intend to do about a fixed radius or possibly decreasing radius turn. Stop or slow or continue running it.
If the radius is decreasing or unknown, I will do one of three things depending on conditions:
1. Stay wide and do not go inside. The reasoning being that when going inside, the turn tightens further by simple geometry. Going inside keeps the nose pointed outside the turn longer thus ending up in a situation at the apex where the actual turn must be conducted tighter and using more traction to not run wide. The tighter the turn, the higher the turn rate (degrees per second) thus the higher traction requirement to maintain within the defined curve limits. Staying outside allows a lower turn rate to be maintained through the longer approach, thus lower turn rate friction through the actual turn. (Think really tight 180 degree turn and you'll have a worst case scenario) The trick is to not run out of total friction before running out of curve. By reducing the degrees/second, the total friction requirement is reduced.
2. Go hard inside, stand the motorcycle up and grab a handful of brake and dump as much energy as possible. If you're proficient at slow school riding and emergency braking, unless you've put yourself in an incredibly stupid situation, you can usually dump way more velocity than you think you can. The slower the vehicle is going, the lower the turn rate is thus lower traction requirement. It's a balancing act. Can you dump enough velocity to counter the higher turn rate friction requirement at the lower velocity? Or in some cases, avoid the boulder that fell in the road that you didn't see because it wasn't there 20 minutes ago when you last ran that curve.
3. A combination of #1 and #2 above in order to dump energy. Sometimes a slight turn towards the inside will allow 10-15mph to be dumped by throttle reduction or moderate braking which will setup a new apex within the limits of the turn. Turn inside a little, grab the binders, dump energy until starting to go outside again, dump brakes and turn, repeat as needed or available space allows. Even at that though, be warned that mere throttle reduction alone or braking in a turn will push the motorcycle wide by reducing the deg/sec turn rate while the road surface continues it's turn rate. Grab a handful of front brake in a turn will result in a low side or it'll stand up and go in a straight line.
Summary: Go inside to dump velocity and reduce degree/second turn rate. Stay outside to maintain velocity and lower overall degree/second turn rate.
There are a lot of variables so there's not one fixed solution to all problems. Obstructions, dirt on the road, road angle and camber, cage up your tailpipes, etc complicate things. Just consider what has to be done to maneuver around a 3" rock that's in your tires line of travel. Just a detour in a turn the width of your front tire isn't as simple as it sounds.
Always enter a turn with reserve traction.
Never ride faster than you can see...or think...or stop.
On a side note when thinking about traction: Total available traction is cumulative and balanced between turning force and braking force. 100% can be used for braking with no turning. 100% can be used for turning with no braking. That implies a linear friction line however the dynamics change in the turn. Cumulative friction in a turn is
NOT linear. Things change when turning and combining turning and braking forces. The reason is that the sideways breakaway force (semi-static friction) of a tire in a turn is lower than when going in a straight line. If you're running through a 50% traction turn, that
does not give you 50% braking traction if you grab the binders. It gives more like 25-30% braking availability. Reduce the deg/sec turn rate and the turning friction reduces thus more braking friction is available. I generally think in terms of 50% reduction in braking or turning capability in any given turn situation. IOW; 50%turn + 25%brake = 75% == 100% available friction. 50% braking only gives you about 20% turning capability. I can't do the actual math right now however you get the idea. ...just something to think about.