Hi Josar,
Just a quick suggestion…
Why don’t you use the standard way of tracking skill or performance improvement?
There are several (very very very good) models of skill improvement, none of which will give you any trouble to understand if you already know how to read basic mathematical symbols or you are prepared to learn them. There’s no need to actually know (dah dah DAH!) CALCULUS in depth just what it means… But to be honest the only way to track, model any change (in anything) is to use the mathematics of change - calculus.
The standard basic models are the learning and performance curves and how they can be quantified from data (the times or quality of performance of the effort put in).
They are equations, differential equations.
And the ESSENTIAL thing that you are talking about above is THE RATE OF CHANGE - NOT THE ACTUAL CHANGE…
Give you a couple of examples (of the top of my head).
Rate of change of (say) memorising 100 digits in terms of time taken over attempts over say twenty eight days.
That can be MODELLED EXACTLY using the following:
K (Min possible time - time taken)
K is a constant.
It’s a curve that can never ever reach the minimum possible and looks roughly like half a parabola or stretched out quarter circle… This is not a bad model to use and track your progress. And will roughly give you a model to track improvement from a point where you are pretty comfortable with what you are trying to improve which has a definate ceiling. This type of curve is actually best used to track a PLANNED improvement from one time to a better target time, it’s used for example for swimmers trying to take four seconds off of a personal best over the course of three months … Or for a formula one motor racing team trying to get an extra one or two seconds off of a three minute lap… Or a student trying to improve his test averages.
That’s dy/dt = k(M-P) where P is current performance.
Better is what is called a sigmoid curve (so called because it looks like an S turned on its side). You can track actual progress and set up future target performance using this FABULOUS model.
The rate of change in this case is modelled by the following or similar: dP/dt = (that says the rate of change of performance with respect to time is equal to: k(P)*(1-P/M) some constant times your present level (at any time) multiplied by the percentage your performance is of the maximum you can actually expect or are targeting.
This is EXTREMELY accurate once you have some data.
Key points off this model are you improve very quickly at first and keep getting better at a faster and faster rate until you reach about half of your target improvement, then assuming the same effort and commitment you’ll find your improvement slows gradually until its non existent (because of you reach P=M, then (1-P/P)=zero.
These two improvement models (and similar ones) model, record and allow you to see at a glance any improvement (or backward step) the rate of change of performance. At a glance.
It’s not easy to give a metaphor to make this improvement model understandable to people who aren’t fluent in maths - but one is. You are on a journey which will take you twenty eight days, your start speed is best near zero and your end speed is most definitely zero, and the fastest speed you ever reached is at half way (fastest rate of improvement) and the shape of the curve of the speed is a parabola or (semi circle stretched out look) and the distance is an S curve.
I’m not sure anyone who isn’t interested in improvement would have read this far, but if they have - learning to model your changing scores in any discipline - any - needs the maths of change and that’s (only) calculus. There’s no other way. So learn it.
Hole that helps.
K
That