Three things, not one number.
Complexity, accuracy and fluency are three dials. Fluency maps cleanly onto automaticity. Accuracy is knowledge too — often explicit knowledge you can check. Complexity is how much of that knowledge you attempt. They share attention, but they are not a simple pair.
How ambitious the language you attempt is — longer clauses, richer words, harder structures. How well-formed it is. That is knowledge: sometimes a rule you can check, sometimes a form you simply have. How smoothly it comes out. This is the easy mapping — automaticity. The filter is off.
Simple language you already have. Accuracy holds. Fluency holds. Complexity stays modest because you are not reaching.
System 2 · System 1
Slow · monitored · you can state the rule · Fast · automatic · it just comes out
Psychologists call them System 1 and System 2. I use that as a plain picture, not as a language-learning theory. System 2 is slow and checked. System 1 is fast and automatic.
Complexity: System 2 Reaching for a harder form you are still constructing.. System 1 Range that is already in the automatic repertoire. Accuracy: System 2 Explicit knowledge plus the monitor — “is that the right tense?”. System 1 Forms that come out right because they are acquired. Fluency: System 2 Hesitation, repair, the filter on. Fluency is not at home here.. System 1 Automaticity. Speech runs without being assembled.
Ambition
Fluency is how you access language. Complexity and accuracy both sit on knowledge — what you have, and what you attempt.
Do you actually have the form? Accuracy is this, first. Often explicit knowledge: a rule you could write down. It can also be implicit: you just know it.
How much of that knowledge you try to use. That is complexity. You can know a simple form well, or attempt a hard one you only half-know.
Automatic or checked. That is fluency. Checking uses System 2; automaticity is System 1.
System 2 → System 1
How smoothly it comes out. This is the easy mapping — automaticity. The filter is off.
Attention is limited
One useful view is that attention is a pool: push one dial and another often pays. Another view is that a well-designed harder task can raise complexity and accuracy together. I use the first as a lesson lens, not as settled science.
ComplexityAccuracyFluency
The knowledge view above is why the second can also be true — if the form is actually known, and you give the monitor time.
What this is not
This is how I think about speaking. It is not a score, and not a level. One number would hide the stretching moment — the moment that matters.
A short CALFA note after sixty seconds of speaking is a note, not a lesson report, and not a history of these dials.
Complexity, accuracy, fluency is Peter Skehan, then Housen & Kuiken. CALFA adds lexis and adequacy. The monitor is Krashen’s picture of explicit knowledge editing output. Automatisation is DeKeyser. System 1 / System 2 is Kahneman — a useful analogy, not an SLA theory. Implicit versus explicit knowledge is Ellis.