How to calculate the current in a PWM LED driver circuit?

I've been fascinated by the simplicity of the driver circuit based in the YX8018 in the prominent solar garden lights, they were able to simplify the circuit a lot in a simple boost topology by just running at fixed frequency and using the LED as the output rectifier. I was interested in building my own circuit using a 555 timer driving a small transistor, just to learn more about the topology, but in my research I was not able to find a equation, or at least a simpler explanation between the frequency, input voltage, and inductor value to be able to calculate the output current to the LED. Could someone help me understand how I can calculate the output current given these parameters?

The closer I got to an answer was by reading the SLVA372C App Note, in the equations section, the inductor ripple current:

$$\Delta Il = \dfrac{Vin \times D}{f \times L}$$

Plugging the values I tested on my solar light's circuit:

$$\Delta Il = \dfrac{1.5 \times 0.5}{200000 \times 330 \times 10^{-6}} = 0.0107$$

But when I measured the current to the LED using my DMM I got 6.3mA. $I_{max out} = (I_{limmin} - \frac{\Delta I_L}{2}) * (1-D)$
$I_{swmax} = \frac{\Delta I_L}{2} + \frac{I_{max out}}{1-D}$