And that's why the Lumens for a real-world Thrower is a very useful measure.
Yes and no.
The beam angle and cd tell you more about what you MIGHT see...but lumens are a part of the equation for sure.
Its a little like trying to judge the track time of a car when all you know is the horsepower.
The combination of torque, handling, aerodynamics, curb weight, etc...can make proportionally more of a difference.
So, for a throw oriented modder - the cd is the number of concern...as that describes the throw.
If you know the cd and the lumens, you might know the total out put, and how far the beam reaches, but you still don't know if the beam is all hot spot like an aspherical tends to be, or has a lot of spill, or a large or small corona, or, the proportion of all those lumens in each of those sub-categories.
For example, I could have a 2,000 lumen light with a cd of 50k, and a 1,000 light with a cd of 50k.
The hot spot for both lights might be the same size, but the 1k L light has all hot spot, and the 2k L light has half its lumens in the hot spot, 25% in the corona that falls off at 1/3 the range of the hot spot, and the last 25% in spill that is making a pool of light around your feet, etc....or any other possible proportion.
The cd gives the range for the maximum section of the beam.
The lumens tell you the total output.
The total beam angle tells you the amount of spread that all of those lumens will need to cover (Not counting spill IE: Hot spot and corona)
The hot spot's beam angle tells you the size of the hot spot at any given range.
So, if you need to draw a picture of the beam, the hot spot and total beam angle, combined with the cd, allow you to draw it. If you knew the PROPORTION of lumens in all parts of the beam, and/or the lux at range for more than just the hot spot, you could make a more detailed drawing.
If you took an aerial picture of a beam - you'd see a tiny spot where it started, and then it would look like a candle flame, where the spill would make it fatter, and then tail off, and be thick until the corona range tapered off, and then a peaked hot spot that grew progressively thinner as the last vestiges of the beam's maximum cd beamed out to their limits...finally tapering off to invisibility in a last hair of light.
That's a predictable pattern for reflector lights. For asphericals, where the beam is a picture of the LED, the beam angles are VERY tight...but, the picture of the LED does get progressively larger as it gets further away....and there is not really much corona/spill to worry about.
So - for the aspherics - If you know the beam angle and the cd, you know pretty much everything...because its simple math after that.