I've been avoiding this question because it's complicated. I was hoping that member Lux Luthor would jump in here but perhaps he hasn't seen the thread yet.
Well, since no one has responded I'll try to answer in the most simple way I know how. You asked how you can compare a Maxabeam's candela claims to the Polarion's lumen claims but you really can't from a technical standpoint. No conversion process will ever give you the information that you're looking for because a "formula" for conversion doesn't contain the necessary information the extract results. You can measure candela for each light, and you can measure the lumen output for each light but it really doesn't tell you how they'll directly compare to one another.
If you're just looking for a good estimate of lumens from the Maxabeam it's about 1400-1600 lumens. Far less than the 3400-5200 lumens from varying models of Polarion HID. This is typical of the differences between short-arc and long-arc technologies.
For an example see this thread where a 60W Short-arc is compared to a 50W long-arc:
https://www.candlepowerforums.com/posts/2976841&postcount=52
Here is a comparison between the 75W Maxabeam and a 50W Polarion:
https://www.candlepowerforums.com/threads/210201
A short-arc light is a very particular type of creature with limited application. They throw much better than any other type of light technology but with fewer lumens. Standard HID lights are the most flexible for general use while still throwing much farther than incan type lights.
You're second question was "why does Polarion give Lumen instead of Lumen per square meter or lumen per feet meter.?" The answer is that the lumen rating is a generic number or raw data from the measuring device, an integrating sphere. It would probably be better convert or to measure lumens per sqaure feet/meter, as they use in science or area lighting but when it comes to hand held spotlights Polarion probably decided to stick with the standard "measuring stick" which is the lumen. Most people who will be purchasing spotlights and flashlights can best relate to the generic value of lumens since that's what's usually used in the industry.
