if they were the same "nature" of lamp, then this would be true.
the lamps however are not directly transferable with one another, from a data perspective.
just because the wattages are nominally the same, the lumens output are substantially different, indicative of both variable light outputs and other forms of energy release, not documented in the graph (ie, heat).
that said, the graphs between any two non-comparable bulbs will definately integrate to a different value. We wouldnt expect a 400w metal halide to integrate equivalently to a 400w HPS...because there are other variables.
You could be right. But I have both a CMH 400W and a HPS 400W. I don't think the heat output could account for the MASSIVE difference in scale of those curves. Perhaps UV output might have something to do with it since higher frequencies are more energy dense.
But I would say the area under the curve of the HPS lamp is a tenth of the CMH lamp, which intuitively makes no sense to me.
Lumens shouldn't enter the picture though since those bear only an indirect relationship to the integral of power spectral density.
I guess what I'm saying is that if they used absolute units instead of relative units for the y axis of both curves so that you would be comparing apples to apples, the yellowish peak in the HPS curve would be way taller.
Or put another way, if the CMH curve was plotted relative to the HPS curve (rather than itself) the peaks would be much shorter.
It's pretty clear that what they've done is scale the power spectral density graphs so that the tallest peaks are roughly equal height. And in order to do that they have to employ different scale factors. Which is deceptive advertising. But that's par for the course in this business.
Personally I think the CMH bulb is a better bulb, but these graphs overstate the case.