This is a difficult problem for the camera ... and it's a situation where you have to take over.
Here's the histogram:
(the advert is because my EXIF view is moderately transparent... thats' the ad in right side of the page on TPF)
The histogram provides a graph of the light distribution for your image. The left edge represents completely black pixels, the right edge represents completely white pixels. And of course every level of tonality in between. The height at each level of tonality indicates how many pixels in your image are at that particular level of tonality.
Notice the "bathtub" histogram... data jammed up against the left wall.... jammed up against the right wall... and flat in the middle. This indicates there were lots of completely black pixels... as well as some completely white pixels ... but not a lot of mid-tones.
Usually when you see the graph data jammed to either left or right walls it means there was more data "beyond" what the graph can represent... because there was more tonality beyond what the camera could record.
The camera was doing it's best to try to get as much data as it could... unfortunately it was more dynamic range than possible.
In this situation, we really only care about the light not the performer... ignore everything else. We can see how bright the performer is and when we look at the graph, we can recognize that the data which is near the right edge of the graph represents the pixels in the spotlighted area.
Since the performer happens to be in the middle, spot metering (which only meters the middle and ignores the rest) would work. The camera wont care what the exposure is for anything outside the metering area ... so it'll just find a good exposure for the area you ARE metering and ignore the rest ... so that'll be extremely dark (nearly black) -- but that's ok.
If the subject moves around (isn't necessarily in the middle ... or if it were say a band and they were all over the stage, you could use evaluative/matrix metering (same idea... just a different name depending on the camera brand) and then use exposure compensation to tell the camera to deliberately under-expose by a bit (probably 1 to 1.5 stops). I play with this a bit at different concerts ... sometimes it's nearly 2 stops. Sometimes it's only 2/3rds of a stop.
Get the exposure on what you care about and just let the rest clip.
This was a dimly lit theater ... I hit this with a small curves adjustment and slightly desaturated a magenta theatrical light on him, but otherwise this is pretty much how it looked live.
That was using spot metering AND -1.3 stops of exposure compensation.
But notice everything else is pretty much just completely black.