An interesting question: how rare are particular rolls?  Thinking about
this, I wonder just how it might be answered.  Is it simply scarcity, or
is there something more wanted?  I suspect the latter -- normally folks
are interested in things that are desirable, as well as being scarce.
Almost by definition not too many will care much for "scarce but
undesirable" rolls!  For fun, let's have a go on these two rolls...

Hupfeld 50317 is Mozart's Sonata A Minor K310 played by Ludwig Wambold.
This is a relatively early 88-note serial number (they started at 50001,
and ran to just above 60000 in some chronological-ish manner) so would
have been on sale for longer than later titles: half of my Hupfeld
rolls are under 52000.

On the other hand, it's a lesser piece by a major composer so probably
sold in relatively small amounts and might attract a serious collector
who wants to fill a gap.  There's no Duo-Art or Ampico roll of it (they
both did K311, the Sonata in A major).  On both scarcity and desirability
[the rating is] perhaps 3 out of 5?  Probably significantly scarcer in
America than in Europe because of Hupfeld's sales distribution.

Ampico 54686 is Saint-Saens' own roll of the Finale to Samson et
Delilah.  The 'M' on the end of the number is a price code and can be
ignored.  The performance itself is taken from Hupfeld 51203, and has
had Ampico expression coding added.  I have no idea of rarity for
Ampico rolls, but on desirability a composer-played piece must rate
more desirable, especially by a major composer such as this.  On the
other hand, Ampico used a lower (poorer) punch step rate than Hupfeld,
so had to re-quantise these rolls, meaning that the performance will
suffer relative to the Hupfeld original.

There are, of course, many other ways which you could approach an
answer, so don't read too much into the above analysis.  Others'
conclusions may differ significantly!

Julian Dyer