There are many factors to consider when determining if a star note is worth more than face value - condition, age, total number of star notes printed for the specific series/denomination/FRB, and the size of the print run. That last two - the total printed and the size of the specific print run - are the more important aspects and what the Star Note Lookup helps you find.
In summary - the order of star note rarity, most to least:
1. Star note print runs of 640,000 notes or less that happen to be the only print run for a specific series/denomination/FRB combination AND it is an older series.
2. A similar star note print run as above, except printed for a more recent series.
3. Star note print runs of 640,000 notes or less, where there are other star note print runs in the FRB.
4. Star note print runs of more than 640,000 notes. The larger the print run, the more common the note is.
Why Are Small Print Runs Rare?
Many collectors try to complete star note sets by obtaining a specimen from each star note print run. Naturally, the smaller the run, the harder they are to find. For example, there are 20 $1 2009 star note print runs as seen here: http://www.mycurrencycollection.com/reference/star-notes/1#2009. It will be relatively easy to find or buy a note from the runs of 1.28+ million, but getting one where the print size is only 32,000 will be very difficult.
Run size can vary greatly - 3.2 million notes is the largest print run size, but they can also be much smaller. 640,000 is generally the threshold of run size when star notes start being considered more rare. Many small runs are printed between 160,000 and 640,000 notes. Some have been printed in quantities of 16,000 or less.
Also Consider The Total Quantity Printed Per FRB
Another consideration is the total quantity of notes printed for the specific series/denomination/FRB combination. Some collectors try to complete sets with one star note per FRB. When a FRB has a few print runs of star notes, there are more notes out there to find or buy to fill the slot in their set. If a FRB has three print runs - 320K, 640K, and 3.2 million - the collector can ignore the first two runs and complete the set with a cheaper, less rare note from the run of 3.2 million. This deflates the value of notes in those first two rarer runs.
The Rarest of Star Notes
On the other hand, sometimes a FRB only has one star note print run, which might be a small run of 640,000 or less. For example, the 2003 $1 "D" FRB has one star note print run, and it is only a quantity of 320,000 notes. People who collect star notes by run and by FRB both need a specimen to complete their sets, so the note's value increases.
The condition of a note plays a HUGE role in it's value. The rarest star note probably isn't worth much, if anything, more than face value if it's dirty and shredded.
For older series notes, their run sizes matter far less. Completing star note sets by print run is more common among modern star notes. Older star note series typically get collected by FRB, so the total quantity printed is more important. Additionally, many reference books don't break down older-series star note value estimates beyond FRB letter. The whole notion of print runs gets diluted.
Current Series Star Notes
For series that are currently being printed (like series 2013 now inFebruary 2017), there is the unknown of future printings. The value of a star note can change depending on whether more notes are printed prior to the series being retired.
Also for series that are currently being printed, there is usually a frenzy around "fresh" star notes. The BEP releases monthly production reports of which series and denominations are printed. There is often a delay of a few months or more between receiving those reports and the notes being found in circulation. The anticipation of finding the next newest, rarest star note often drives value up initially.