Try using a rolling avg based on starts to find the number of starts that are required when your sample reaches the normal lifetime stdev.

also you may want to try folding the data in a way that your example horse who has had only 3 starts and you need a 12 races before you have confidence.
This 3 start animal may have rated 45 most recent start, 48 , 50
you might feel the most recent is more important so you
would create a synthetic stdev
45,45,45,45,45, 5 times
48,48,48, 3 times
50,50 2 times
and so on an you move to a better stdev.
or if you have a good database
you select all runners that have exactly this type of avg rating for 3 starts, then look at that group and see how they performed their next start and make that type of adjustment to todays expected rating