Is there a formula for determining the value of coins in mint state between each or is it determined by auction results or past sales?
Between each what? A formula could give you a very good approximation of an existing relationship, but it does nothing to control the future. Ultimately, price will always be determined by the intersection of supply and demand. You could make a formula for a curve fit, for example, between prices of different grades of a coin, and it would be a good starting point. New information can slightly shift the demand curve as people have a closer idea of what something may be worth to other potential buyers. But relationships change over time, and so the formula will drift to become less and less accurate as new data makes it obsolete.
Lets say for example a coin in the price guide catalog shows a coin at MS 60 and has a value of 1650.00 and you can't find any more reference to the value and you had the coin graded MS 64 how would you determine the value jump? Hypothetically speaking of course and yes I feel like I have this scenario
It's whatever any one person is willing to pay. If you think there is some nice formula that says every +1 grade equates to 0.356 more value then, no, there is nothing concrete like that. Sometimes, certain series, MS60-MS64 might all be very similarly priced, as everyone is say chasing MS65+ examples which cost considerably more than the MS64 and lower coins float at their base medal values. For example, generic gold coins. Other series, maybe AU grades are all very common, and are all similar in priced, and so you could pick up a AU58 for same price as AU53, but as soon as you hit MS, they are leaps and bounds between each MS grade 61,62,63... Sometimes certain dates of a series are particularly scarce, or particularly sought after for non-scarcity reasons, and that one date might behave very differently than other coins in the same series. The other thing, which is probably the most important thing, is that every coin is it's own special creation. Just because you see 50 examples of a 1923 Peace Dollar in MS66 all within say $10 of each other, doesn't mean that the very next example of that same date and condition wouldn't sell for 3x as much. Does it have some beautiful buttery luster that people are chasing? Do people think it's really a 67? Is it in a desirable holder, such as a Doily, is it CAC approved, does it have a uncharacteristically sharp strike, does it have a desirable provenance, etc? If you see each coin as its own special child, totally unique from its siblings, you will understand that a secret pricing formula makes no sense, unless you only concern yourself with the most generic or generic coins. Also, if you really do come across a particular coin and date and grade that has zero pricing examples on www.ha.com, then I would think it is incredibly rare to the point of any guess as to pricing needs to be thrown out the window. You might as well figure a 10x or 100x over your MS60 pricing, and no real way to know until the auction ends where it will end up. HA has a seriously large database of prices realized, so always start there for an approximate value, and add or subtract as necessary based on the qualities of the specific coin. Hope this helps.
Remember, the Sheldon scale was developed based on the relative price of a specific Early American Copper cent (I don't remember which one). It was worth 2x in Fair vs. Poor all the way up to 70x for a hypothetical perfect specimen... That's the last time anybody tried to create a mathematical pricing formula.
