I suggest:

8 points -- 1st
5 points -- 2nd
3 points -- 3rd
2 points -- 4th
any other placing = 1

some time ago I posted a spread sheet on this forum that assessed a horses chances based purely on form factors -- I adopted the above point scale (based on extensive research)

btw -- the point of the spread sheet was to demonstrate how to parse a string in excel

ps -- thanks for your hard work and sharing your findings (mathematical formula) on the relationship between win% and place% -- I also posted a spread sheet on how it might be put to good use

have the best day!

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