The preceding post was based on an assumption that the relationship between prices (Price Index) and results (PPI) is pretty close to linear.
I feel pretty certain that if your prices are above 1.00 and your results are below 1.00, that is a poor result. Conversely, if your prices are below 1.00 and your results are above 1.00, that is a good result.
I also feel pretty certain that prices and results below 1.00 correlate well. I am not so certain of the correlation between prices and results above 1.00.
My assumption has been that if you have a Price Index of 2.00, your PPI (results) should be around 2.00 as well. And the corollaries to this are that if your results are below 2.00, you underperformed, and if your results are above 2.00, you overperformed.
I have not really proved that this relationship is that close to perfect. It would take a lot of mathematics (correlation and regression, feeding a large amount of data into a computer) to establish the exact degree of correlation and to finger out the equation that describes the relationship between the two factors more exactly.
For example, it could be that a Price Index of 2.00 should produce a result of 1.90 or thereabouts (instead of 2.00, as I have so far assumed).
I decided to try a shortcut method to pin down the linearity (or lack thereof) of this relationship. I examined all sales nags of 2003-2007 sold for $1,000,000 or more. That is obviously the highest end of the price spectrum. The closer the Price Index for that group is to its PPI (result), the closer the relationship between the two numbers.
I counted 233 nags sold for $1,000,000 or more in this group. That included 35 stakes winners (15.02%, not bad). Those 35 stakes winners averaged 823 Performance Points apiece, compared to the overall average of 603. That worked out to a PPI (result) of 6.03 (approximately what was expected, given that the C group had a PPI of 3.12).
Those 233 foals had a maverage of 1,106 (1,100 being the equivalent of $2,000,000). That yields a Price Index of 6.78. PPI 6.03. Price Index 6.78. Pretty close. Close enough that one more good stakes winner would have made them almost even.
For example, Lion Heart was sold for $100,000 as yearling in 2002 and for $1,400,000 as a two-year-old in 2003. When I originally compiled these lists of stakes winners for sales foals of 2003-2007, I excluded stakes winners such as Lion Heart who had previously sold (in 1999-2002). I had counted them once as a stakes winner in 1999-2002. I did not want to count them again as stakes winners in 2003-2007. So I followed that precedent and did not count Lion Heart among these 35 stakes winners.
If I had counted Lion Heart and his 2,591 Performance Points, the PPI for these 233 foals would have been 6.57, even closer to its Price Index of 6.78. The point is that PPI and Price Index might not be 100% correlated, but based on $1,000,000+ sales foals, they appear to be pretty damn close. And that encourages me to believe that I have not been barking up a tree without any coons.