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I've waded into a few of these threads on Twitter over the past year, most recently about Diodoro (who was 17 for 42 from opening day 1/24 through about 2/8).
Putting aside the comments horses move up a lot, re-break, etc... just based on statistics alone I'm unconvinced using statistics to make a case a trainer is taking an edge has any validity. I'm saying this as someone who once made a public comment about McKnight's win percentage off the claim, but when someone I respect privately challenged me I did some more research and agreed I was out of line.
Regarding Joseph - in the last 12 months, Joseph has started 404 horses and won with 107, a 26% rate. Maybe people smarter than me will say 404 horses is enough of a sample so I went back two years and his record is the same 26% (172 on 662).
I'll agree it's a decent sample. If someone deeply versed in statistics states 662 is a statistically significant sample and the results are not due to chance alone that ends one of the discussion points.
By the way, his record first off the claim for the last 2 years is 25 for 104 (24%).
Back to the straight win percentage discussion. For me, the 26% win rate just isn't high enough, relative to average, or if plotted on a curve it would not be more than two standard deviations from the mean of all trainer's overall win percentage to make any allegations.
I'm not an statistics expert, but I am a cynic, I and believe its very difficult to prove any of these results are not explainable by chance alone.
Back to Diodoro at Oaklawn, through 2/20 his record is 24 for 65 (37%) but his five year record is 161 for 625 (26%) which is high but not implausible for the kind of operation he runs.
From a handicapping perspective, I certainly do pay attention to these trainers who win at a consistently high percentage, but in my opinion there needs to be more substance before suggesting something nefarious from these numbers.
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