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My guess is that the reason you're seeing an inversion between high and very high desire to win is that the parameter is unimportant and it's just a statistical fluctuation.
More importantly, though, I wonder what is the correlation between each personality trait? For instance, if you assign a numeric value to each possibility, and calculate the correlation matrix between all of the parameters.
i.e., desire for win may be correlated with work ethic, and while desire for win on it's own is unimportant, it may be correlated with making it to the big leagues only because it's correlated with work ethic.
Also, do you know the full sample size of players?
I realize you said it was an old test and you probably don't have these numbers, but just throwing it out there.
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