My problem with z-scores is because it's a "cumulative" score, if you have 1 really bad negative like in Staal's case (+/-), that negative gets exasperated even though it's only 1 stat. Same could be said, if I plugged in Dorsett, his PIMs would singlehandedly boost him positively because he's so much more above the average, but it's only 1 stat.
I don't think you're applying z-scores correctly -- Staal shouldn't have a negative z-score when compared to the population of owned centres. If you're comparing him to the top-14 centres, then he should because among that population, his +/- really stands out. Your example is a little misleading here because he has one stat that's really bad when compared to the very best centres out there, which is also a scenario where his positive attributes are more "average". His poor +/- is closer to the mean amongst a larger population, where his positive attributes would likely be farther from the mean.
In general, I get what you're saying here, I just think we differ philosophically on how best to manage a team. There's a difference between punting a category for a player (ie he has terrible PIM so I'm just not worried about it
) and punting a category for a team (ie I don't think I need PIM to win a matchup so I'm going to systematically draft players who perform better in the other stats at the expense of PIM
I would never argue against the latter, if it's a viable strategy. But player valuation doesn't really play into either of these things -- that's team management. Player valuation is about understanding the breadth and limitations of a player's contributions, and a player that has a higher z-score is a greater net contributor.
There are very few category-special players whose overall value exceeds that of a well-rounded player. It would take an insane number of PIM to offset the crappiness Dorsett has for the rest of his categories.
The inherent risk in disregarding or even acknowledging "punt" categories (on a player-by-player basis) is that if that player is slumping and/or injured, the rest of your team might not be able to adequately pick up the slack. Having a team full of 10 guys that are each 25 PIM (or whatever category) below average leaves a big hole to fill if that player isn't performing.
If we're moving to a discussion about "value to a team", my view is that it is a separate and distinct issue to manage than player valuation, and that while they are linked, both can be managed upwards without necessarily costing each other.
I think that's the difference that you guys made with z-scores than zeroing the average... That's why your rankings aren't as "by the numbers" as a mathematical theorem.
Yes and no -- the integrity of the math is still exactly in tact, we've just adjusted the presentation to reduce that cognitive bias.