Z-score describes how a datapoint compares to a population of datapoint, so of course Staal comes out with a negative z-score when you compare him to a population of 14 centres! By definition, a z-score of zero is exactly average within a population... so since Staal likely isn't top-7 within that group of 14 players, he's going to be negative. When you calculate z-scores, you need to compare to a larger population, and in my view the most reasonable player population to compare to is the "owned" players at a given position in a league.

So if I'm reading between the lines correctly, your issue with z-scores is that they cover a span of negative and positive numbers (with the average at zero) and that people have an inherent cognitive bias against negative numbers (ie whoa Staal's a -1.6, I'm not touching him with a 10-foot pole)? If you've got an issue with negative numbers, blame the player not the game!

We haven't adjusted the rankings - the numbers are the numbers! The league setup that Terry used to back his article probably had a different number of teams and possibly different starting rosters, all of which affect the valuation of a player.

But, of course, why would you calculate all this stuff yourself and be forced to deal with that ugly cognitive bias? Seeing as though we at FHG are so user focused and we don't want our users to mistakenly believe that Staal shouldn't be touched with a 10-foot pole, we've transformed the distribution of value so that zero sits not at the average but at the lowest owned player.

I think z-scores (modified FHG style, of course) are absolutely the best approach to player valuation since they automatically adjust to your league size/settings. With the same stats, a league that dresses 3C/3LW/3RW/5D is going to have very different player populations at each position when compared to a league that dresses 4C/4LW/4RW/6D.

However, as we've both pointed out, player valuation does not equate to team performance.

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Yes and no...

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.

In fantasy hockey (especially in H2H), the scoring isn't based on a cumulative score of all the players, they're individual categories, so when Staal is better than the average in 3 of the 6 categories, and on average for 1, below average for 2. To me he still has "positive" value, so I don't buy the fact that in a "cumulative" scoring summary that he should be a negative player and mostly punished for the 1 +/- category.

It's like you said before, if that's my "punt" category, if I win 4 out of 6 tied 1 and completely tanked +/-, I'm still winning my small battle in H2H leagues, so how can it be negative? And if Dorsett really only provides me an advantage in 1 stat, how can he positively affect my fantasy team and lead me to a championship when he only influences 1 stat...

But one thing that absolutely makes sense is as you said, FHG is great a determining player valuation, but that's just it, it doesn't take into account "team value"...

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Dobber Expert Pool Champion 2011-12

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.

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Dobber Expert Pool Champion 2011-12

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.

Yes and no -- the integrity of the math is still exactly in tact, we've just adjusted the presentation to reduce that cognitive bias.

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Yep, should be compared to all owned players. Typically it takes about 5-7 iterations (re-sorting by z-score totals using a pool of 500 skaters, for instance, until the top 210 players out those 500, stay in the same order when you sort them) to find the theoretical top 210 players that should be owned.

Z-scores challenge the thought that certain categories matter more than others, or that it's acceptable to be weak in categories like PIM or Hits because "hey, it's not a negative value, so it can't hurt my team". It's a lot more obvious when a goalie has a bad GAA or SV% because you think "damn, he's killing me!" In reality, Kessel is "killing you" in Hits and PIM by having such a low total.

That said, there are also caveats that certain stats are more predictable and should have more value placed on them. +/- is not nearly as predictable as G, A, Hits, Blocks, or PIM. In fact I did a little experiment recently. Dobber's projections unfortunately only offer grades of A, B, C, or D for players to gauge predict their +/-. Guideline's are given such as A = +5 to +15, B = 0 to +5, etc. Last season, the group of players that were in group D - that is to say, the worst of the worst - ended up with a better average +/- than the players in group C. So even with a large group of players where you'd assume the outliers would cancel each other out, the error in projection was extremely large. This tells me one thing: do not place much emphasis on +/- when summing up z-scores. I didn't do the same test for goals or assists, but I can almost guarantee that the group of players projected for 65-80 points scored a lot more than the group of players projected for 50-65 points. Same goes for PIM, PPP, Hits, etc. My way to deal with this is to cut the z-score total for +/- in half. So every other stat is weighted twice as much as +/-. It woudl probably be a good idea to get an ideal weighting for each category based on predictability, but I'm not a mathematician.

Nonetheless, the fact remains that players with huge negative values in certain categories deserve to be docked severely for those shortcomings. Nobody has an issue with this when docking Chris Neil for his lack of goals or PPP. So why is it such an issue for Kessel and PIM, Hits, or +/-? His value should take a huge hit, and the fact that it doesn't is precisely because of faulty logic.

Music to my ears, Skin Blues -- couldn't agree more.

(as an aside and/or plug, any stat set on FHG that's projecting into the future has significant downweight -- less than 50% of true value -- of the "less predictable" stats like +/-, SHG, GWG, etc etc)

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Good thread.
I have to say I agree with FHG & Skin Blues.
Fantasy hockey value is cumulative and spills over across categories. It requires some iterations to get there.

In this link, I have a pdf called test9... which is a multi-cat scoring system that I set up and I finally hit a huge comfort level with it when all the category scores for the entire player pool summed to similar amounts. Ma has seen it. PIM, in my models, always seems like it has inflated value (based on the rank of PIM-goons... but I actually think it's accurate "actual value". It's a good example of the spill-over value of having one category-strong player. (and the converse is true). Having a PIM-monster allows the GM to focus more on offensive-cats since PIM will be taken care of. That strategy is an example of the spill-over value from having one guy that is so incredibly great in just one category.
(Of note: the best value I extracted from my work is this: PPP should be the main category invested in on the front-half of a draft... because it is the category that drops-off/diminshes fastest. Approx 66% of PPP are found in the top 90 of 180 players. After that, there are much fewer to be found. PIM/Hits/BkS, as we are all learning, are by far the easiest category to find/stock at the end of a draft.)

As for the players,
Kessel falls in around #55 forward based on his low PIM/hits.
And E.Staal falls around #64 forward based on his low +-/hits... though I did buy on E.Staal (& Rick Nash) in several leagues this year... mostly expecting a correction in their +/-.

I actually had some off-site number-crunching discussions with temek (who is probably among the Dobber elite with number-analysis) a few month ago.
He's another solid-mind for getting into the numbers. I was impressed.
Yourselves (FHG, Skin Blues, Ma) included. Hey Robbie & horrorfan are a couples others with a good grip on these numbers.

We need a club.

Yeah definitely great discussion...

I think we're boiling down to personal opinion rather than actual fantasy impact of numbers... We're all on the same page in terms of using numbers to help guide decisions, it's about how we interpret those numbers to form our judgements that we're differing on.

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Dobber Expert Pool Champion 2011-12

This thread is going to explode from brain-power overload...

Or weed out those who are weak-minded, hahahaa!

Survival of the fittest!

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Dobber Expert Pool Champion 2011-12