“I never understood the attraction of tiers. To me, it just seems like a shortcut to value/rank players. Why do I need tiers if I already have calculated actual dollar values?”

I agree that they don’t provide any new information for an auction. I think the value is for drafters, who might not usually bother with dollar values.

Basically, if you are in an auction OR a draft, go ahead and build dollar values. They will tell you much more than a list of ranked players.

Some are, though. R, HR, RBI, and especially rate stats have a pretty nice bell curve distribution.

Saves, SB, W, and K don’t, though.

The thing is, you’re not really using standard deviation to compare to a normal distribution. The way this z-score system works, someone 3 standard deviations above the mean simply gets 3 times the value for that stat as someone 1 standard deviation above the mean, as you’d expect. Someone with 30 HR gets a value of 30/SD, someone with 10 gets a value of 10/SD, so the 30 home runs is simply worth 3 times as much as the 10.

You are going to still overvalue the non-normally distributed stats a bit, but it still does a pretty good job of estimating the value of one stat w.r.t another.

Essentially, you are calculating z-scores for each category and summing everything up to get a total ranking. The problem is that the z-score method assumes that all categories are normally distributed. If categories are normally distributed, you could then actually convert z-scores to percentiles. For example, a z-score of +2 is at the 98th percentile. However, some categories (e.g., stolen bases and saves) are clearly not normally distributed. Thus, players with very high totals in these categories (i.e., outliers) are going to have total scores that are inflated. Do you correct for this inflation?

I’m not sure how to do it though, as the method I was thinking of is clearly wrong when I think about it more, so I’m not sure that doing an adjustment like this is feasible or even correct.

If it is calculable, I would think we should be able to calculate it in advance, since we ‘know’ that the top 2 SS’s will be gone when it comes time to assess the 3rd.

I often color code or the like as well, but the fact that in circumstances like the Atkins one we thus stray from our ‘precise’ rankings illustrates the problem – I would think a slight correction to boost the computed $ value of the last 3B in a tier (or to lower the highest in a tier) would improve the situation (i.e., one wouldn’t be stuck as often having to decide whether to ‘go with your rankings’ or a vaguer tiered approach).

In an actual (snake) draft, where appropriately reacting to position runs is a crucial skill, this probably isn’t important – I was just thinking that for theoretical purposes (like the ‘Retrodrafting’ that is used for testing the Price Guide against other rankings) a ‘tiering’ correction might add value.

I think it’s mostly for people who don’t know how to or don’t want to calculate dollar values, since it requires less work, but it’s obviously much less precise.

The example of taking Atkins before those 2nd basemen based on tiers is EXACTLY what I do. Although I technically just draft with my spreadsheet of players in descending order of dollar value, I color code each position which in essence illustrates the tiers. If there is a cluster of OFers, for example, at the top of my sheet for my next pick, with a 3B in between them and no others for another 40 players, then I go with the 3B even though a couple of OFers I valued a little higher.

Think about your final standings, you don’t care about where you get your 250 HR, just as long as you get 250. A HR is worth the same regardless of position. A system like this doesn’t work because it can’t compare between positions. What if you had a utility/DH spot? Then you end up with player A having more value than player B at his position, but at DH player B has more value than player A. This is clearly not right.

To prove this, I ran the 2008 stats for my NL only league.

Pujols is worth $38 as a 1B, but he’s worth $41 as a utility player, and Berkman is worth $39 as a 1B but he’s only worth $35 in the utility slot.

Things are even more screwed up if you have an SP and an RP slot: the top two relief pitchers are Hong Chih Kuo and Carlos Marmol! Low ERA/High K/High Win relievers are absurdly valuable under this system. A win from a reliever isn’t worth more than a win from a starter in the final standings, but doing positional z-scores it’s almost 2.5 times as valuable!