Now if only the sytems would adjust for 4×4 leagues….

>What if one fantasy owner hoards 1st basemen?

>Of course, it’s important to note that the bench won’t necessarily be filled with the highest z-scores. Most managers will want a backup at an MI position, even if there are OF, 1B, or DH types available with higher z-scores.

These two statements I think pretty much sum up the situation.

My basic assumptions when creating a valuation system are:
(a) everyone in the league is using the same valuation system
(b) teams aim to strictly maximize their own value, not their own value relative to others
(c) my projections are 100% accurate
(d) if ranking for a snake draft, if player x > player y, then you will want player x over player y if you have no knowledge of who else is already on your team

In your league of robo-1B, my assumption (b) covers the hoarding argument. It’s not in a team’s interest to hoard bench players, since you’re foregoing value elsewhere. You can’t assume before hand that someone will hoard. You have to value players as if all starters will be drafted before bench players are.

No one is ever going to draft straight according to value and in auctions you’ll end up paying wildly different values for some players. All we’re looking to do here is put a value on a player and what he can expect to contribute.

When you spend extra money on your bench, you are not paying for a “solid backup”. What you are paying for is upside. You may not want to start Justin Upton, but you might still spend $5 on him. That has nothing to do with bench, replacement, or depth. That has to do with the fact that he’s one of about 15 players that can even dream about hitting .300 with 40 HR.

In my latest calculations, I’ve been running two $ values. The first is using the normal last starter picked model. The second is a “true” replacement level. For my league, that’s about 2.5 pts for pitcher, 1.5 pts for hitter, 1.0 pts for catcher. So I subtract those points from the starters, and that’s the “True Value”. That makes 150 players worth $1+ opposed to 240. That’s a pretty good estimation of how I draft.

Once we get down to that level, I go by points instead of $. If I’ve got money left, I’m going to try and maximize the value I get, even if that means overpaying for the best available player. At this level, that means the guys I want, which are usually young and talented but not anywhere near proven. Sometimes it’ll even be a minor leaguer!

I like your thought experiment of all players being drafted. One more thought experiment: assume we had 15 robot first basemen who all performed at the same level X. Assume the other 15 first basemen are absolutley terrible and perform at level Y. Assume 14 teams in the league. Positional adjustment says the value of the 1st basemen is nil because the starters are all equivalent. But what if we allow benches? What if one fantasy owner hoards 1st basemen? Another owner would presumably pay X-Y in value to get a robot 1st baseman on his/her team. So to say that benches don’t affect positional adjustment seems counter-intuitive. I’m sure there’s a game theory solution to this problem I’m not smart enough to figure out.

To recap: If you have n starters in the league, the positional valuation theory says you subtract the (n+1)th z-score from every player in that position to adjust for positional scarcity. But that logic assumes you can get the (n+1)th player ‘free’, or for $1 perhaps, in waivers. What if (n+1,2n) players of that position are on the league’s bench? In that case, the minimum stats generated argument doesn’t seem to apply, because you can’t get the (n+1)th player so easily. There is no free market for the replacement player.

Then what baseline z-score do you subtract for positional adjustment? The (n+1)th, or the (2n+1)th? Or something else?

I think we then have to ask what would the average replacement level be among players on your bench? I’m thinking a reasonable assumption is to make it the mean or median of the additional players. So to the example in the previous paragraph, wouldn’t the positional baseline be either the median or the mean of the (n+1,2n) group of players at that position?

The order, perhaps, might be to first do the adjustment you mention — adjust everyone’s zscore to account for the worst player on the bench. And then do a positional scarcity adjustment based on the median/mean bench value of players remaining.

Of course, it’s important to note that the bench won’t necessarily be filled with the highest z-scores. Most managers will want a backup at an MI position, even if there are OF, 1B, or DH types available with higher z-scores.

While having players on the bench changes the replacement level, what it doesn’t do is change the minimum stats generated at a position, which is what you’re really concerned with.

Imagine a league where you started 9 hitters but had so many bench spots that every player on each 25 man roster is drafted.

You don’t want all of your baseline values to be set at the worst player in the league, as none of those bench players are going to get you stats. This would be the same as not doing a positional adjustment at all.

However, some bench players are certainly better than others. If your league drafts 60 bench players, the first bench player drafted won’t be the same value as the 60th, so you don’t want to pay $1 for both of them.

I think the best way to do it is to set your positional adjustments and determine the values as you would without any bench players. Then, say there are 60 bench players. Find the 60th player not yet taken and subtract that player’s adjusted z-score from everyone else such that the 60th bench player is now a zero and redo the dollar values based on that.

This doesn’t adjust the baseline for each position, but will make it so that the last starting SS is still worth more than the last bench SS.

Technically it’s the 15th best catcher, but he isn’t freely available — he’s on somebody’s team, most likely.

Another ad hoc option is to split the bench. So total # of starters to enter in price guide is # of actual starters + (bench/2).

BTW, I have been able to run the price guide with fractional positional requirements. Does the Price Guide work differently if there are fractional positions, or does it just round anyway?