Fantasy Value Above Replacement: New and Improved!

You may remember that earlier this year I put together a series of three posts outlining a system for objective fantasy player rankings and valuation. The system was (and still is) titled Fantasy Value Above Replacement, or FVARz for short. Some flaws were pointed out in Februrary, and it’s about time I recognized them and corrected the system to allow it to be even better and more accurate.

The major flaw that was pointed out was the way I was adjusting for position. A players’ raw stats were only being compared to others at his position, instead of the entire player pool as a whole. After the changes to the FVARz system, this is no longer the case. Players raw stats are now compared to the entire player pool, while hitters and pitchers are separated for obvious reasons.

After comparing players to the entire pool, their zWAA is compiled and compared to their position. After the positional adjustment for replacement level, a players’ final value (zWAR) is produced. This value is then put through the same auction converter as before, yielding a projected (or retrospective) value for each and every player inserted into the system.

While the FVARz system is now a tad more complicated and difficult to use, I feel it now gives us a very accurate representation of a players’ auction value as well as an accurate way to rank players across positions.

There are a few specific things the changes outlined above have brought to light, and I have detailed them below. Stayed tuned to RotoGraphs today, as I will be publishing final values for the 2011 season.

Noted Improvements
- Players that had rare stats for a position — such as SB for catchers and first baseman — were being overvalued. Yes, 15 steals from a catcher is harder to obtain then 15 steals from an outfielder, but in the grand scheme of things, they are equal on your roto ledger. Players with the rare stats for a position will still get a boost simply because it helps their overall value, but that boost will no longer be just because they are different from the norm at their own position.

- Before, I took value away from pitchers because they only filled up four of the five stat categories. Now, because relievers are being compared directly with starters, an artificial adjustment is no longer needed.

- Saves are now more valuable. As starting pitchers and their lack of saves were introduced to the pitching mix, each save became more valuable and boosted closers in the rankings. A good non-closer can still crack the top-10 in the reliever rankings, but it will be near impossible to reach the top of the ladder now.

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Zach is the creator and co-author of RotoGraphs' Roto Riteup series, and RotoGraphs' second-longest tenured writer. You can follow him on twitter.

13 Responses to “Fantasy Value Above Replacement: New and Improved!”

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  1. OaktownSteve says:

    I recall seeing this series at the beginning of the year. Nice to see an update. I’ve given this topic a fair amount of thought and there are couple of things which I believe remain somewhat elusive.

    1. I believe there is some value in players who have what you called “rare” stats for their position. I believe the value comes from a number of different factors. It helps distribute risk, for one thing. Consider that there are three positions from which you can count on very few steals, for example: 3rd base, 1st base and catcher. This means that in order to compete in steals you have to have a high concentration of players in the other positions that will give you steals. This often leads to being forced into players who just steal and have few other contributions. This means that risk is clustered in those players and that players at those positions who might offer more value might not be able to be considered because they don’t steal any bases.
    2. Which brings me to the second point, which is that looking at value by measure component parts of each category misses something that I am still working on quantifying, but which I believe exists, which is the additional value created by players who contribute in multiple categories. That is to say, the stats are equivalent when you have a homer and steals specialist versus two balanced players. One obvious advantage is, again, the distribution of risk. Balance also seems to contribute to roster flexibility. I haven’t yet come up with a way to put numbers to it, but my instinct tells me that Matt Kemp as a fabulous 5 category contributor is very significantly more valuable than is reflected in your system.
    3. Finally, the position scarcity factor continues to be difficult to do. First off, the pre-auction valuation is very different from a post-auction valuation. What I mean is that pre-auction, the valuation must tell you how much to spend on each player in order to fill out the required number of players on a roster. After the auction is complete, those valuations no longer apply because a home run hit by an outfielder contributes identically to the standings as a home run hit by a shortstop. Using a value that considers position scarcity is really either mostly or perhaps exclusively important before the auction because the task it to create a valuation that gives you relevant information about allocating resources (limited) within the strict guidelines of roster requirements.
    4. Furthermore, there are not actually and infinite number of players with infinite characteristics. If you did have an infinite number of players then you could ultimately construct a roster where you were paying the correct $ amount for the correct component parts of contribution (x dollars for home runs, y for rbis, z for sbs, etc). But the scattered distribution of value by player by stat means that you won’t always be able to map the dollars you wish to spend to a player with the correct characteristics. In that sense, players like Joey Votto or Eric Hosmer (sbs by a 1st baseman) or Tulo (power at ss), may have special value because of the impact that those unique characteristics have on the overall roster construction.

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  2. Geoff Buchan says:

    A home run counts the same whether it’s hit by a catcher, a shortstop , or an outfielder. What makes a catcher more valuable than a first baseman with the same stat line is that the replacement player at catcher is typically much worse than the replacement at first.

    In my pricing model, I only consider position for determining replacement level. Otherwise all players are given a normalized score for each category (so the categories could be weighted arbitrarily), and then positive prices are given to those players with total values above the replacement level for their position.

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  3. Zach (not Sanders) says:

    How do you account for multi-positional players? I started by assuming that positional values were ranked as follows: SS, C, 2B, 3B, OF, 1B. So, every SS/2B was included in the SS pool, every 1B/3B was a third baseman, every 1B/OF was a first basemen, etc. However, that means all players with 1B eligibility are taken out of the 1B sample, which is a large share of 1B, and leaves only 21 first basement with >=400 PA, less than the 23 determined as above replacement. This essentially makes Adam Dunn (the worst eligible 1B, by far) and his -5.79 total Z score replacement level, giving 1B the largest positional adjustment.

    And of course, shifting those multi-positional players from 1B into other positions boosts overall production at those positions and decreases those positional adjustments, widening the gap between 1B and others.

    Zach (Sanders), how did you systematically approach multi-position players? I’ve posted this comment in Part Two of your original series as well.

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  4. Zach (not Sanders) says:

    I should have searched the comments from your original post on replacement levels. I see now that your approach is to include a player in each position for which he is eligible (of course, only counting him once for purposes of calculating Z-scores).

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  5. Zach (not Sanders) says:

    I agree with some of the comments from your end-of-year rankings that the dollar values seem low. I’ve attempted to implement Zach’s process for determining true talent (weighted average of 2011 projections and actual stats) using the Ottoneu 4×4 setup (40 roster spots, $400 budget, etc.) and have found that the distribution of values does not resemble the distribution of actual salaries across all leagues with this setup, especially at the top end. The top 5 hitters from the valuation method were worth $39, $34, $32, $31, and $31 whereas the top 5 average salaries were $63, $56, $54, $54, and $50 – an average markup of about 67%!

    I agree that the Z-score method is appropriate and the mathematical conversion of scores to dollars is straightforward, so I’m not sure where the disconnect is. Perhaps the definition of replacement? Or is it that people are systematically and grossly overvaluing top-end production?

    Also, in case you were wondering, I assumed that the average team used 5 roster spots and $25 on minor leaguers, which seemed appropriate for my league, so I accounted for this in the auction conversion equation.

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  6. Trey says:

    Zach – must have missed the link but are you making this tool available for others to use/download? If so, where?

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    • Herbstr8t says:

      Yeah, where are the details on your improvements, e.g., step-by-setp instructions?

      When I used your system last yr I found the same problems and made what sounds like similar fixes, but I’d like to see exactly what you did.


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  7. DaBulls says:

    Apologies for joining the conversation late.

    By this method (which I generally agree with), a player’s value is determined by the combination of his own statistical accumulations and the replacement level at that position. The value of players at certain positions, however, are more heavily influenced by the replacement level half of this equation than by the individual contribution half (for example, Victor Martinez gains more from his position as a percentage of his total value than does Mark Teixeira). The question is, does it matter which side of the equation value contribution comes from?

    The higher the percentage of value coming from the positional contribution (as with catchers, for example), the more a player’s value is dependent on our ability to project not only the player’s stats but also those of the replacement-level player at that position. To the degree a player’s value relies on our ability to predict two sets of performances rather than one, the potential variance in actual performance relative to projected performance rises (as we must add two sets of variances rather than just one), and the reliability of our value estimate falls. A less stat-speak way of thinking about this might be as follows: given the choice between a second-tier first baseman and an elite catcher with the same calculated value, the catcher’s value is more volatile (and drafting him is therefore more likely to backfire) because his value is more significantly effected than the first baseman’s should each player hit 5 homeruns fewer than projected and the replacement-level at each position hit 5 more.

    It would seem from the above that there either be some measure of volatility to accompany the value estimate, or, if we would still want to bake everything into one number, that the value contributed by positional weakness be discounted at some rate to account for the inherent volatility.

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  8. Sean says:

    So did you edit last year’s posts after realizing the improved methodology, or are they as they were?

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  9. John says:

    So when i search for this on the lists would it be equated to the value in dollars or is there a separate actual Frep value category. Thanks guys!

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  10. anwfoste says:

    Like the other commentators, I wonder how exactly you are doing this conversion. We can calculate the position scarcity, but do we have steps for adding in the comparison to the player pool at-large? Any help would be great!

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  11. Saevel25 says:

    For me, i rather keep analyze by category, i am not a one number fan. Given i have to pitch out a value in an auction draft, but i rather know, ok this value is made up of SB’s. I really would like to know, ok, this much money has been spent on HR’s, do i need to spend more money on HR’s, is there inflation on HR’s or SB’s. Because, in auction drafts the logic usually follows,

    Early Rounds, every on is fighting for premiere players, getting the backbone of there team
    Middle Rounds, looking at deals, more specialized hitters (SB only, or HR only) players
    Late Rounds, trying to fill some gaps, maybe pick up some cheap prospects

    This varies depending on money left over. I know one guy who will have a good amount of money late, he does pretty well, not my style, but he can be a bully in the late rounds. Money is leverage, but when there isn’t value there it doesn’t matter really. I know one guy who will throw out 1 dollar players early, trying to get them then, because in the late round, 1 dollar players sometimes goes for 2-5, maybe 10+ dollars because people are scrapping for categories they missed, and they have money to spend.

    So dynamics change, but i think looking at categories specifically can lead to advantages later on in the rounds if you know, ok, there was 500 dollars in HR’s to being with, now there’s only 100 dollars left, but there’s 300 dollars left in SB. If you can keep track of that per person, you can get a feel on how they are drafting, and know, if you can pick up a steal later on in the draft

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