## Replacing Replacement Value in Fantasy Auctions

With the baseball season rapidly approaching and recent posts by Fan** G**raphs authors converting projected statistics into auction values, I thought I would share my approach towards valuation I have used in a long-standing A.L. league with 12 teams, 23 player rosters selected through auction (C, C, 1B, 3B, CI, 2B, SS, MI, 5 OF, 1 DH), a $260 budget, a 17-player reserve snake draft and the ability to keep up to 15 players from one year to the next, an attribute that inflates the value of the remaining pool and can further distort disparate talent across positions and categories.

We have traditionally used a 4×4 format, and while I have persuaded my co-owners to switch to a 5×5 for the coming year, what follows is my process for a 4×4 league.

There was a distant time when I was a whiz at math but my utter lack of a work ethic for advanced math collided with university-level calculus and I crumbled as surely as a weak-kneed lefty facing Randy Johnson. So my understanding of some key statistical processes is compromised. And by some I mean most.

But what I lack in math I hope I make up in approach:

(1) For categories over multiple years in this league, teams finish in a standard bell-shaped curve, with two or three teams well ahead, two or three well behind and six to eight clumped more closely together.

(2) In a 12-team league, a third-place finish in a category bets you 10 points. Across eight categories, averaging a third-place finish gets you 80 points, which is enough points to win out league between 80% and 90% of the time.

(3) Given both (1) and (2), my goal is to finish in third in every category, because doing do will far more often than not win my league, and because that target is a comfortable space above the pack in the middle, creating a margin for error within which I can still secure a win.

(4) I calculate what totals I need for each category to finish third based upon the specific history of our league, giving greater weight to more recent and relevant trends.

(5) I calculate the totals needed to finish dead middle in the pack for each category, again based upon the specific history of our league, giving greater weight to more recent and relevant trends.

(6) The difference between the third-place totals and the median totals become my spread, in a sense, the yardstick against which I then measure all projected player performance.

(7) I don’t weight pitchers and hitters evenly because my league does not – the marketplace of my league places significantly less value on pitchers, spending between $70 and $100 on them, and I adjust values to account for that. Perhaps that is also justified by either greater volatility or more injuries for pitchers. In any case, I divide the total value for hitters by 14 and for pitchers by 9 to come up with the average value for hitters or pitchers.

(8) I calculate what each of 14 hitters and 9 pitchers would need to contribute per player for each category for both the top and the bottom of the spread.

(9) For each category, I divide the median production per player by the difference in the gap to find the incremental value of each unit of production.

(10) For each player and for each category, I start with the median value of median production for all four categories, than add or subtract the incremental value depending upon if their projected production is above or below the median.

(11) I do the same for keepers to calculate inflation value, then list both the value and inflated value next to each player, broken down by position, so I can track both availability and the ebb and flow of inflation in real time.

(12) Finally, my league is mostly inelastic except for dumping trades. That means it is not easy to trade surplus categories for deficit categories. So I create a running tally of my projected production, starting with my keepers and adding players I gain in the auction with the goal or at least reaching each of the target levels needed for projected third-places finished in each category.

(13) I don’t adjust assigned value based on the position played but of course I consider position as I bid in order to reach my targets in an inelastic league. I may deliberately pay somewhat more than inflation cost for a good player if the likely alternatives is paying over inflation value for a poor player and being left with more money to spend then there is talent to spend it on. I do so knowing my keepers will produce to much surplus value that I can win simply getting players close to inflation value.

At least in my league, my projected values, adjusted for inflation, are pretty close to the mark notwithstanding the outliers that will come in any marketplace, both for individual players and for more systemic biases (my league overpays for closers, for example). I don’t win every year, but when I fall short, it is not because my valuations were off but because of too many failures in projecting specific players.

Is there a statistical basis for tossing replacement value as a baseline for creating auction values or statistical benefit to instead using league-specific gaps between middling and winning teams? Frankly, I don’t know, however intuitive my system seems to me. But I’d welcome feedback on my approach, statistical arguments for and against it, and whether it warrants further exploration.

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This is sort of a fortuitous post for me. I am thinking about the same situation with creating my own values.

For me I am using the minimum in each category as the baseline over replacement player. I came to the same thinking. You pay for stats. You pay so you end up certain number of spaces above last place, or for your method middle of the pack. I think the math works similarly because it is the same method.

Taking the players stat minus the minimum average per player in that category (which is shockingly consistent per year when considering how volatile projections and injuries are) I can find out how much that player contributes over the worst team in the league. From there I divide that by the slope of that category. This allows me to see how many spots that player will help my team if I bid on them.

From there I figure out how many dollars I have per incremental improvement. Then I can just multiply each category by that amount to get the dollar value they contribute.

Though I am thinking that average does work better. Primarily, at least from what I read that you want to spend $260 dollars, but you want player values of 30% higher. The middle ground would be someone who gets straight face value. This is where keepers come into place and inflation, ect. I doubt the last place team is spending $260 dollars in value.

Great post, looking forward to more comments to hash out this concept more. I just have issues with replacement level because it is based on player ability distribution.

For me, if you have a catcher valued at -$9.00, you are required to spend $1.00 on them. Then that should be taken into account in the inflation adjustment. You can just say, OK i am going to spend an extra $7.00 on a better catcher because I will be wasting $10.00 dollars on getting a -$9.00 valued catcher.

I think the typical replacement value poorly adjusts the other positions trying to adjust for this.

I am delighted I could be of some help!

Thanks for sharing your thoughts and methods. Here are my initial thoughts and questions:

(1) When you calculate the minimum average per player in each category, how precisely do you do that?

(2) I think you are correct in suggesting you can chose as a baseline the minimum or the median of each category. One advantage of the median, though, is that it will be subject to less variability from year to year since last place finishers can be outliers while those near the median, by definition, are not, though it’s interesting that you have not found much variability.

(3) Is slope uniform or varied? Put another way, is each increment the same or different? Using my method, while I don’t specifically calculate slope, I can see the increments are relatively small towards the median and large the last two or three increments in either direction.

(4) To be clear, since I didn’t state the inflation rate in my keeper league, it tends to be close to 20%. In leagues with higher levels of expertise, the inflation rate is higher as owners generally make more astute choices in choosing keepers who are undervalued (and the converse is true as well).

(5) You are absolutely correct about the relationship between keepers, inflation and prices one should target in an auction. Some owners fail to do so, drop out of bidding before it reaches the expected value unadjusted by inflation, thinking there will be plenty of players who they will get for less than expected value. While there will be bargain players in virtually all auctions, there will be fewer in keeper leagues as owners have more cash to spend than there is value in the players to be auctioned. So getting a player at projected value, excluding inflation, or even between expected value and the inflated price, is a positive acquisition in a keeper league.

(6) Your comment about negative values using replacement value as a basis is an interesting one. I know some suggest simply setting the lowest valued player to be picked to $1 and adjusting other values accordingly, but I agree that seems problematic with a static budget of $260. Using my method, a $1 player truly contributes 1/260th of the budget needed for a league average team, at least if my concepts and math stand up to scrutiny.

Rotofan,

(1) I take a look at the last place team. Lets say a team finishes with 170 HR. From there I just divided that by 14 since there are 14 starting positions. In theory, even if you use, at least in the leagues i am in at least 16.5 hitters on average over the whole season. Basically how many extra players there are in reserve. Still, in the end the overall stats can be brought back to a single player average as if you were having 14 exactly the same players at each position.

(2) That is true, and I am kinda subjective with the last place values. Also I think some leagues the median can flucuate as well with how the overan MLB stats go. Hitting has been on a downtrend for years now. At least in my league it always seems like the final place team is near a certain area that I would deem acceptable. Really the last place team is hardly ever that way off. The primary reason I believe is because they still have to field the roster positions. Unless their whole team goes IR on them, and even if they field a team of replacement players, which they wouldn’t. You would still wouldn’t see a drastic outlier position. Even if you see it you can always just subjectively adjust it.

(3) I just use Excel’s slope function. It seems to work. I wouldn’t say that the slopes near the median or mean are volatile. I have seen some leagues were the top three teams are really close, lets say 10 HR between the three in difference. Then you can have a 40 HR drop to 4th place. Yet from 4th to 10th you might see a tight dispersion as well. So you can add in a wide gap, but decrease that gap if you include all the stats. I rather include them all, and if i really see an outlier in the first and last place team I would just kick it out. in the end I am getting +/- 1 HR SGP in slope over the past three years. I think that is pretty good, less than 10% error. In the end, actual baseball stats are more varried then that, usually 30% error on average.

(6) I just think that if you calculate the value of a player that his value. Now it is up to the person to bid on them. Now there is the idea, well you want to have your values close to the others or use the same methods for calculating the values because if you don’t then you are undervaluing everything since you did not actualy adjust for replacement values. I am working on trying to add in an inflation factor into the base auction value to see how close this gets me to other methods such as replacement players.

In reality I don’t think this will show up in most areas except maybe for the catcher position. Yet that is the draft theory right. Do you want to overvalue catchers because of the overall production scarcity. I am not sure yet. I almost rather have the value of what they REALLY produce based on league data and then make that judgement call while drafting. Again my only concern is how does that effect the other non-catcher position auction values and will I have to be mindful of that in the draft.

Thanks for sharing your system. I’m curious how you you started with it. I see that Art McGee has written a couple of books book using SPG (standing gains points) and other have tried to tweak and improve it. It’s an approach I am not familiar with but I am curious to take a look — I know there are a few blogs/websites that take that approach.

To the extent that owners in a league overvalue a position like catcher of a stat such as saves, that will have a deflationary effect on the rest of the player pool, but that effect is spread out over so many player it might be hardly noticed.

From a strategic perspective, it’s important to understand which positions, categories or type of players that your league tends to undervalue and to position yourself to take advantage of that market inefficiency. That’s easier said than done because other owners may also react to the inefficiency.

One fun part of the auction for me is that to perform well, you must prepare a smart strategy but be nimble enough to adjust to event you did not anticipate. I try to walk in to an auction with some “If, then” scenarios. If I can get one of three players at first at a certain price range, them I will target other specific positions at specific price range.

One year I had an especially strong keeper list, so much so that one owner seemed to determine to bid on any player I bid on in an attempt to drive up the price. Twice I ended up paying more than I preferred before I came up with a tactical response: I nominated a player who was good but didn’t fit my needs or plans and allowed the rival owner to bid him higher and higher, then I let him have the player — it really bankrupted the rest of his auction.

My approach just came from a mesh of a lot of different concepts. I just never liked replacement player theory. I get the idea, a person needs to find a way to value players. Some will say replacement player is the best theory. Some would say that Z-Score is good for teams who do not have league data (SGP). I think in the end a person needs to find what fits their ideology and their league. I am partial to SGP. Even with Art McGee book he uses SPG in conjuction with replacement players.

It can be. When I did my initial calculations I found that ever player got about a $1 dollar reduction in value because I had to bump up catchers to the minimal bid of $1 dollar. So When you have catchers actually worth -$5, -$10, it can add up quickly.

I don’t think people undervalue SB or Saves. I just think replacement theory overvalues them. When I did my method the saves were valued pretty well. The problem with replacement player theory is that you have to make the replacement player the actual set of players you are replacing for that players position. Also when you divide the marginal stats left over by the sum of possible drafted stats to get the ratio to figure out the values. This dividing can throw stats like SB and Saves into the stratosphere because saves and SB are mostly a specialists area so they are limited. Which people would say, well then you need to value them higher. Well no, because in ROTO leagues you are accumilating stats versus 8-11 other teams. So, those saves are only as valuable as to gain you an extra position. If it was head to head were you can gain a statistical advantage then yes replacement player would work better because a specialist can give you an advantage because they are more consistent in SB than someone who is collecting stats over a whole year.

This actually parallels two concepts in real-life baseball:

1. To measure the value of a player, irrespective of what team he plays for, you use WAR.

2. To translate the player’s value into actual dollar, you would also look at the marginal value per win. This marginal value is the greatest for a team whose expected win total is right on the bubble for the post-season.

So, for a lot of auction fantasy players, I’d guess that the value above replacement is a good proxy for “target” value. However, in the heat of the auction process, the task at hand switches into more of an optimization problem – how to get the most marginal expected points with your remaining auction $. In those situations, your method of using the spread around 3rd place (i.e. the “bubble”) is probably a better reflection of what you should pay.

And your league’s historic trade patterns are a further point for your method. In a league with frequent trading and/or waiver wires, you can manage away any category imbalances, which would make value above ‘replacement’ work a lot like MLB. But when transactions are rare, and you have to ensure you’re at least passable in all categories, then you really need to track your target values in real time and adjust your value. Your system probably gets you closest to the right value (adjusting for ongoing inflation of course) as you move towards the end-game part of the auction.

I do think, in a deep league like yours with many keepers, that you should at least guess a positional adjustment based upon how bad the 24th best catcher or 36th best MI looks. Some years it’s not a big deal, but in others the bottom feeder in those pools is far worse than your bench-warming OF/1B types.

Thanks for your thoughtful comments and placing my approach in a context that makes sense.

As to deep leagues and positional adjustment, while I don’t formally adjust the values I assign players based on their position, I do adjust how I approach each auction with those positions in mind as well as the targets I have for each category.

For example, I generally try to avoid having to depend upon successfully bidding on the last quality player available for either a position or category because I believe there will be a greater chance at a bidding war that will push the price well above the inflationary price. There isn’t always a bidding war but I do believe the risk is higher.

That approach doesn’t always work. Last year, for example, there were only two third basemen available in our auction who were assured a starting position, David Freese and Kyle Seager, so I nominated the player with less projected value first, thinking I would get Freese at a reasonable price and that Seager’s value would be pushed to the stratosphere. I did end up getting Freese at a reasonable price, below his projected inflationary value, but then Seager went for a reasonable price too. The risk I feared and anticipated didn’t materialize.

Another way I adjust for relative positional or category scarcity is in my choice of whom I nominate and when — the Freese example being one.

You are absolutely right that some sort of adjustment is needed because in many deep league auctions, owners end up getting no value for the last few catchers or middle infielders and that can result in having more cash to spend than there is value to acquire. Even worse, there are sometimes bidding wars on very marginal players.

I don’t know whether my implicit adjustments in strategy are as effective as making explicit adjustments to value before the auction and I’d be curious to hear from people who do make explicit adjustments and their methodology for doing so.

What methodology adjustments will you be making to move to a 5×5 league given there is no league history in the new categories?

I should add, when looking for stats from other leagues it is important to find leagues whose rules don’t differ from your own in a way that will affect the accumulation of stats. I’m in a weekly league; a daily league with streaming allowed will have higher counting stats because active owners will have fewer empty position in which a player isn’t in the lineup a particular day. For my league, Tout Wars is a good comparator since it too has weekly activations and only allows a daily activation to replace a player placed on the DL or dropped.

Good question. While my league archives the 4×4 results from past years, it does not for other categories, so there is no ways to retrieve historic information for the three new categories, runs, OBP and strike outs without tracking every roster change and trying to replicate what the results would have been, something that would be far too time consuming.

So for runs, I will obtain the difference in recent years between real American League totals for runs and RBIs (there will be more runs because RBIs aren’t awarded for errors, steals of home, fielder’s choice), than adjust upwards the RBI category from our league stats by that percentage to get the median and third-place run totals. That method assumes that that distribution of runs is similar to the distribution of RBIs. I will also check that against other 5×5 leagues whose results from past years are posted on the web.

I will also seek other 5 x 5 league results for OBP and strikeouts. Some expert leagues such as Tout Wars have their results available on the web. Expert leagues are not a perfect proxy for my league, where there is more of a mix of ownership, but it may be the best information I can get and still be adequate for my purposes.