## Replacing Replacement Value in Fantasy Auctions

With the baseball season rapidly approaching and recent posts by FanGraphs 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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saevel25

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.

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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.

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saevel25

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.

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tz

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.

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wsmith

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