## 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.

## The Curious Case of Jason Castro

As we look for candidates to regress in 2014, a popular choice is Houston catcher Jason Castro for it seems the Astros backstop has two targets on his back: a high strikeout rate last year of 26.5% and a high BABIP of .351. Steamer and Oliver both project a steep drop in BABIP that will drag his batting average from a solid .276 to the .250s. As Brett Talley wrote, Castro screams regression.

Or does he?

Talley points to Castro’s strikeout rate that has been topped only 61 times in the past decade, and only four times the player matched or bettered a batting average of .276. But that measure may miss the mark. No one is suggesting Castro’s strikeout rate will worsen. When it comes to batting average, the critical question, then, is whether he can come close to maintaining a high BABIP.

On that question the evidence is more promising. In the last decade, only 38 of 1,509 batters have had an infield-fly rate lower than Castro’s 1.8%. Only 47 had a line-drive rate higher than Castro’s 25.2%. Taken together, those two select groups actually have 10 matches — players who managed both a lower infield-fly rate and higher line-drive rate. Here they are along with their BABIP, batting average and strikeout rate:

Player, year, BABIP, Avg., K-rate

Joe Mauer, 2013, .383, .324, 17.5%

Joey Votto, 2011, .349, .309, 12.9%

Howie Kendrick, 2011, .349, .297, 17.3%

Matt Carpenter, 2013, .359, .318, 13.7%

Michael Young, 2007, .366, .315, 15.5%

Joey Votto, 2013, .360, .305, 19%

Adam Kennedy, 2006, .313, .273, 14.3%

Bobby Abreu, 2006, .366, .297, 20.1%

Michael Young, 2011, .367, .338, 11.3%

Chris Johnson, 2012, .354, .281, 25%

What might we gather from this evidence?

(1) All but one of the players topped .276.

(2) The skills involved seem somewhat repeatable: Votto and Young each appear twice and as a group they generally in their careers combined a high LD rate, low IFFB rate and a high BABIP.

(3) We wouldn’t expect a player who whiffs a quarter of the time to have a batting average as high as someone who strikes out half as much while putting up similar LD and IFFB rates. Castro is unlikely to approach the median average of this group of .307.

(4) Castro doesn’t need to approach the median average to avoid significant regression. He is more likely to hit closer to last year’s mark than he is to hit in the .250s.