December 10, 2013

Fantasy Freestyle

Mixed-League Hitter Valuation

by Mike Gianella

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In his upcoming book, Winning Fantasy Baseball, Larry Schechter has a chapter subheading called Why Mixed League Value Formulas Are Mostly Worthless. While this statement contains some degree of hyperbole, in my experience it is mostly accurate.

However, it is certainly a worthy endeavor to try to measure what a mixed league hitter is worth. Below are the steps I went through to derive what I consider valid mixed league values, a cursory examination of some truisms surrounding mixed league values and whether they are correct or not, and how you can apply these values to your mixed league and—perhaps more importantly—how you can’t.

The values below assume 12-team mixed leagues with the same rules as a “standard” Rotisserie-style league (5x5 category scheme, $260 budget per team, etc.)

Step 1: Establishing the Baselines
When deriving National League or American League valuation formulas, I use auction rosters to establish a baseline for mono-league values. I do this because the $3,120 that is spent in a 12-team, NL or AL-only league auction with a $260 per team salary cap is spent on auction day, not throughout the regular season.

Distributing $3,120 worth of value across the best 276 players is an interesting exercise, but isn’t useful in measuring what a player is worth on a league’s typical auction day. Including the complete duds and the players who didn’t quite live up to their expectations produces dollar values that are far too low and won’t provide earnings that can be applied to an auction environment.

As a result, the baseline for mixed league dollar values is less than it is for NL or AL only stats, but not as extreme as you might expect.

Table 1: NL Only, AL Only, and Mixed Hitter Baselines by Player

Table 1 takes the 168 most commonly auctioned/drafted hitters in the American League, National League and mixed leagues and provides the average stats on a per player basis. Looking at this on a per player basis, it doesn’t sound like much of a difference. One home run, five runs batted in, six runs, and two stolen bases. It doesn’t sound like a lot, but using the best 168 mixed league hitters instead of the 168 most likely to be auctioned adds an additional 177 HR, 826 RBI, 230 SB, and 858 runs. It adds up, and would have quite an impact on player value.

Likewise, looking at the difference between a mixed league player and an only league player sounds trivial when you look at it on a per player basis; however the difference between each format’s average auctioned hitter is quite dramatic.

Table 2: NL Only, AL Only, Mixed Hitter Values For Each Counting Stat

Table 2 shows what one of each at bat, run, hit, home run, RBI, and stolen base are worth using a raw, auction-based formula. Again, it doesn’t sound like much on a per-stat basis, but it makes a difference the more stats each player accumulates. The better the player, the bigger gap there is going to be between his only league stats versus his mixed league stats. Tables 3 and 4 illustrate this gap and the differences upon the impact on the top hitters and the hitters toward the bottom of the (mixed) league heap.

Table 3: Mixed League Versus Only League Values, Top 10 Hitters

Table 4: Mixed League Versus Only League Values, 161-170 Ranked Hitters

So that’s that, right? Since there is so much value at the bottom of the heap, it makes sense that Cabrera, Trout, and the other superstars get dinged the most while the guys in the middle get dinged less. Thank you for reading Mike Gianella’s 2013 Mixed League Hitter Valuation at Baseball Prospectus. Have a nice day.

Unfortunately, it’s not that simple.

Table 4 wasn’t included here by accident. In a player auction, the 168^th-best hitter in a 12-team league should cost $1. This doesn’t mean that the 168^th-best hitter should earn $1, because hitters who aren’t purchased at auction do wind up earning more than hitters who are. However, eight dollars for the hitters at the bottom of the heap is too high for this bracket. The valuation formulas for mixed leagues should come closer to replicating the valuation formulas for AL and NL-only leagues. Last year in AL-only, the 168^th-best hitter, Nate Freiman, earned $4. This is also true for the 168^th-best hitter in the NL, Erik Kratz. $4 is a reasonable baseline for these hitters in this income bracket, not $8.

This isn’t an arbitrary decision on my part. The shallower the league, the more players at the top should be paid and the more players at the bottom should get penalized. This fits in nicely with the concept of a replacement level player. Dayan Viciedo, Andy Dirks, and Mike Carp all put up $8 seasons in 12-team mixed leagues 2013. If you owned Viciedo, you could have easily flipped Dirks or Carp in for Viciedo and had the same relative level of production. In mono formats, Dirks was owned while Carp was owned in some formats. Maybe you get Carp in an AL-only, maybe you don’t, but you definitely have your pick of players like this in the free agent pool if Viciedo doesn’t work out… or if you decide that you’re tired of Viciedo and want to roll the dice on Dirks or Carp.

On the other hand, there is only one Miguel Cabrera and—if you lose him to injury—the player who plug in for him isn’t going to measure up. Even if you hit the lottery in your 12-team mixer and grabbed Josh Donaldso— the best player who wasn’t among the top-168 choices in a mixed league, there is still a $12 gap between what Cabrera earned and what Donaldson earned. This, of course, is assuming someone else didn’t take Donaldson or that you were lucky/savvy enough to get to Donaldson first.

This is why the players at the top get a bump. The hitters at the bottom are interchangeable cogs, whereas the hitters at the top are not. The question then becomes, what is the best way to do this?

One way would be to take the best hitters by dollar value and bump their values up, take the hitters in the middle and leave their values static or downgrade them slightly, and then downgrade all of the other hitters. This is easy, since it only requires one manual intervention. However, the problem with this approach is that it ignores a crucial difference between mixed league and mono league formats: one category players are far more of a liability in mixed leagues than they are in mono formats. There are enough dead spots in AL/NL only leagues that it is (mostly) irrelevant if you put a 20 steal guy who does nothing else into one of your outfield spots. In a mixed league, with so much production sitting in the free agent pool, your goal is to get production at every slot from every category if possible.

Chart 1: Valuation Adjustment by Category, Mixed Leagues

The chart above is a representation of the adjustments I made to mixed league hitters by category. The x-Axis lists how each adjustment was made by bracket, while the Y-Axis shows the adjustment. For example, for the 12 best home run hitters in Major League Baseball in 2013, I took their raw adjusted valuation from the original mixed league formula (above) and added 21.49 percent of value to the hitters in those categories. Without breaking down the chart into granular detail, the top 60 hitters in each category received an increase in value while anyone below that was docked.

There were 634 hitters who had at least one and another two—Freddy Guzman and John Hester—who either scored a run or stole a base without the benefit of an AB. However, the chart above does not continue docking hitters past the negative percentage shown on the chart above. The baseline dollar value for a player who doesn’t play is somewhat arbitrary, but I selected negative seven dollars for a player who didn’t play at all in 2013 but was inserted into a typical Rotisserie league squad’s lineup.

For an example of how this works for one player, here is 2013 Miguel Cabrera:

Table 5: Miguel Cabrera, AL-Only, Mixed Raw, and Mixed Adjusted Values

By adjusting the best fantasy hitter in 2013 back up using a scarcity model, Cabrera gets a six dollar bump. However, he doesn’t quite make it back to his AL-only stratosphere (and he does get docked in stolen bases, the one category where he isn’t a strong contributor).

The new mixed league Top 10 looks like this.

Table 6: Top 10 Mixed League Hitters 2013

These are the same hitters that were in Table 3 (above). Some of them are in a different order and some of them receive different adjustments than others. Ellsbury sees the smallest increase of all of the hitters because a good chunk of his value is wrapped up in stolen bases, but it is important to note that he does receive an increase. One thing my methodology does that is somewhat different than other mixed league valuation is that it doesn’t penalize one category players as much as other systems do…particularly if that one player is a categorical monster like Ellsbury was in 2013. In Ellsbury’s case, he is penalized in home runs and RBI but sees a slight bump in batting average in runs and a large bump in stolen bases.

For comparative purposes, here are the 161-170^th ranked players using this modified mixed valuation model:

Table 7: 161-170 Mixed League Hitters 2013

Adjusting the formulas shuffles the deck (some of the players here are different) but the adjustment does what I intended it to do: shifts value of the players in this value range from $8-9 down to $4. If the players at the top of the valuation spectrum are going to get some additional money, the players at the to bottom are going to get robbed.

I can’t possibly anticipate all of the questions that will derive from this pricing, but I can anticipate three of them before they are even asked. So to preempt the objections I know I’ll get, here are those questions and here are my answers:

1. Some mixed league formulas assign greater value to the top players while cutting even more value from the players at the bottom? Why don’t you do this?

Some mixed league pricing models do add more money to the top players in the pool while taking even more money from players at the bottom. And I can’t argue that this isn’t a valid method either, depending on what it is you are trying to reflect with your valuation.

In my case, I would argue that the “replacement level player” isn’t the 168^th player in the pool at the end of the season, but a player with a much lower level of statistics. Even in mixed leagues, there is a difference between the level of anticipated statistics and the level of predictability that the players in the pool have. Danny Espinosa, Tyler Colvin, Corey Hart, and Derek Jeter were all owned in at least some mixed leagues on Opening Day last year. While in a perfect world we would all like to think that we would have plugged Jed Lowrie, Domonic Brown, and Michael Brantley into our starting line-ups, the reality is that we sometimes do far worse. The “replacement”-level player I’m generating is a guy whose line looks like this:

Generic Mixed League “Replacement Level” Guy: 5 HR, 25 RBI, 1 SB, 30 Runs, .269 BA

This assumption takes away less value from the guys at the bottom than other models do, which means that it adds less value to guys at the top. If you disagree with this assumption, that’s perfectly fine; just remember to add more money to guys at the top if you take more money away from the players at the bottom.

2. Steals are worth a lot less in mixed leagues and should be devalued considerably. Unless a player is a top stolen base option, if all he offers are stolen bases, he isn’t even worth being on your roster

There were a number of assumptions I made about mixed league pricing during this study that held up. But one of the assumptions that didn’t is that stolen bases lose a significant amount of value in mixed formats.

Table 8: Mixed League Hitters with Stolen Base Value Comparison

Most of these players aren’t worth owning. But a few are and one of them—Rajai Davis—would have been quite valuable in mixed leagues last year.

Some of the reason for this is the formula modifications that I mentioned above. Some of this is because stolen bases aren’t as readily available as they were a generation ago. In 1986, for example, the average Major League team stole 127 bases. In 2013, the average big league team stole 90. While steals are worth less in mixed formats, the lack of stolen bases has made it harder to ignore the contributions of a 40-plus steal monster like Rajai Davis, even if he does absolutely nothing else.

3. Is any of this information useful for mixed league auctions?

The short answer to this question is “probably not.” The reasons why this information isn’t useful are complicated.

In another excerpt from Schechter’s book, he took a look at four sources of expert prices (magazines, web sites, etc.) and what the players actually were purchased for in the Tout Wars mixed league auction.

Table 9: Mixed League Suggested Bids and Actual Prices

Without delving too deeply into the details in the chart, the higher the prices are in the mono leagues and the suggested expert prices, the more closely the suggested bids come close to resembling reality. The cheaper the expert prices get, the more variance there is in the price schemes. Does this mean that the experts are off base and have no idea how to price mixed league hitters?

No, this isn’t the case at all. Without even looking at the specific prices in Schechter’s chart, it is fairly simple to intuit what is happening.

In mono leagues, while there is some variance on player prices, nearly everyone has the same general idea of what a player “should” cost. In 2014, Russell Martin might go for anywhere between $10-14, but it is extremely unlikely that he would go for $20 or two dollars. There is a very narrow range of prices for Martin, and this is the case for most players in mono formats.

In mixed leagues, there is far more variance in player prices. This in part is because there is a much larger player pool to choose from and thus a far greater range of opinions. Someone might have had Matt Carpenter unranked in mixed league formats while someone else might have had an $8 price tag on Carpenter. Neither of these rankings was unrealistic on Opening Day. The expectations for Carpenter were fairly broad and with all of the other players available for auction, there is greater latitude for a difference of opinion.

Pricing mixed league players is an interesting exercise in trying to come up with a valid yardstick for what players will earn. But even more than in only leagues, it is more important to try and observe the auction trends in your league than the hypothetical earnings of the players in your player pool. It is possible to use some of the information I have provided to your advantage, but for the most part, the idea that every auction is different takes on an even deeper meaning in mixed leagues.

Mike Gianella is an author of Baseball Prospectus. Follow @MikeGianella
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