Hanley Ramirez had a roller-coaster 2013 marked by bad luck with injuries and exceptional production with the bat. He missed the first month with a torn thumb ligament and tore his hamstring in his third game back, causing him to miss another month of action. Overall, Han-Ram played only 86 regular season games, but when we played he hit the cover off the ball. In 336 plate appearances he hammered 20 home runs and a .442 wOBA (second only to Miguel Cabrera for players with over 100 PA). While the title of this post should lead the reader to believe it is primarily about Han-Ram, that would be false. In fact, it’s mainly about different methods to measure fantasy value, with Han-Ram used to illustrate a point.
Fantasy value above replacement (FVAR) is a metric that has been used (for example on FanGraphs) to estimate the auction value of historical or projected baseball statistics in a rotisserie league. The most popular way to measure FVAR uses z-scores: the number of standard deviations above the mean for any given statistic(s). Z-scores are handy because they put different stats, such as HR and SB, on a level playing field. An unresolved question is whether FVAR should be calculated using total stats (e.g., Han-Ram hit 20 HRs) or rate stats (e.g., Han-Ram hit 0.06 HR per plate appearance). In this post I’m calling the method using total stats the z-score and the method using rate stats the zz-score. I looked at how Han-Ram’s fantasy value changed using both methods (assuming 12-team mixed 5×5 with $160 auction budget for hitters per team).
Han-Ram’s Value Based on z-Score
The table below summarizes the calculation of Han-Ram’s z-score in 2013. The data is drawn from players with at least 100 plate appearances. The z-score is Han-Ram’s stat minus league average (mean), divided by league standard deviation.
Han-Ram’s overall z-score sums to 5.4. The next table shows how that compares with other shortstops. For an explanation of how the auction values were calculated see here and here. (Erick Aybar was the replacement level shortstop, but his auction value is greater than zero because his z-score was higher than the replacement level Util player, Justin Ruggiano.) Using the z-score method, Han-Ram ranked fourth among shortstops even though he played in only 86 games.
Han-Ram’s Value Based on zz-Score
The calculation of Han-Ram’s zz-score is illustrated in the table below. It’s identical to the z-score calculation, but rate stats (per PA) are used instead of season totals.
Han-Ram’s zz-score in 2013 summed to 10.7, putting him at the top of the heap for shortstops. To calculate Han-Ram’s FVAR in 2013 I multiplied his zz-score by his plate appearances, adjusted for replacement level and then calculated auction values. Results are shown below.
Han-Ram’s Fantasy Value
Depending on how we look at the world, Han-Ram was either the most valuable fantasy SS in 2013 or the fourth-best. I think both methods are legitimate, but I prefer zz-score for a few reasons. As Zach Sanders has noted on FanGraphs, z-score makes a broad assumption:
“These rankings are meant to reflect a player’s value should he have occupied this spot in your lineup for the entire year.”
In other words, z-score assumes my SS roster spot was empty when Han-Ram was on the DL. That’s obviously not a good assumption, because in a 12-team mixed league I would have easily found a replacement-level SS to plug in while Han-Ram was sidelined.
To illustrate the point, I looked at the 2013 stats for Jean Segura (the highest-ranked SS using z-score) compared to Han-Ram for 86 games plus a replacement SS. Using the zz-score method, and the league assumptions noted above, Asdrubal Cabrera was identified as the replacement level SS in 2013 with a zz-score of 0.4. For the sake of this comparison I assumed the replacement added value in steals and was league average in all other categories. It should be pretty obvious that Han-Ram plus a replacement was more valuable than Jean Segura.
Han-Ram + Replacement SS
What does this tell us? In leagues where it is fairly easy to plug in replacement-level players (e.g., shallow leagues with daily transactions and plenty of DL spots) zz-score is a better method for determining fantasy value. In leagues where it’s hard to replace an injured player or plug in serviceable options, playing time becomes a more valuable commodity and z-score is probably a better reflection of real value. As is often the case, the truth probably lies somewhere in the middle, between z and zz.
One of the best features of the wins above replacement (WAR) statistic is that it allows us to compare the greatest single-season performances across different eras in baseball history. Anyone who has browsed the FanGraphs Leaders page should know that Babe Ruth had the top-five WAR seasons in history, all in the 1920s. In terms of offensive runs added (batting and base running), Ruth’s 1921 season ranks as the best ever, followed by Barry Bonds’ 73 home run “asterisk” season of 2001. But what about fantasy baseball? Were these also the greatest (read most valuable) rotisserie seasons ever recorded? That’s the question I set out to answer.
Using a slightly modified version of Zach Sander’s fantasy value above replacement (FVAR) system for valuing fantasy players, I estimated the auction value for every hitting season from 1920-2013. First, I determined every player’s position eligibility based on some simple assumptions (meant to reflect Yahoo’s approach) whereby a player is eligible for a position if they meet any of the following criteria:
With that established, I proceeded to calculate the z-scores, FVAR and auction values (FVAR$) for roto leagues. Based on a 5×5 12-team mixed league with $260 budget per team (and quite a few other assumptions) here are the ten most valuable fantasy seasons for hitters since 1920 (5×5, 12-team mixed):
At this point you’re probably asking: “What, A-Rod?!?!” I know, as a Red Sox fan and sentient being I was not happy to see A-Rod at the top of the heap. As much as you may like or dislike A-Rod in real life, if you drafted him first overall in your 2007 fantasy league you were not disappointed with his across-the-board production. But, you might also be asking, as I did, how was A-Rod’s 2007 season worth $5 more than Babe Ruth’s 1921 season? Ruth’s hitting and base running in 1921 added 119 runs compared to 75 runs added for A-Rod in 2007, so what gives? As best I can tell, here are some reasons why A-Rod-2007 had a higher FVAR$ than Ruth-1921:
Does this make sense? Yes actually, I think it does. What it means is that in 2007 A-Rod and Melky Cabrera together were worth more than Babe Ruth and Ralph Miller together in 1921. In a fantasy auction in 1921 it would have been unwise to spend too many fake dollars on the best players like Ruth and Hornsby (or drink in public because of that Prohibition thing) because you would have been stuck with the bottom players, like Ralph Miller, who were really, really bad (there were only 16 teams back then and no DH).
For fun, below is a dream fantasy lineup with the best hitters since 1920 at each position (5×5, 12-team mixed). Enjoy.
I’m hoping to write more posts like this using historical FVAR, especially if readers/commenters think it worthwhile.