## On Han-Ram’s 2013 Fantasy Value

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.

 AVG R HR RBI SB Han-Ram 0.345 62 20 57 10 Mean 0.259 43 10 41 6 Std. Dev. 0.036 25 8 26 9 z-score 2.4 0.8 1.2 0.6 0.5

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.

 Name G PA AVG R HR RBI SB z-score FVARz\$ Jean Segura 146 623 0.294 74 12 49 44 7.2 \$          24 Elvis Andrus 156 698 0.271 91 4 67 42 6.7 \$          22 Ian Desmond 158 655 0.28 77 20 80 21 6.4 \$          21 Hanley Ramirez 86 336 0.345 62 20 57 10 5.4 \$          17 Troy Tulowitzki 126 512 0.312 72 25 82 1 5.4 \$          17 Alexei Ramirez 158 674 0.284 68 6 48 30 4.3 \$          12 Ben Zobrist 157 698 0.275 77 12 71 11 3.8 \$          10 J.J. Hardy 159 644 0.263 66 25 76 2 3.7 \$          10 Jed Lowrie 154 662 0.29 80 15 75 1 3.7 \$          10 Everth Cabrera 95 435 0.283 54 4 31 37 3.6 \$          10 Brian Dozier 147 623 0.244 72 18 66 14 3.6 \$             9 Jose Reyes 93 419 0.296 58 10 37 15 2.6 \$             5 Andrelton Simmons 157 658 0.248 76 17 59 6 2.5 \$             5 Asdrubal Cabrera 136 562 0.242 66 14 64 9 2.2 \$             3 Erick Aybar 138 589 0.271 68 6 54 12 2.1 \$             3

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.

 AVG R/PA HR/PA RBI/PA SB/PA Han-Ram 0.345 0.18 0.06 0.17 0.03 Mean 0.259 0.11 0.02 0.10 0.01 Std. Dev. 0.036 0.02 0.01 0.03 0.02 zz-score 2.4 3.1 2.3 2.1 0.8

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.

 Name G PA AVG R HR RBI SB zz-score FVARzz\$ Hanley Ramirez 86 336 0.345 62 20 57 10 10.7 \$          33 Troy Tulowitzki 126 512 0.312 72 25 82 1 5.6 \$          25 Jean Segura 146 623 0.294 74 12 49 44 3.2 \$          17 Ian Desmond 158 655 0.28 77 20 80 21 2.9 \$          16 Elvis Andrus 156 698 0.271 91 4 67 42 2.1 \$          12 Everth Cabrera 95 435 0.283 54 4 31 37 3.0 \$          11 Jose Reyes 93 419 0.296 58 10 37 15 2.9 \$          11 Jhonny Peralta 107 448 0.303 50 11 55 3 1.6 \$             6 Mike Aviles 124 394 0.252 54 9 46 8 1.6 \$             5 Jed Lowrie 154 662 0.29 80 15 75 1 1.0 \$             4 Stephen Drew 124 501 0.253 57 13 67 6 1.0 \$             4 J.J. Hardy 159 644 0.263 66 25 76 2 0.8 \$             3 Brian Dozier 147 623 0.244 72 18 66 14 0.7 \$             3 Brad Miller 76 335 0.265 41 8 36 5 0.9 \$             3 Josh Rutledge 88 314 0.235 45 7 19 12 0.6 \$             1

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.

 G PA AVG R HR RBI SB Jean Segura 146 623 0.294 74 12 49 44 Han-Ram 86 336 0.345 62 20 57 10 Replacement SS 60 287 0.259 31 7 29 6 Han-Ram + Replacement SS 146 623 0.305 93 27 86 16

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.

Website: fvarbaseball.wordpress.com

Print This Post

Member
PutOnSwole

I like the concept of comparing players based on their zz-scores. We can’t assume players who battle injuries one season will have the same issues the next. Is there anywhere I can find z-scores and zz-scores for other positions?

Guest
nick

Any chance of getting a similar article regarding pitchers?