## 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

## Ten Most Valuable Hitting Fantasy Seasons Since 1920

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:

• Played at least 20 games at the position in the previous season.
• Started at least 5 games at the position during the current season.
• Played at least 10 games at the position in the current season.

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):

 Rank Season Name POS PA AVG R HR RBI SB FVAR\$ 1 2007 Alex Rodriguez 3B 708 0.314 143 54 156 24 \$56 2 1997 Larry Walker OF 664 0.366 143 49 130 33 \$55 3 1985 Rickey Henderson OF 654 0.314 146 24 72 80 \$55 4 1983 Tim Raines 2B 720 0.298 133 11 71 90 \$53 5 1963 Hank Aaron OF 714 0.319 121 44 130 31 \$53 6 1988 Jose Canseco OF 705 0.307 120 42 124 40 \$53 7 1993 Barry Bonds OF 674 0.336 129 46 123 29 \$52 8 1982 Rickey Henderson OF 656 0.267 119 10 51 130 \$52 9 1921 Babe Ruth OF 693 0.378 177 59 171 17 \$51 10 1974 Lou Brock OF 702 0.306 105 3 48 118 \$51

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:

• Ruth’s replacement in 1921, Ralph Miller, was much worse than A-Rod’s replacement in 2007, Melky Cabrera.
• As a result Ruth-1921 had a much higher FVARz score than A-Rod-2007, but the average above-replacement player in 1921 also had a higher FVARz than the average above-replacement player in 2007.
• As shown in Zach Sanders’ third post on FVAR, the auction values are a function of FVARz divided by the average FVARz for above-replacement players.  Hence, Ruth’s FVARz was divided by a larger number to calculate FVAR\$.

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.

 Order Season Name POS PA AVG R HR RBI SB FVAR\$ 1 1983 Tim Raines 2B 720 0.298 133 11 71 90 \$53 2 1985 Rickey Henderson OF 654 0.314 146 24 72 80 \$55 3 2007 Alex Rodriguez 3B 708 0.314 143 54 156 24 \$56 4 1927 Lou Gehrig 1B 717 0.373 149 47 175 10 \$48 5 2006 David Ortiz Util 686 0.287 115 54 137 1 \$34 6 1997 Larry Walker OF 664 0.366 143 49 130 33 \$55 7 1963 Hank Aaron OF 714 0.319 121 44 130 31 \$53 8 1997 Mike Piazza C 633 0.362 104 40 124 5 \$45 9 1998 Alex Rodriguez SS 748 0.31 123 42 124 46 \$48

I’m hoping to write more posts like this using historical FVAR, especially if readers/commenters think it worthwhile.