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.

Twitter: @FVARBaseball

Website: fvarbaseball.wordpress.com