The new modified NERP

In John's most recent blog, he refers to Dean Carrano's offense vs defense article. In this article, Dean proposes a simple formula by which one could establish the value of a player as compared to another.

viewtopic.php?f=15&p=5559635&sid=208640c3ac31e037c9c8dc1bf5c89327#p5559635

As John says, Dean's formula is very useful to compare one player with another, and its simplicity is a strength.

If you like simplicity, I guess you should stop here!! The purpose of this post is to show the work I did over the last year or so to better the formula and generate a new modified NERP that would be the best rating system.

Dean's proposal is summed up by this simple formula:
(TB * .318) + ((BB+HBP-CS-GIDP) * .333) + (H * .25) + (SB * .2) - (AB * .085) minus DEFENSE (as valued by his charts at the end of his article).

As I've already written elsewhere, if you round up the decimals, this formula above is mathematically the same as the one below which will sound more familiar for those among you who have been playing with linear weight formulas :

=bb/hbp*0.33+si*0.48+do*0.80+tr*1.12+hr*1.44 - outs * 0.085 - GIDP*0.418 + (SB * .2) - cs*.333 minus defense

and it's roughly equivalent to following one (by changing GIDP to gbA), which has the great advantage to match the information that is present on the SOM rating files

=(bb+hbp)*0.33 + hits*0.16+ tb*0.32 - outs * 0.085 - gbA*0.08 + (SB * .2) - cs*.333 minus defense

(just to make clear: if you go through this formula, gbA has the value of -0.165, since gbA are also computed in outs).

Take note that this formula has the form:
offense + running - defense

This formula is simple, but it has several limitations, many of which are acknowledged by Dean himself. Some are self-evident:

¬ it cannot easily compare players at different positions

¬ The formula does not consider player usage

Dean's formula is great if you're undecided about who should start the game, but it's less adapted about whom to draft, since you're mostly interested about

Taking the last two points together, the ideal formula should have the following shape:
offense + running - (defense + positional adjustment), all adjusted by playing time

¬ clutch is considered as meaningless when it's not
Even if you think clutch has little value, you'll concede that it's not worth zero. I already wrote on this here, so I won't repeat the argument. If interested, please see:
viewtopic.php?f=17&t=639124

¬ it does not provide catcher's rating for defense
I already wrote on this topic. Please see The catcher database
viewtopic.php?f=17&t=639093

¬ speed is restricted to stolen bases and caught stealings. The capacity to take an extra base or to be held at first is not taken into consideration. I've also written on this, see
viewtopic.php?f=5&t=639129&start=10

¬ Except for double plays, outs are giving the same value. Ideally, you'd like to have a rating system that value differently gbC, flyB, and lineouts, since their impact is different (admittedly, these are subtle differences). On that topic, gbA is attributed the value of a GIDP, but they're not the same. gbA can generate positive value (for example, gbA can advance runners in some contexts). So the value of gbA is not as bad as -0.165.

Then, there are a few more limitations that need further explanation:

¬ Dean's formula is based on a false assumption that every player will have the same number of rolls, that is 216 PA, or something close to 648 PA over the full course of a season. Intuitively, this makes perfect sense, as every player has 108 chances on his card and 108 chances on the pitcher's card/defensive charts. More formally, the value of a card, over the course of a season, will be determined by:
A) What's on the card (which is given by offensive NERP)
B) How many times you'll read the card (which Dean assumed constant for every player (other things such as injury risk being equal).

In fact, B is not constant across the set. What's constant is the number of outs a team will generate over the course of a season. Every team has 162 games X 27 outs to win a game. What is constant is that every team will have 4350 outs or so. If team A has better on-base than team B, then team A will generate more rolls (will draw more dices) until it reaches 4350 outs. And since teams are made up of players, players with higher on-base are the one responsable for the extra value generated by rolling more dices.

Consider Reddick and Turner. If I'm not mistaken, with BP HR=10, Reddick and Turner have the same NERP vs rhp. But Turner will generate 20 less outs for every 216 PA (I let aside lefty/righty matchups). So over the course of a full season, having Turner instead of Reddick will yield 60 more rolls for the team with Turner. There will be 3-4 additional readings on Turner's card, 27 additional readings on his teammates, and 30 additional readings on the defensive cards. By plugging in league average value (assuming a 80M), Turner will generate almost an extra 4 NERP than Reddick to his team over the course of a season. Turner is underestimated if you use Dean's formulas.

Final issue: the weights (the values) plugged in the NERP formula were generated by analyzing baseball stats. Strat is a very close approximation of baseball, but it has also its own logic, which can be computed sometimes with more accuracy than baseball. The best example of this is clutch. Clutch is not in the NERP original formula because in real-life, clutch is not captured by the statistics, but it's an important part of strat. And the difference between baseball and STRAT is subtle but undeniably present in other contexts. Consider the value of outs, which I touched upon above. In strat, it's much more easier to distinguished between the value of gbC from the value of gbA. To do so, I generated matrices of linear weights and probabilities of events, and I calculated for each "strat" event its weight, or value. I would need to give more details in another post, but the net results is that some events appear to weight differently in strat. For example, doubles seem to have a value closer to singles than in baseball.


Making the sum of it all, here is what I have for the offensive value

offensive value=(walks/hbp)*0.33+hits*0.21+tb*0.28+hr*0.1-regular_outs*0.1-gbC/flyA*0.04-gbB/flyB*0.07+stadium adjustment+weak adjustment+clutch*1.3*0.116-gbA*0.15 + extra points generated by the extra on-base: (81-outs)*(8/9*0.15+1/9*0.15*value/24)


I need to stop here.

Nice work. I've incorporated some similar adjustments to Dean's NERP, but not nearly in as much detail as you have shown. The adjustment based on "on base" is very interesting, as is that for GB and Fly outs. I have only been using GB(A).

I also appreciate you earlier discussion about catcher fielding. I had used Dean's notes in my sheets, but have sensed that they overstate to spread of values for fielding and arms.

In my last post, I made a few mistakes. Instead of editing, I will write the formula here

Offensive value =

on the plus side
(walks/hbp) * .33 +
hits * .17 +
tb * .30 +
hr * .05

minus
regular_outs * .10 (lineouts, K)
gbC/flyA * .04
gbB/flyB * .07
gbA * .15

plus these adjustments:
stadium adjustment (roughly 1 NERP for singles and 0.5 NERP for every diamond assuming BP HR/SI 8/8/8/8)
weak adjustment (roughly 1.5 NERP for BP HR=8)
clutch * 1.3* .116 (value of clutch X the probability to have a clutch situation)

plus the extra points generated by the extra on-base: (81-outs)*(8/9*.15+1/9*.15*value/12)/2 (instead of dividing by 24)

where value is the sum of everything above---the ".15" comes from the fact that, in a typical 20XX season, each at-bat is expected to generate .15 runs (roughly 5.3 runs per game)---it could be less if you play in a low-scoring environment. 12 is the NERP baseline for offensive players and I use a baseline of 0 NERP for pitchers (being conservative here---in majority, pitchers allow some NERP).

A few things I forgot to write`:

1) Dean proposes a 25%/75% lhp/rhp, but I find that this proportion is too low for online strat (although it's dead on for face-to-face strat). For on-line purpose, I rather assume the following:
everyday player: 30% lhp vs 70% rhp
platoon vs lhp: 21.4% lhp vs 7.1% vs rhp
platoon vs rhp: 8.6% lhp vs 62.9% rhp

2) If you have the rating disk, you don't have the number of gbC, flyB and what I call regular outs. But K is given. So what I do is I calculate the sum of chances taken by on-base, ballpark homeruns and singles, and K. I substract that sum from 107 (everybody has a lineout max). Whatever left, I assume a 30%/70% ratio of gbC and flyB, up until I get 6/14---I give a 7th gbC to account for the flyA that is often (but not always) there for sluggers with 8 BP----and I assume that everything else is a lineout or flyC.

3) You can adapt weights to specific scoring environment. Weights for singles and doubles correlate with run-scoring environment AND with the relative presence of speed on a team (the faster, the higher). Walks also correlate with run-scoring environment, but not with speed. The values I posted in the previous post is those I used for my latest team. In contrast, homeruns and sb are much more constant, so I never change them. If you want to tweak some weights, consider that, in "normal scoring" environment, according to the matrices I created, si* = 0.37, si** = 0.51, 2b** = 0.68, 2b*** = 0.84, so make sure to use values between these numbers, and make sure to change the weight specific to hr so that a hr is worth 1.42. The numbers I post here, in this specific post, is the one I use in typical environment, before draft.

4) A technical point: it took me a while to understand that the weight given to outs is somewhat arbitrary. A regular out is worth -0.10 if the goal of a rating system is to estimate how many runs a team will produce at the end of the year. But it's worth -0.16 if the NERP is meant to indicate how better a player relatively to replacement player. The important part is that the gap between the different outs remain constant---a gbA is always 0.05 worse than a lineout.

5) One limitation: these values assume that no outs are made on the basepaths (no out on base), which of course is not the case. With the "add baserunning decision" set on, this limitation affects all events except homeruns, so there is a case to provide more weight to homeruns, but I resisted to do it.

6) The weak adjustment is about lowering the NERP because a player is weak. In this case, all the homeruns met on the pitcher's card will be transformed in singles**, and the weights for (single**) is 0.51 as opposed to 1,42. To get the right value, we must estimate the frequency of this happening on the pitchers cards, which depends on which environment you play (80M vs 200M, homerun stadium vs small-ball stadium, etc). Furthermore, as a whole, lefty pitchers might allow more (or less) homeruns as righty pitchers. So it's not easy to get that adjustment right.

OK, next post, I'll go over defense.

These boards need a "like" button. This is great stuff.

These boards need a "like" button. This is great stuff.

Yeah. Very interesting reading. Thanks Marc. Looking forward to reading more.

Question: Dean's article also takes into account runs off of pitcher's cards. Specifically, he formulizes (is that a word?) that, all things being equal, a switch hitter will get more runs when the reading is off of a pitchers card than L or R batters will - at least I think that's what he's saying. Does that need to be figured in here somehow?

Thanks guy.

Robert, I thought of using your website to post a paper and make it available to the world wide web. Would that be possible?

Knerrpool, you're absolutely righ about upgrading the value of switch and lefty hitters, but traditionally I don't do it in the NERP process, I rather do it when I make final adjustments relative to playing time. So you'll see it appear later.

Okay, last week, we went through the formula for NERP_offense. For a recall, the formula is based on 216 PA, adjusted for the additional at-bats that come from players with more on-base. On average, the formula adds 7 PA per hitters priced over 3M, so in fact, the formula is roughly based on 223 PA.

Because the running game will be based on seasonal data, I need to multiply the NERP_offense formula so that it applies for a whole season (at this point, not adjusted for playing time and injuries). Dean assumes 648 PA per player, and I've read somewhere that defensive charts are based on 667 PA per player, but after doing the maths, assuming that the average on-base in 80M leagues are around .320 (assuming dh-league), and assuming a fair level of outs on-base and double-plays, my own assumptions is that a full season is made of approximately 6200 PA per seasons, or 688 PA per player. Based on this assumption, we need to multiply the NERP_offense by 3.08 to get it based on 688 PA. Of course, if you play in non-dh league, where on-base is typical lower, you can multiply the formula by a lower factor.

Let's us come back to the ideal formula

3.08 X offense + running - (defense + positional adjustment), all adjusted by playing time

For the running game, there are four stats that contribute to creating run:

i) stolen bases (sb)
ii) caught stealing (cs)
iii) speed rating (speed)
iv) the probability to be held (the held_prob)

My final formula incorporates all four elements:

running NERP =(exptected_SB*0,17-expected_SB*0,28)+(((speed-8)*0,23-0,6)+(162-sb-cs)/162*held_prob*2.57))

The probability to be held varies roughly from 100% to 0% based from the ability of the runner to be held (100% for A-rated stealers, to 0 for runners with no running numbers (or E-rated with stealing opportunity within 2-12 (3-1)) In fact, I go above 100%, up to 130% for excellent runners (80+ SB, AA-rated) to reflect the fact that they can be held at second-base too.

In fact, you could use this formula with your own way to predict the expected SB/CS for each runner. In his paper, Dean uses the real-life SB/CS adjusted to 648 PA, but this formula, in my opinion, tends to overestimate the sb results (unless the number of CS skyrockets too, which tells us more about the coaching style of the owner rather than about the value of a player).

expected_SB = real-life SB / real-life PA X 688 PA X 85%
expected_CS = real-life SB / real-life PA X 688 PA

After many months of trials and errors, here is my own, length way, to estimate the expected SB/CS.

When it comes to SB/CS, players can be divided into two broad categories:
a) Runners with a (3-1) or no stealing rating---for these, you can simply put
expected_SB= 0
expected_CS=0 (you could give 1cs if the probability to get the lead is high to reflect the rare occurrence where a runner might try to steal)

b) Runners with a (13-1) rating or better (ex. (19-14), (20-6))

expected_SB=
=[sent*(first-12)/20*9,3*(first/20-0.13)] minus cs_d plus held_prob
expected_CS=
=[0.85*sent*(first-12)/20*9,3*(1.15-first/20)] minus cs_d/36*expected_SB
where CS is never more than SB+2.

and where
sent = chances that the runner is sent to second base
first = first steal number
second = second steal number
cs_d = chances that the runner is directly caught stealing
held_prob is the probability (based on 100%) that the runner will be held (as explained above)

For best results, I round down all results for sb (so 6,7 SB is reduced to 6 SB) and round up all results for cs (0.3 CS becomes 1 CS).

For runners whose second number is higher than 13 (ex. (19-14),we need to add an element to each formula

expected SB=
=[sent*((first-12)/20*9,3+(second-13)/20*7,2)*(first/20-0.13)] minus cs_d plus held_prob
expected_CS=
=[0.85*sent*((first-12)/20*9,3+(second-13)/20*15)*(1.15-first/20))] minus cs_d/36*expected_SB

again, with the rule that CS is never more than SB+2 (I use this rule to limit the impact of players with very bad stealing chances, since it's so easy on online strat to cut-off the stealing game for these players).

Once I have estimated the expected SB/CS, I can then plug them in the NERP_Running formula I gave above:

running NERP =(exptected_SB*0,17-expected_SB*0,28)+(((speed-8)*0,23-0,6)+(162-sb-cs)/162*held_prob*2.57))

(In a later post, I will write on how I arrived to those weights, and why I use different weights than Dean on SB and CS).

Running NERP
My ratings Dean's rating
Altuve 7,3 Altuve 7,6 lead-off
Gordon 7,3 Gordon 6,6 lead-off
Schafer,J 10,3 Schafer, J 10,2 lead-off
Revere,B 7,6 Revere, Ben 7,5 lead-off
Ellsbury,J 6,5 Ellsbury, J 6,4 lead-off

Dyson,J 9,6 Dyson, J 11,2 pr
Garcia,L 8,8 Garcia, Leury 8,1 pr
Carrera,E 8,5 Carrera, E 9,6 pr
Jones,J 7,8 Jones, James 10,1 pr
Florimon,P 5,9 Florimon, Pedro 9,3 pr
Ciriaco, P 5,5 Ciriaco, P 11,0 pr

Cain,L 6,3 Cain, L 5,2 good runner
Escobar,A 6,3 Escobar, A 4,5 good runner
Gomez,C 6,3 Gomez,C 2,9 good runner
Span,D 6,1 Span 3,8 good runner

My ratings compared to Dean's uncomplicated approach are comparable for players who often play a lead-off role, such as Altuve and Ellsbury, but my ratings play down the value of players who, in real-life, are typically used as pinch-runners (such as Ciriaco), and increase the value of players who are good runners like Cain or Gomez even though they had less than 30 stolen bases in real life.

Defense is next.

3.08 X offense + running - (defense + positional adjustment), all adjusted by playing time

If you don't want to mess up with these estimations, you could simply use this rule of thumb:

Schafer (a AA runner with a (19-16) stealing rating) was best at 10.3 NERP_running, followed by Dyson (9.6) and Young (9.0)

and

runners with no chance to steal and a 8 speed rating were the worst at minus 0.6 NERP_running (actually, Freese, despite his 9 speed rating, was the worst because of his 5/9,10 (13-1) at minus 0.7 NERP)

and everything in between.

Speed rating---running NERP

AA-rating: average of 7.5 NERP (varies from 5.6 to 10.3)
A-rating: average of 5.7 NERP (varies from 3.1 to 7.8)
B-rating: average of 4.1 NERP (varies from 2 to 6--except for one outlier)
C-rating: average of 2.3 NERP (varies from 1.5 to 4.9 except for those with many direct caught stealings)
D-rating: average of 1.0 NERP (between -0.5 to 2.6)
E-rating: average of 0.2 NERP (between -0.7 to 2.0)

Thanks, Marc. Looking forward to reading more. Just curious, what was your Nerp for T. Holt? Not that I've ever used him, but he's got 15-8 with a bunch of pickoff chances, so I would probably just set him to never steal. But, he does have 16 speed which should give him something.

Defense:

I don't have much to add to what Dean already wrote at length about the methodology to calculate defense NERP. So I'll refer to his article once again:
http://www.mfooz.com/bblog/wp-content/u ... efense.pdf

There are a few differences though:

¬ Dean applies a value to gb A (-0.165) and to any other outs (-0.085). Since I am capable of calculate the weight of any event, I can allow different values for gbB/flyB (-0.07), gbC/flyA (-0.04), lineouts/flyC (-0.10). The overall impact is that my estimated NERP slightly favours a bit the better fielders (less gbC/flyA are found on their parts of the chart) than Dean's NERP.

¬My understanding of the rule of "more baserunning decisions" is that it applies to all situations EXCEPT for events coming from the defensive chart. When using the defensive chart, an E2 is a two-base error period and the runner is never caught on trying to extend his run. So the defensive chart is a rare case where distinguishing between si* and si** can make sense. Dean applies a value for singles (0.48) and doubles (0.80) whereas I can distinguish between si* (0.37) and si**(0.51), and between do** (0.68) and do*** (0.84). The overall impact is that my estimated NERP slightly favours a bit more 1-rated fielders (less si** and no do*** are found on their parts of the chart) than Dean's NERP.

¬ Finally, what I wrote about the impact of on-base also applies for defense:

¬ Dean's formula is based on a false assumption that every player will have the same number of rolls, that is 216 PA, or something close to 648 PA over the full course of a season. Intuitively, this makes perfect sense, as every player has 108 chances on his card and 108 chances on the pitcher's card/defensive charts. More formally, the value of a card, over the course of a season, will be determined by:
A) What's on the card (which is given by offensive NERP)
B) How many times you'll read the card (which Dean assumed constant for every player (other things such as injury risk being equal).

In fact, B is not constant across the set. What's constant is the number of outs a team will generate over the course of a season. Every team has 162 games X 27 outs to win a game. What is constant is that every team will have 4350 outs or so. If team A has better on-base than team B, then team A will generate more rolls (will draw more dices) until it reaches 4350 outs. And since teams are made up of players, players with higher on-base are the one responsable for the extra value generated by rolling more dices.

Hence, defensive players allowing higher on-base are responsable for some extra value generated by rolling more dices, since what's constant is the number of outs a team need to complete a season. So my ratings incorporate a small benefit to the best defenders that allow less on-base.

So if you thought that Dean's NERP was too generous about 1-rated fielders, my own system is even more generous. My ratings yield almost 4 more NERP to 1-rated middle infielders, and yield some worse NERP to bad defenders across the field.

A last improvement is that I incorporated the value of arms for outfielders.

My logic was quite simple. Arm ratings come in action from two different ways:
A) when players have a chance to advance and take an extra base on a hit
B) when players have a chance to advance one base on a flyB

A) is how I determine the value of speed. In a preceding post, when I incorporated the value of speed in my ratings, I provided the following formula:

(((speed-8)*0,23-0,6)

It's easy to see that each increase of one unit in speed rating implies a NERP increase of 0.23.

If the three outfielders have an arm rating of -1, then collectively, the value of this asset can simply be computed with the same unit (0.23) X 9 (to go across the lineup) = 2.07. Then I must distribute that value (2.07 defensive NERP for each -1 arm rating) between the left fielder, the center fielder, and the right fielder. Not knowing how to do this, I took the arbitrary decision (based on my experience of playing online strat) to distribute the value the following way:
1) 2.07*arm_Rating*15% for left fielders
2) 2.07*arm_rating*50% for centerfielders
3) 2.07*arm_rating*35% for right-fielders

B) was computed based on the difference between the number of outs in 80M leagues as registered by outfielder assissts MINUS the outs in 80M leagues as registered on the misc page about runners. I don't have the numbers right now, but going from memory, I noticed that, on a typical league, you would have about 25-30 outs per team registered in the baserunning section of the misc page, and you would have roughly 30-35 assists per team by outfielders as registered in the fiedling section of the stat page. I interpreted this difference as indicating that the flyB? and flyB (rf) were probably not registered in the baserunning section. This said, the betters arms don'T have more outs---they prevent runners from advancing rather than retiring them. So the net value for this part I came up with is rather small: 1 NERP per unit of arm rating. I distributed the value similarly between left/center/and right.

For catchers, I gave a detailed account here.
viewtopic.php?f=17&t=639093

One inconvenience when calculating the defensive NERP value is that ss and 2b prevent so many runs and turned so many double-plays compared to other positions that their defensive NERP is massive and are out of factor with other positions. It's a common problem in sabermetrics. The solution I choose is to center around the salary structure of SOM, so that I have a same amount of bargains and busts at each position, while at the same time arrive at a final ranking for DEFENSIVE NERP that "makes sense", with the best ss and 2b at top of defensive NERP, followed by the best catchers, 3b, and cf. Technically, I add 2 and 1.5 NERP from ss and 2b to make them look worse, and I substract 2 and 5 from first basemen and third basemen. In the outfield, I substract 4 NERP at cf, 6 at rf and 6.5 at lf. As for catchers, since their value is computed toward the mean, rather than specifically on NERP, I substract 10.

So here's the ranking for all players with negative DEFENSIVE NERP

Code: Select all

Tulowitzki   -21.30
Pedroia,D_   -20.06
Phillips,B   -20.03
Gregorius,   -19.15
Cozart,Z__   -19.15
Molina,Y__   -18.94
Lemahieu,D   -17.88
Escobar,A_   -16.98
Ramirez,Al   -16.94
Hardy,J___   -16.91
Simmons,A_   -16.91
Kinsler,I_   -16.83
Barney,D__   -16.79
Perez,S___   -15.48
Martin,R__   -13.83
Dozier,B__   -13.59
Galvis,F__   -13.48
Crawford,B   -12.45
Seager,K__   -12.26
Bradley Jr   -11.90
Markakis,N   -11.78
Heyward,J_   -11.55
Gose,A____   -11.27
Brantley,M   -10.84
Hamilton,B   -10.72
Hanigan,R_   -10.69
Gordon,A__   -10.58
Gosewisch,   -10.51
Lucroy,J__   -10.30
Ellsbury,J   -10.25
Gardner,B_   -10.20
Cain,L____   -10.09
McCann,B__   -10.06
Blanco,G__   -10.02
Yelich,C__   -9.64
Joseph,C__   -9.43
Jones,A___   -9.29
Avila,A___   -8.97
Bourjos,P_   -8.91
Marisnick,   -8.83
Gomez,C___   -8.74
Perez,J___   -8.50
Trout,M___   -8.44
Span,D____   -8.28
Beltre,A__   -8.18
Pena,R____   -8.16
Cabrera,A_   -8.09
Goins,r___   -8.08
Lagares,J_   -8.03
Ramirez,J_   -7.56
Forsythe,L   -7.56
Rollins,J_   -7.56
Mathis,J__   -7.41
Reddick,J_   -7.13
Molina,J__   -7.13
Sanchez,C_   -7.04
McDonald,J   -7.04
Mesoraco,D   -6.88
Posey,B___   -6.74
Marte,S___   -6.61
Aybar,E___   -6.49
Harrison,J   -6.48
Arias,J___   -6.48
Drew,S____   -6.48
McCutchen,   -6.47
Dyson,J___   -6.38
Lawrie,B__   -6.37
Chirinos,R   -6.33
Machado,M_   -6.21
Rivera,R__   -6.16
Espinosa,D   -6.00
Gonzalez,A   -5.92
Venable,W_   -5.74
Ramos,W___   -5.69
Zunino,M__   -5.68
Kratz,E___   -5.59
Calhoun,K_   -5.43
Florimon,P   -5.41
Kelly,D___   -5.36
Bernadina,   -5.32
Uribe,J___   -5.29
Saunders,M   -5.03
Cano,r____   -4.98
Sogard,E__   -4.97
Schoop,J__   -4.97
Pollock,A_   -4.90
Suzuki,I__   -4.90
Gomes,Y___   -4.89
Castillo,W   -4.87
Kiermaier,   -4.84
Pennington   -4.82
Puig,Y____   -4.78
Headley,C_   -4.78
Vazquez,C_   -4.67
Victorino,   -4.60
Flaherty,r   -4.45
Zobrist,B_   -4.29
Gentry,C__   -4.29
Frazier,T_   -4.27
Dominguez,   -4.27
Goldschmid   -4.23
Fuld,S____   -4.10
Heisey,C__   -4.10
Lough,D___   -4.10
Arenado,N_   -4.01
Kendrick,H   -3.94
Utley,C___   -3.94
Pena,B____   -3.92
Schierholt   -3.81
Pujols,A__   -3.78
Sandoval,P   -3.76
Campana,T_   -3.72
Gwynn Jr,T   -3.72
Denorfia,C   -3.68
Ackley,D__   -3.53
Den Dekker   -3.49
Robinson,S   -3.49
Ryan,B____   -3.32
Jones,J___   -3.30
Freeman,F_   -3.29
Hechavarri   -3.27
Parrino,A_   -3.27
Morneau,J_   -3.27
Longoria,E   -3.24
Franco,M__   -3.24
Sucre,J___   -3.23
Perez,R___   -3.20
Holt,T____   -3.19
Bruce,J___   -3.16
Suzuki,K__   -3.09
Lobaton,J_   -3.09
Hicks,A___   -3.06
Cervelli,F   -2.94
Hicks,B___   -2.89
Susac,A___   -2.88
Schafer,L_   -2.87
Wieters,M_   -2.84
Hosmer,E__   -2.77
Barnhart,T   -2.77
Ozuna,M___   -2.77
Iannetta,C   -2.76
Davis,C___   -2.75
Colvin,T__   -2.69
Danks,J___   -2.69
Pence,H___   -2.58
Donaldson,   -2.41
Ishikawa,T   -2.27
Schafer,J_   -2.26
Harper,B__   -2.22
Romine,A__   -2.21
Stanton,G_   -2.16
Barnes,B__   -2.07
Ellis,A___   -2.07
Nieves,W__   -2.02
Rojas,M___   -1.85
Beckham,G_   -1.79
Jennings,D   -1.77
Flowers,T_   -1.70
Crawford,C   -1.70
Federowicz   -1.69
Butera,D__   -1.67
Segura,J__   -1.67
Cowgill,C_   -1.65
Ruiz,C____   -1.56
Chavez,Er_   -1.51
Lamb,J____   -1.51
Nieuwenhui   -1.46
Castro,J__   -1.39
Montero,M_   -1.36
Byrd,M____   -1.36
Cruz,T____   -1.20
Andrus,E__   -1.17
Stewart,C_   -1.08
Inciarte,E   -1.04
Bourn,M___   -1.03
Hundley,N_   -0.96
Fryer,E___   -0.94
Parra,G___   -0.93
Loney,J___   -0.90
Rizzo,A___   -0.90
Navarro,E_   -0.90
Rendon,A__   -0.69
Adams,M___   -0.45
Vogt,S____   -0.33
Corporan,C   -0.18
McGehee,C_   -0.08
Negron,K__   -0.08
Petit,G___   -0.08
Soto,G____   -0.03
Belt,B____   0.00