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Before I explain to you what this new metric – SkaP – does, I am first going to warn you that I can’t provide you with a formula or individual statistics for it.  It’s a theory right now, and something for which I need access to data I don’t have in order to find a formula.

This statistic was inspired in part by Colin Dew-Becker’s article the other day here on FanGraphs Community Research.  In his article, he argued that the the way a hit or out is made matters – not just the result of the hit or out.  A single to the outfield, for example, is more likely to send a runner from first to third or from second to home than an infield single.  Likewise, a flyout is more likely to advance runners than a strikeout is.

This statistic was also inspired in part by UZR.  UZR attempts to quantify runs saved defensively by a player partially by measuring if they make a play that the average fielder would not.  In the FanGraphs UZR Primer, Mitchel Lichtman explains that

“With offensive linear weights, if a batted ball is a hit or an out, the credit that the batter receives is not dependent on where or how hard the ball was hit, or any other parameters.”

This means that a line drive into the gap in right-center that is a sure double but is caught by Andrelton Simmons ranging all the way from shortstop (OK, maybe that was an exaggeration) will only count for an out, even though in almost any other situation it would be a double.  The nature of linear-weight based hitting statistics (and most other hitting statistics as well) is that they are defense-dependent.  Hitters have been shown to have much more control over their batted balls than pitchers do, which is why so far only pitchers have commonly used defense-independent statistics, but it would probably be useful for hitting too, no?

Now, if we want a defense-independent and linear weights-based hitting statistic, it would not be possible to formulate something similar to the hitting equivalent of the current model  of tERA (or tRA) because that generalizes all batted balls into categories such as grounders, line drives, or fly balls, because hitters can control where and how hard and at what angle their batted balls are hit at least to some extent.  Instead, what I would use is something more similar to a hitting equivalent of this version of tERA I found on a baseball blog.  What that article proposes is something much more detailed than what we have now (by the way, tERA has been supplanted by SIERA, but is still an interesting theory).  Their idea is that instead of finding expected run and out values for grounders, line drives, and fly balls, find the expected run value for a ball, to use their words, “with x velocity and y trajectory [that] lands at location z.”  This is similar to UZR in that exact (or as close to exact as possible) batted-ball data is processed and the expected run/out values are calculated.

So now for the statistic:  SkaP, or Skill at (the) Plate, is a number that uses all that batted-ball data to find the expected run and out values of each at-bat.  It would weight the following things:  home runs (although maybe a regressed version could use lgHR/FB%*FB instead), walks, strikeouts, HBP, and each ball put in play by the player.  This makes it so that it is not defense-dependent, and so that Andrelton Simmons catching that sure double does not penalize the hitter.  I haven’t calculated this statistic, though, so I don’t know if this would be best as a rate, counting, or plus-minus statistic (maybe all three?).

There’s one catch to this, however:  Skill at the Plate is really only a measure of skill at the plate.  It doesn’t account for some batters’ ability to stretch hits or beat out infield singles.  Billy Hamilton is going to be more likely to reach on an infield single than Prince Fielder.  However, this stat would treat them both the same, and not reward Hamilton’s speed for allowing him to reach base on what might have most likely been an out.  It would be very hard to separate defense independence and batter-speed independence for hitting statistics, though, and I’m not sure it’s possible to do without an extreme amount of effort.  Maybe a crude solution would be to quantify a player’s speed using Spd, UBR or BsR and add it somehow to this statistic.

I can’t calculate this myself, as I don’t have access to Baseball Info Solutions’s (or some other database that tracks batted balls) data.  FanGraphs does, however, and I would love to see this looked into further.

Last week’s post ended with a chart comparing power and patience, or, more accurately, league-wide extras bases and times on base (excluding pitchers), year-by-year. Here it is again:

Fig. 1 – No, Not a Fig Leaf

One question this chart does raise, at least to me: does it merely indicate the general effectiveness of offenses, or are there actually times where power goes up relative to getting on base, but offense stagnates or declines? After all, it dipped in 1968 when offense dipped; it increased from 1918-21 as the dead ball era ended; it rose in 1987.

There have been 113 seasons since 1901. Running some R^2 numbers when comparing XB/TOB to various statistics over these 113 seasons gets us some interesting results. I suppose it’s possible than in the year 2514, these stats will correlate better or worse, and that a sample size of 113 seasons is too small. I don’t really have the time to wait and see, though, and I’m fairly sure you don’t either, so:

• wOBA .0014 (.016 w/pitchers–and for only pitchers, .004)
• OBP .217 (.083 w/pitchers–and for only pitchers, .006)
• R/G .246 (.238 w/pitchers)
• HR/PA .958 (.960 w/pitchers)
• ISO .968 (.971 w/pitchers)

So, no, we’re not looking at a proxy for overall offense here. But we are looking at a proxy for power itself. The plan here was to investigate the relationship between hitting for power and getting on base through the years. And instead, all we have done with this chart is look at league-wide power proficiency, not even really compared to league-wide getting-on-base proficiency.

Well, there is an alternative explanation, which we will get to.

The good news is, we don’t have to throw away these numbers. We just have to bring OBP and ISO back into the picture, re-separating the two elements of that chart. You can’t really guess a league’s OBP in any given season from ISO, or vice versa, as the R^2 for OBP and ISO is .373:

Fig. 2 – No, Not a Fig Newton

To some, this may indicate a problem with the premise of this series: there’s a solid but not overwhelming correlation between power and patience, it turns out. Well, first, it’s still worth looking into. Part of the reason for that is that is, in smaller sample sizes, there often is more of a correlation: the R^2 between OBP and ISO from 1901-20 is .792; in the last 20 years, it’s .583. Granted, you can mess with the numbers all you want here; for instance, go back 21 years, and suddenly the R^2 between OBP and ISO is .461. Nevertheless, there are brief stretches in baseball where OBP and ISO correlate quite well, and each season is a set of tens of thousands of plate appearances, for what that’s worth. (Little, I know; it just means that the figures for each season were unlikely to change much if the season were longer.)

Also, while they don’t correlate well, or at least well enough that you can predict one from the other, OBP and ISO do correlate pretty well for two independent rate statistics. For example, the R^2 for BB% and K% is .007. There seems to be something to the idea that power threats can get on base more effectively, or that it’s easier to get on base as a power threat. How much is part of the point.

Now for some graphical representations of annual changes in OBP and ISO.

First, here they are on one chart, with the all time figures represented for comparative purposes.

Fig. 3 – Yum, Fig Newtons

Next, we remove the lines representing the all-time marks and then scale ISO to OBP. FIP is scaled to ERA by adding a constant, so we’ll try a similar technique. The all-time OBP, remember from last week, is .333, and the all-time ISO is .130. So, we’re now going to add .203 to each year’s ISO. I call it scaled ISO, or sISO. (I don’t expect this to catch on as anything as it really just has a purpose limited to this series.) Since we’re just adding a constant to ISO, “sISO” and ISO have a perfect correlation, so we’re cool in that regard. Regard:

Fig. 4

The line for “sISO” is the same shape as the line for ISO. (I’m sure this point is patently obvious to some, but perhaps not everyone.) Now we can see really see the seasons ISO was above its all-time norm relative to OBP, so let’s graph those gaps between each line above. Scaled ISO vs. OBP:

Fig. 5 – I Thought It Would Be More Fun For You to Guess the “Horizontal axis title” and That’s My Story and I’m Sticking to It

ISO peeked above OBP in 1953, dipped back below in 1954, and then sharply increased in 1955 and 1956. Before that, however, getting on base was always “easier” vs. the historical norms than hitting for power was. This was true even in the post-Ruth era, with players such as Ruth, Gehrig, Foxx, Ott, and even the beginning of Ted Williams’ career, right up until the end of the Korean War. Actually, league OBP through 1952 was slightly higher, .334, than the current average, while ISO was at .107, still well below the current average.

If baseball ended in 1952 (perish the thought!), the dead ball era would still be a distinct period in baseball history. From 1901-18, league OBP was .316 and ISO .081. From 1919 to 1952, the figures were a .343 OBP and .120 ISO.

Since 1956, power has mostly been above its historical norms relative to OBP, with some exception. Part III will look further into all of this.

Astute observers might have noticed something, though:
   

The R^2 of the figures comprising each chart (sISO-OBP and XB/TOB) is .885.

So, what do we have here, then?

One possible conclusion is still that we’re still only looking at power. But having now observed changes in OBP over time as part of this exercise, perhaps something else is at play. I think there is.

It’s not particularly obvious in the chart that shows OBP vs. its historical average, but OBP, despite what we know about the dead ball era, and other seasons such as 1968, has actually been relatively consistent historically. Even at the hardest time in history for players to reach base, during the dead ball era, it was still much harder to hit for power. When I looked at a sort of OBP+ and ISO+ vs. their historical averages (just using 100*OBP/historical OBP), here were some things:

• Range: OBP+ 18 (89-107), ISO+ 80 (51-131)
• Standard Deviation: OBP+ 3.79, ISO+ 19.6

It’s not necessarily that looking at extra bases per times on base, or the arithmetical difference between OBP and ISO, is the same at looking at power. Rather, OBP has been so consistent historically relative to ISO, that the observations in this article are effectively only an observation of ISO, regardless of the specific numbers that go into them. This is a not uninteresting takeaway to me.

Next week, we’ll use four factors–XB/TOB, sISO-OBP, OBP+, and ISO+–to run through the relationship between power and patience throughout baseball history, and maybe even try to look into the future a little bit. Parts IV and V will then bring us back to the beginning of Part I as we return to observing OBP and ISO through the lens of the efforts of individual players. That’s the tentative plan at least.

Before we start, I want to get a few things clear:

-Yes, I know the whole “Jacoby Ellsbury to the Dodgers” thing was probably a product of Scott Boras and the media.

-Yes, I know Matt Kemp should be ready by the start of 2014 to play center field.

-Yes, I know the Dodgers already have four outfielders, three of which have massive contracts, and three of which are injury prone.

-Yes, I know Ellsbury is injury prone. This example is operating in a vacuum.

-No, I don’t think the Dodgers will end up signing Ellsbury. There are just too many things that need to happen in order for the signing to make sense. And even then, depending on contracts, the signing STILL might not make sense due to Ellsbury’s injury history, along with how much money the Dodgers would have to eat on the contracts of their traded outfielders, and how badly that money would hamstring them for the future.

Okay. Now that we’ve gotten that cleared up, let’s begin.

The Los Angeles Dodgers, when healthy, have one of the best offensive outfields in the league. But, despite having a couple gold glove winners out there, they lack something when it comes to the fielding department, specifically in center field.

In 2013, the Dodgers trotted out five different players for a combined total of 1450.1 innings in center field, with Andre Ethier (645.1) and Kemp (576.1) getting the lion’s share of playing time. Now, Kemp hasn’t looked awful in center field (besides running into walls, which we’ll cover in a second), but UZR has less-than-friendly reviews on him. With Ethier, he looked somewhat usable while healthy in center, but just looked bad in the NLCS while trying to play with one good ankle. For the record, UZR gives Ethier a -1.8 for his efforts this season. The other three that played center for the Dodgers this season were Skip Schumaker (167 IP, -1.3 UZR), Yasiel Puig (55.1 IP), and Nick “Chili” Buss (6.1 IP). Schumaker shouldn’t be a starter, Puig’s natural position is right field, and I’m not even going to talk about Buss being in there as a viable option.

So, that brings us to comparing UZR for Kemp and Ellsbury.

If we take the three seasons with the greatest sample size, Ellsbury is clearly the optimal choice in the field. Granted, he doesn’t have the arm strength that Kemp has, but UZR factors that into its ratings as well. The signing of Ellsbury to play center field would likely move Kemp to left, and would make Ethier and Carl Crawford expendable. Moving Kemp to left field also saves him from the rigors of center field that have plagued him over the past couple years.

Offensively, the acquisition would be relative. Yes, Ethier would probably hit more home runs, but Ellsbury would offset that with stolen bases. In 2013, Ethier posted a wRC+ of 120 without being able to hit lefties at all (wRC+ of 73 vs LHP) and Ellsbury wasn’t far behind with a 113 RC+ and troubles against lefties of his own (w RC+ of 78 vs LHP). Ellsbury represents more of an upgrade in speed over both Crawford and Ethier, and would give the offense a new dynamic to go with Puig atop the order in front of Hanley Ramirez, Adrian Gonzalez, Kemp, and newly-signed Alexander Guerrero.

Given what a healthy Kemp has meant to this team in the past (which was just as recently as April, 2012), he is arguably the most important piece in their lineup. If moving him out of center field and into left field can save him from some of the numerous hamstring and shoulder injuries that he has experienced, it would be a huge win for the Dodgers to finally acquire a proper center fielder without giving up any value on offense.

It is generally a marked advantage for a batter to face an opposite-handed pitcher. Platoon splits across the league are evidence of this well documented phenomenon, and managers are quick to take advantage of matchups.

One of the chief advantages of switch-hitting is that the opposite-handed pitcher’s release point is closer to the center of the hitter’s field of vision. This allows him to get a better look at the ball, and judge whether the pitch is worth swinging at. If a switch-hitter generally gets a better look at the incoming pitch he should, in theory, be better at commanding the strike zone than his one-sided counterparts, walking more and striking out less. Do switch hitters have a better BB/K split than other hitters?

While we are limited by a small sample size of switch-hitters who accrue a enough at bats against lefties to possibly stabilize (according to work done by Russell Carleton), we can calculate their splits and compare it to the average split for batters who always hit from one side.

If we assume that switch-hitters would ‘naturally’ hit from the side in which they throw, we can roughly estimate what their split might be if they were not switch-hitters by calculating BB/K split for righties when facing left-handed pitchers (LHP) and right-handed pitchers (RHP).

Right-handed batters (RHB), on average, post a healthy BB/K ratio of .63 against LHP and more dismal .38 against RHP. The table below shows how splits for switch-hitters who throw right-handed compared to those righties who do not swing from both sides of the plate.

Or if you prefer to see the splits visually, and compared to the mean for all non-switch hitters:

We can see the results are relatively mixed. If switch-hitters really did display a better ability to draw walks and avoid strikeouts we would expect to see smaller than league-average (below the red line) splits, in the positive direction. Among righties, hitters from Kendrys Morales to Chase Headley in the chart above do not display as severe a split as the average right-handed batter, and may derive a significant benefit to never seeing a same-handed pitcher. However, a surprising number of hitters display reverse splits, improving their ratio considerably when batting from their own weak side.

The extreme negative splits of Coco Crisp, Victor Martinez, and Nick Swisher are all consistent with their recent career numbers. Indeed, these negative splits are even evident when examining their wOBA splits for the last several years.

Alberto Callaspo’s outlier split belies a an impressive ability to avoid strikeouts while taking walks at a accelerated pace. Against lefties he posts an outstanding BB/K of 1.5, and his ratio of 1.03 vs. RHP is still impressive. The dropoff from facing LHP to RHP is steep in absolute terms, but his knowledge of the strike zone is still elite.

The BB/K ratio for Jarrod Saltalamacchia, and Justin Smoak both see a slight benefit in switch-hitting, featuring splits a bit lower than the league average. Justin Smoak, however, suffers from a serious power outage, posting a .218 ISO when hitting from his left side, and a miserable .082 ISO from his left. Salty’s power split is not as egregious, but the .128 point drop in ISO is troubling for a player who’s contact % is only slightly above Dan Uggla and Pedro Alvarez. Andres Torres, a natural right hander, sees a similar decline in his wOBA splits– .318 against LHP but a paltry .249 against RHP. These players enjoy a nonexistent or marginal advantage in BB/K ratio as a switch hitter, and hitting primarily from their strong side might be an experiment worth performing.

The Shane Victorino Experiment

 Shane Victorino’s ratio of walks to strikeouts reduces by .07 when facing RHP as opposed to LHP. After tweaking his hamstring in the second half of 2013, he decided to at least temporarily abandon switch-hitting for the remainder of the season. Since mid-August had almost 50 plate appearances as a RHB vs. RHP,  offering a real-life counterfactual case. How does not switch-hitting affect a productive hitter’s BB/K ratio?

From September and into the postseason, Victorino has managed to walk just twice and strike out over 20 times, giving him a miniscule BB/K ratio of just .09, much smaller than his .33 season average. Still, with a wOBA of .356 right in line with his season long average, his overall production at the plate has not suffered despite the more aggressive and less patient approach.

Victorino’s small sample size of hitting exclusively right-handed fails to reliably estimate the counterfactual scenario. However, his case is interesting because, while switch-hitters like J.T. Snow did abandon their dual approach, most did so because of a decline in production from their weak side. Players who eventually decided the advantages of switch-hitting did not offset the challenges of being ambidextrous were already in decline mode—Victorino on the other hand is coming off a great season. While he has officially achieved veteran status, the 32-year old proved this season that reports of his bat’s death have been greatly exaggerated. If he and his coaches are encouraged by his recent wOBA spike, and he abandons hitting from the left side entirely, his BB/K may continue to steadily decline even if his power improves.

Conclusions

The results seen here do not strongly support the hypothesis that switch-hitters have an inherent advantage over others when considering the ratio of bases on balls to strikeouts. While there is some evidence that switch-hitters do enjoy better splits, it is not overwhelming and may provide only marginal benefit to players like Andres Torres, Dexter Fowler and Justin Smoak. Overall, lefties like Carlos Beltran and Daniel Nava joined Alberto Callaspo as possible examples of the reverse, a larger than average split when going from the strong side to weak side.

There are obvious limitations to this study, starting with a  small sample size. We only examined 2013 splits, and the number of left-handed hitters who switch-hit is very low. It may be possible moving forward to use career splits for lefties going back decades to determine if left handed switch-hitters generally have worse BB/K splits than their counterparts.

Currently, switch-hitters account for slightly less than 15% of major league hitters.  To say that having the platoon advantage is always an advantage for the hitter may not be accurate– players whose weak side bat is significantly less powerful, like Justin Smoak or Jarrod Saltalamacchia, may inadvertently harm their value as a hitter by sticking to switch-hitting in all cases. Baseball is a game of adjustments and gaining incremental advantages, and switch-hitting is no different. Some players use it to gain an upper hand, and others may be wasting their potential.

Attempting to accurately estimate the number of runs produced by players is one of the most important tasks in sabermetrics. While there is value in knowing that a player averages four hits every ten at-bats, that value comes from knowing that more hits tend to lead to more runs. On-base percentage became popularized through Moneyball in the early 2000s because the Oakland Athletics, among other teams, realized that getting more runners on base would lead to more opportunities to score runs.

Knowing a player’s batting average or on-base percentage can be informative, but that information does nothing to quantify how the player contributed to a team’s ability to score runs. The classic method for determining how many runs a player contributes to his team is to look at his RBI and runs scored totals. However, both of those statistics are extremely dependent on timely hitting and the quality of the rest of the team. A player will not score many runs nor have many RBI opportunities if the rest of the players on his team, particularly the players around him in the lineup, are not productive.

One of the more popular sabermetric methods to estimate a player’s run production is to find the average number of runs that certain offensive events are worth across all situations and then apply those weights to a player’s stat line. In this way, it doesn’t matter if a player comes to the plate with the bases loaded every time or the bases empty every time, just that he produced the specific type of event.

Here is a chart that shows the average number of runs that scored in an inning following each combination of base and out states in 2013^^.

We can see in the chart that in 2013, with no men on base and zero outs, teams scored an average of 0.47 runs through the end of the inning.  If a batter came to the plate in that situation and hit a single, the new base/out state is a man on first with zero outs, a state in which teams scored an average of 0.82 runs through the end of the inning. If the batter had instead caused an out, the new base/out state would have become bases empty with one out, a state in which teams only averaged 0.24 runs through the remainder of the inning. Consequently, we can say that a single in that situation was worth 0.58 runs in relation to the value of an out in the same situation. If we repeat this process for every single hit in 2013, and apply the averages from the chart to each single depending on when they occur, we find that an average single in 2013 was worth approximately 0.70 runs in relation to the average value of an out.

This is known as the linear weights method for calculating the context-neutral value of certain events. Check this article from the FanGraphs Library, and the links within, for more information on linear weights estimation methods.

There have been a variety of statistics created to estimate a player’s performance in a context-neutral environment using the linear weights method over the last few decades. Recently, one of the more popular linear weight run estimators, particularly here at FanGraphs, has been weighted On-Base Average (wOBA) introduced in The Book: Playing the Percentages in Baseball. wOBA is arguably the best, publically-available run estimator, but I think it has potential for improvement by incorporating more specific and different kinds of events into its estimate.

wOBA is traditionally built with seven statistics: singles, doubles, triples, home runs, reaches on error, unintentional walks, and hit by pitches. While some versions may exclude reaches on error and others may include components like stolen bases and caught stealing, I will focus exclusively on the version presented in The Book that uses those seven statistics. By limiting the focus to just those seven components, wOBA can be calculated perfectly in every season since at least 1974 (as far back as most play-by-play data goes), and can be calculated reasonably well for the entire history of the game.

While it can be informative to see what Babe Ruth’s wOBA was in 1927, when analyzing players in recent history, particularly those currently playing, accuracy in the estimation should be the most important consideration. Narrowing the focus to just seven statistics, some broadly defined, will limit how accurately we can estimate the number of runs a player produced in a context-neutral environment. The statistics I refer to as “broadly defined” are singles and doubles. I say that because it is a relatively easy task to convince even a casual baseball fan that not all singles are created equally.

If we compare singles hit to the infield with singles hit to the outfield, we’ll notice that outfield singles will cause runners on base to move further ahead on the basepaths on average than infield singles. For example, in 2013, with a man on first, only 3.2% of infield singles ended with men on first and third base compared to 29.9% of outfield singles. If outfield singles create more “1-3” base states than infield singles, and we know from the chart above that “1-3” base states have a higher run expectancy than “1-2” base states in the same out state, then we know that outfield singles are producing more runs on average than infield singles. If outfield and infield single are producing different amounts of runs on average, then we should differentiate between the two events.

Beyond just breaking down hits by fielding location, we can refine hit types even further. If we differentiate singles and doubles by direction (left, center, right) and by batted ball type (bunt, groundball, line drive, fly ball, pop up) we can more accurately reflect the value of each of those offensive events. While the difference in value between a groundball single to right field compared to a line drive single to center field is minimal, about 0.04 runs, those minimal differences add up over a season or career of plate appearances. Reach on error events should also be broken down like singles and doubles, as balls hit to the third baseman that cause errors are going to have a different effect on the base state than balls hit to the right fielder that cause errors.

The two other ways that wOBA accounts for run production by a batter are through unintentional walks and hit by pitches, notably excluding intentional walks. If a statistic is attempting to estimate the number of runs produced by a player at the plate, I believe the value created by unskilled events should also be counted. While it takes no skill to stand next to home plate and watch four balls go three feet wide of the strike zone, the batter is still given first base and affects his team’s run expectancy for the remainder of the inning. Distinguishing between runs produced from skilled and unskilled events is something that should be considered when forecasting future performance as unskilled events may be harder to repeat. However, when analyzing past performance, all run production should be accounted for, no matter the skill level it required to produce those runs.

There is an argument that the value from an intentional walk should just be assigned to the batting team as a whole, as the batter himself is doing nothing to cause the event to occur; that is, the batter is not swinging the bat, getting hit be a pitch, or astutely taking balls that could potentially be strikes. However, as the players on the field are the only ones who directly affect run production — it isn’t an abstract “ghost runner” on first base after an intentional walk, it’s the batter — the value from the change in run expectancy must be awarded to players on the field. While it can be difficult to determine how to award that value for the pitching team with multiple fielders involved in every event (pitcher and catcher most notably and the rest of the fielders for balls put into play), the only player on the batting team who can receive credit for the event is the batter.

If we accept that the intentional walk requires no skill from the batter, but agree that he should still receive credit for the event, then we can extend that logic to all unskilled events in which the batter could be involved. Along with intentional walks, that would include “reaching on catcher’s interference” and “striking out but reaching on an error, passed ball, or wild pitch.” In those cases, it is the catcher rather than the pitcher causing the batter to reach base but it doesn’t matter to the batting team. If the team’s run expectancy changed due to the batter reaching base, it makes no difference if it was the pitcher, catcher, or any other fielder causing the event to occur.

When building wOBA, the value of the weight for each component is calculated with respect to the value of an average out, like in the example above. Using the average value of all outs is very similar to using the broad definition of “single,” as discussed earlier. Very often we hear about productive outs, and yet we rarely see statistics quantify the value of different types of outs in a context-neutral manner. If a batter were to exclusively make all of his outs as groundballs to the right side of the infield, he would hurt his team less than if he were to make all of his outs as groundballs to the center of the infield. Groundouts to the right side of the infield allow runners on second and third base to advance more easily than groundouts to the center of the infield. Additionally, groundouts to the center of the infield have more potential to turn into double plays than groundouts to the right side of the infield. As above, the differences in value are minimal — around 0.04 runs in this case — but they add up over a large enough sample.

To deal with the difference in the value of outs, all specific types of outs should also be included in any run estimation, weighted in relation to the average value of an out. For instance, in 2013 the average value of all outs in relation to the average value of a plate appearance was -0.258 runs while the average value of a fly out to center field in relation to the average value of a plate appearance was -0.230 runs. Consequently, we can say that a fly out to center field is worth +0.028 runs in relation to the average value of an out. We can do the same for groundouts to the left side of the infield (-0.015) or lineouts to center field (+0.021), as well as every other type of out broken down by direction, batted ball type, and fielding location. Interestingly, and perhaps not surprisingly, all fly outs and lineouts to the outfield are less damaging than an average out while all types of outs in the infield are more damaging than an average out, except for groundouts to the right side of the infield and sacrifice bunts.

Taking the weights for each of these 104 components, applying them to the equivalent statistics for a league average hitter, and dividing by plate appearances, generates values that tend to fall between .280 and .300 based on the scoring environment, somewhat similar to the batting average for a league average player. In 2013, a league average player would have a score of .256 from this statistic compared to a batting average of .253. To make the statistic easily relatable in the baseball universe, I’ve chosen to scale the values in each season to batting average. The end result is a statistic called Offensive Value Added rate (OVAr) which has an average value equal to that of the batting average of a league average player in each season. So, if a .400 batting average is an historic threshold for batters, the same threshold can be applied to OVAr. Since 1993, as far back as this statistic can be calculated with current data, Barry Bonds is the only qualified player to post an OVAr above .400 in a single season, and he did it in four straight seasons (2001-2004).

Where OVAr mirrors the construction of the rate statistic wOBA, another statistic, Offensive Value Added (OVA), mirrors the construction of the counting statistic weighted Runs Above Average (wRAA). Here is the equation for OVA followed by the equation for wRAA.

OVA = ((OVAr – league OVAr) / OVAr Scale) x PA

wRAA = ((wOBA – league wOBA) / wOBA Scale) x PA

OVA values tend to be very similar to their wRAA counterparts, though they can potentially vary by over 10 runs at the extremes. In 2013, David Ortiz produced 48.1 runs above average according to OVA and “just” 40.3 runs above average according to wRAA, a 19.4% increase from his wRAA value. Of Ortiz’s extra 7.8 runs estimated by OVA, 4.3 of those runs came from the inclusion of intentional walks, and 2.5 of those runs came from Ortiz’s ability to produce slightly less damaging outs through his tendency to pull the ball to the right side of the field.

You won’t find many box scores or player pages that list direction, batted ball type, or whether the ball was fielded in the infield or outfield, but the data is publicly available for all seasons since 1993. While wOBA gives non-programmers the ability to calculate an advanced run estimator relatively easily, if we have data that makes the estimation more precise, then programmers should take advantage. Due to the relative difficulty in calculating these values, I’m providing links to spreadsheets with yearly OVAr and OVA values for hitters, Opponent OVAr and OVA values for pitchers, splits for hitters and pitchers based on handedness of the opposing player, and team OVA and OVAr values for offense and defense, with similar splits. Additionally, I’ve included wRAA values for comparison. Those values may not exactly match those you would find on FanGraphs due to rounding differences at various steps in the process, but they should give a general feel for the difference between OVA and wRAA.

I’ve obviously omitted the meat of the programming work, as I felt it was too technical to include every detail in an article like this. For more information on run estimators built with linear weights methodology I’d highly recommend reading The Book, The Hidden Game of Baseball by John Thorn and Pete Palmer, or any of a variety of articles by Colin Wyers over at Baseball Prospectus, like this one. I used ten years of play-by-play data to get a substantive sample⁺⁺ of when each type of event happened on average, and I used a single season of data to create the run environments. Otherwise, the general construction of OVAr mirrors the work done by Tom Tango, Mitchel Lichtman, and Andrew Dolphin in The Book.

The next step for this statistic is to make it league and park neutral (nOVAr and nOVA). I chose to omit this step for the initial construction of these statistics as it was also omitted in the initial construction of wOBA and wRAA. Also, the current methods to determine park factors used by FanGraphs and ESPN, among other sites, are somewhat flawed and not something I want to implement. Until that next step, enjoy a pair of new statistics.

OVAr and OVA, Ordered Batters

OVAr and OVA, Alphabetical Batters

OVAr and OVA, Ordered Batter Splits

OVAr and OVA, Alphabetical Batter Splits

OVAr, Ordered Qualified Batters

OVAr, Ordered Qualified Batter Splits

Opponent OVAr and OVA, Ordered Pitchers

Opponent OVAr and OVA, Alphabetical Pitchers

Opponent OVAr and OVA, Ordered Pitcher Splits

Opponent OVAr and OVA, Alphabetical Pitcher Splits

Opponent OVAr, Ordered Qualified Pitchers

Opponent OVAr, Ordered Qualified Pitcher Splits

OVAr and OVA, Teams

OVAr and OVA, Team Splits

OVAr and OVA, Ordered Weights

OVAr and OVA, Alphabetical Weights

^^ These averages exclude all events in home halves of the 9^th inning or later to avoid biases created by walk-off hits and the inability of the home team to score an unlimited number of runs in 9^th inning or later like they can in any other inning.

** A number in the Base State column represents a runner on that base, with 0 representing bases empty.

++ I have one note on sample size that I didn’t think fit anywhere comfortably in the main body of the article. The biggest issue with a statistic built with very specific events is that some of those events are extremely rare. For instance, groundouts to the outfield have happened just 111 times since 1993, compared to groundouts to the infield that have happened 891,175 times since 1993. Consequently, the average value of outfield groundouts, split up direction, can vary substantially from year to year as different events are added or taken away from the sample. I choose to use a ten-year sample to attempt to limit those effects as much as possible but they still will be evident upon close examination. With that sample size, in 2013 a groundout to left field was worth -0.447 runs in relation to the average value of an out. In 2006 the same event was worth -0.089 runs, while in 2000 it was worth +0.154 runs.

As long as the statistic is built in a logically consistent manner, I don’t mind that low frequency events like outfield groundouts and infield doubles vary somewhat from year to year in estimated value, as the cumulative effect will be quite minimal. That being said, as I am trying to estimate the value of events as accurately as possible, the variation in value is a bit off-putting. It may be that a sample of 20 or more years would be necessary for those rare events, with a smaller sample size for the more common events. That adjustment will be considered for the nOVAr and nOVA implementations, but for OVAr and OVA I wanted the construction to be completely consistent.

FIP, xFIP, SIERA are all very good ERA estimators, and their predictability is well documented. It is well known that SIERA is the best ERA estimator over samples that occur from season to season, followed very close by xFIP, with FIP lagging behind. FIP is best at showing actual performance though, because is uses all real events (K, BB, HR). Skill is commonly best attributed to either xFIP or SIERA. ERA is also well known to be the worst metric at predicting future performance, unless the sample size is very large <500IP with the pitcher remaining in the same or a very similar pitching environment.

FIP, xFIP, and SIERA are supposed to be Defense Independent Metrics, and they are. Well, they are independent of field defense, but there is one small error in the claim of defense independent. K’s and BB’s are not completely independent of defense. Catcher pitch framing plays a role in K’s and BB’s. Catchers can be good or bad at changing balls into strikes and this affects K’s and BB’s. Umpire randomness and umpire bias also play a role in K’s and BB’s. It is unknown how much of getting umpires to call more strikes is a skill for a pitcher or not. Some pitchers are consistent at getting more strike calls (Buehrle, Janssen) or less strike calls (Dickey, Delabar), but for most pitchers it is very random (especially in small sample sizes). For example Jason Grilli was in the top 5% in 2013 but was in bottom 10% in 2012.

I wanted to come up with another ERA estimator that eliminates catcher framing, umpire randomness and bias, and eliminates defense. I took the sample of pitchers who have pitched at least 200IP since 2008 (N=410) and analyze how different statistics that meet this criteria affect ERA-. I used ERA- since it takes out park factors and adjusts for the changes in the league from year to year. I looked at the plate discipline pitchf/x numbers (O-Swing, Z-Swing, O-Contact, Z-Contact, Swing, Contact, Zone, SwStr), the six different results based off plate discipline (zone or o-zone, swing or looking, contact or miss for ZSC%, ZSM%, ZL%, OSC%, OSM%, OL%), and batted ball profiles (GB%, LD%, FB%, IFFB%). *Please note that all plate discipline data is PitchF/X data, not the the other plate discipline on FanGraphs, this is important as the values differ*

The stats with very little to absolutely no correlation (R^2<0.01) were: Z-Swing%, Zone%, OSC%, ZSC%, ZL% (was a bit surprised as this would/should be looking strike%), GB%, and FB%. These guys are obviously a no-no to include in my estimator.

The stats with little correlation (R^2<0.1) were: Swing%, LD%, and IFFB%. I shouldn’t use these either.

O-Contact% (0.17), Z-Contact%, (.302), Contact% (.319), OSM% (0.206), and ZSM% (.248) are all obviously directly related to SwStr%. SwStr% had the highest correlation (.345) out of any of these stats. There is obviously no need to include all of the sub stats when I can just use SwStr%. SwStr% will be used in my metric.

OL% (0.105) is an obvious component of O-Swing% (0.192). O-Swing had the second highest correlation of the metrics (other than the components of SwStr%). I will use it as well. The theory behind using O-Swing% is that when the batter doesn’t swing it should almost always be a ball (which is bad), but when the batter swings, there are a two outcomes, a swing and miss (which is a for sure strike) or contact. Intuitively, you could say that contact on pitches outside the zone is not as harmful to pitchers as pitches inside the zone, as the batter should get worse contact. This is partially supported in the lower R^2 for O-Contact% to Z-Contact%. It is more harmful for a pitcher to have a batter make contact on a pitch in the zone, than a pitch out of the zone. This is why O-Swing is important and I will use it.

Using just SwStr% and O-Swing%, I came up with a formula to estimate (with the help of Excel) ERA-. I ran this formula through different samples and different tests, but it just didn’t come up with the results I was looking for. The standard deviation was way too small compared to the other estimators, and the root mean square error was just not good enough for predicting future ERA-.

I did not expect/want this estimator to be more predictive than xFIP or SIERA. This is because xFIP and SIERA have more environmental impacts in them that remain fairly constant. K% is always a better predictor of future K% than any xK% that you can come up with. Same with BB% Why? Probably because the environment of catcher framing, and umpire bias remain somewhat constant. Also (just speculation) pitchers who have good control can throw a pitch well out of the zone when they are ahead in the count, just to try and get the batter to swing or to “set-up” a pitch. They would get minus points for this from O-Swing, depending on how far the pitch is off the plate, but it may not affect their K% or BB% if they come back and still strike out the batter.

So I didn’t expect my statistic to be more predictive, but the standard deviation coupled with not that great of RMSE (was still better than ERA and FIP with a min of 40IP), caused me to be unhappy with my stat.

I then started to think about if there were any stats that were only dependent on the reaction between batter an pitcher that are skill based that FanGraphs does not have readily available? I started thinking about foul balls and wondered if foul ball rates were skill based and if they were related to ERA-. I then calculated the number of foul balls that each pitcher had induced. To find this I subtracted BIP (balls in play or FB+GB+LD+BU+IFFB) from contacts (Contact%*Swing%*Pitches). This gave me the number of fouls. I then calculated the rates of fouls/pitch and foul/contacts and compared these to ERA-. Foul/Contact or what I’m calling Foul%, had an R^2 of .239. That’s 2nd to only SwStr%. This got me excited, but I needed to know if Foul% is skill based and see what else it correlates with.

This article from 2008 gave me some insight into Foul%. Foul% correlates well to K% (obviously) and to BB% (negative relationship), since a foul is a strike. Foul% had some correlation to SwStr%, this is good as it means pitchers who are good at getting whiffs are also usually good at getting fouls. Foul% also had some correlation to FB% and GB%. The more fouls you give up, the more fly balls you give up (and less GB). This doesn’t matter however, as GB% and FB% had no correlation to ERA-. Foul% is also fairly repeatable year to year as evidenced in the article, so it is a skill. I will come up with a new estimator that includes Foul% as well.

I decided to use O-Looking% instead of O-Swing%, just to get a value that has a positive relationship to ERA (more O-looking means higher ERA), because SwStr% and O-Swing are negatively related. O-Looking is just the opposite of O-Swing and is calculated as (1 – O-Swing%).

The formula that Excel and I came up with is this: (I am calling the metric TIPS, for True Independent Pitching Skill)

TIPS = 6.5*O-Looking(PitchF/x)% – 9.5*SwStr% – 5.25*Foul% + C

C is a constant that changes from year to year to adjust to the ERA scale (to make an average TIPS = average ERA). For 2013 this constant was 2.68.

I converted this to TIPS- to better analyze the statistic. FIP, xFIP, and SIERA were also converted to FIP-, xFIP-, and SIERA-. I took all pitchers’ seasons from 2008-2013 to analyze. The sample varied in IP from 0.1 IP to 253 IP. I found the following season’s ERA- for each pitcher if they pitched more than 20 IP the next year and eliminated any huge outliers. Here were the results with no min IP. RMSE is root mean square error (smaller is better), AVG is the average difference (smaller is better), R^2 is self explanatory (larger is better), and SD is the standard deviation.

Wow TIPS- beats everyone! But why? Most likely because I have included small samples and TIPS- is based off per pitch, as opposed to per batter (SIERA) or per inning (xFIP and FIP). There are far more pitches than AB or IP so TIPS will stabilize very fast. Let’s eliminate small sample sizes and look again.

Now, TIPS is beaten out by xFIP and SIERA, but beats ERA and and is close to FIP (wins in RMSE, loses in R^2). This is what I expected, as I explained earlier K% and BB% are always better at predicting future K% and BB% and they are included in SIERA and xFIP. SIERA and xFIP take more concrete events (K, BB, GB) than TIPS. I didn’t want to beat these estimators, but instead wanted a estimator that is independent of everything except for pitcher-batter reaction.

TIPS won when there was no IP limit, so it obviously is the best to use in smaller sample sizes, but when is it better than xFIP and SIERA, and where does it start falling behind? I plotted the RMSE for my entire sample at each IP. Theoretically these should be an inverse relationship. After 150 IP it gets a bit iffy, as most of my sample is less than 100 IP. I’m more interested in IP under 100 anyhow.

Orange is TIPS, Blue is ERA, Red is FIP, Green is xFIP, and Purple is SIERA. If you can’t see xFIP, it’s because it is directly underneath SIERA (they are almost identical). This is roughly what the graph should look like to 100 IP:

Looking at the graph, at what IPs is TIPS better than predicting future ERA than xFIP and SIERA? It appears to be from 0 IP to around 70 IP.

Here is the graph for 1/RMSE (higher R^2). Higher number is better. This is the most accurate graph as the relationship should be inverse.

The 70-80 IP mark is clear here as well.

I’m not suggesting my estimator is better than xFIP or SIERA, it isn’t in samples over 75 IP, but I think it is, and can be, a very powerful tool. Most bullpen pitchers stay under 75 IP in a season. This means that my unnamed estimator would be very useful for bullpen arms in predicting future ERA. I also believe and feel that my estimator is a very good indicator of the raw skill of a pitcher. It would probably be even more predictive if we had robo-umps that eliminated umpire bias and randomness and pitch framing.

2013 TIPS Leaders with 100+IP

And Leaders from 40IP to 100IP

Every year, at the conclusion of the Major League Baseball season, the MLB hands out awards to many of the games premier players. Every year, these awards are panned by critics and fans alike, usually wondering why their favorite players weren’t chosen.

Perhaps the most condemned award, especially by those of us who are more analytically inclined, is the Gold Glove Award.

After years of Derek Jeter winning Gold Gloves at shortstop, with some Rafael Palmeiros and Michael Youngs peppered in, the Gold Glove Awards pretty much became a joke among the MLB community.

The MLB seemed to catch on to that fact this season and implemented a “sabermetric component” in an attempt to help revitalize the legitimacy of the award.

This year’s Gold Glove finalists were recently announced and, to me, there appears to be progress being made. The inclusion of someone like Juan Uribe shows that the MLB is paying attention to the numbers, as Uribe is not someone who would typically pass the “eye test” that people have long based their defensive judgments on, but in reality was a pretty great defender and has been for the entirety of his 13-year career, especially at third base where he played 900 innings for the Dodgers this season.

However, this is not to say there weren’t still some odd picks in the list of finalists. The managers vote still constitutes a large portion of the selection process and these managers are still using the same “eye test” method, probably mixed in with some offensive contribution, that has controlled the fate of the award since its inception

To me, the eye test is a total cop-out, as no fan, let alone manager, can possibly watch every fielding attempt by every fielder throughout the course of a season through completely unbiased lenses as the advanced defensive metrics do. I will admit that the defensive metrics we currently have are far from perfect. But they at least account for every play on the same fair and unbiased scale for each player.

With that being said, here are what the finalists and winners of the Gold Glove Awards at each position might look like if voting were based strictly off advanced defensive metrics, free of human bias. So as not to overly complicate things, I used four defensive metrics to evaluate players. First, UZR and DRS made up the majority of the basis for my selections as they are the two most accepted and accurate defensive metrics. Though a little outdated, I still like to use RZR as sort of a tiebreaker for when UZR and DRS are too close to call. Then, just because, I included fielding percentage too. Though errors aren’t a good way to measure a defender’s ability or value, it’s safe to say that if a guy never makes an error of the course of a season he was probably pretty good, and if he made a ton of errors he probably struggled.

For catchers, the FanGraphs defense stat was used as a substitute for UZR, and rSB and RPP were used as substitutes for RZR and FP%. Pitchers aren’t included in the study.

Behold:

American League
Catcher – Salvador Perez

The MLB included Perez and Wieters, but also had a weird pick in Joe Mauer. Mauer won the Gold Glove at catcher from 2008-2010, despite never being great behind the dish. These likely came as a result of his offensive achievements. Perez gets the nod here for being the best all-around catcher. Wieters, despite being hated by DRS this year for some reason, was still the league’s best pitch-blocker and has a sound reputation for being a good defensive catcher and pitch-framer. Yan Gomes was the snub at his position, having the most valuable arm behind the plate in the American League.

First base – Mike Napoli

This was the weirdest one, on both ends of the spectrum. First, the MLB included Chris Davis – who is average at best in the field – and Eric Hosmer, who one might think would be good based on his athleticism but is actually quite terrible. Then, Mike Napoli came out on top on in the numbers. Napoli, a 31-year old lifetime catcher, played his first full season at first base this year. He also was diagnosed with a degenerative hip condition at the beginning of the year that voided his original contract with the Red Sox, and in reality he would have DH’d for almost any team in the AL that didn’t have David Ortiz. He basically had no reason to be good in the field. Yet, no matter what metrics you look at, Mike Napoli was the best defensive first basemen in the American League, and it really wasn’t close.

Second base – Dustin Pedroia

Pedroia – who already has two Gold Gloves under his belt – and Zobrist were head and shoulders above the rest of American League second basemen this year. Robinson Cano had a great year defensively in 2012 and rightfully won the Gold Glove. This season, it seems he was included by the MLB more for his reputation and offense, as he didn’t grade out much better than average by any defensive metric. Kinsler wasn’t loved by UZR, but he still had the second best DRS and RZR of any qualified second basemen, which is why he edged out Brian Dozier and Cano for my third finalist.

Third base – Manny Machado

This one was easy. It’s no secret that Manny Machado is incredible defensively, as his conversion from already Gold Glove-caliber shortstop to third base went even better than expected. Longoria and Donaldson were second and third, respectively, in each of the remaining categories, making them easy choices. Notably absent is Adrian Beltre, who has been an elite defensive third basemen his whole career and has won four of the last six Gold Gloves. However, at 34 years old, his age may be starting to wear on him as he posted his first negative defensive season since 2007.

Shortstop – Alcides Escobar

After the AL third base being the easiest choice, the AL shortstops were the hardest. The two Escobars had almost identical stats, and Yunel has been a better defender over his career, but Alcides had a miniscule edge in UZR and RZR. Florimon was also a sneaky choice to rival the two Escobars, as he led all qualified shortstops in both DRS and RZR. J.J. Hardy was a fine choice by the MLB, as he has been one of the premier defenders at shortstop for nearly a decade, but the defensive talent pool at shortstop is deep, as always, and Hardy just missed the cut this year.

Left field – Alex Gordon

Gordon has won the American League left field Gold Glove the last two seasons, and will likely win his third consecutive this season. He had the best ARM rating of any qualified outfielder in the American League with above-average range to go with it. The MLB’s selection of Andy Dirks was panned by some analysts, but I find it to be justified as he had the highest RZR of any left fielder with 500+ innings and was second in UZR.

Center field – Lorenzo Cain

Noticing a trend? This is now the third Kansas City Royal deserving of a Gold Glove and we still have one position to go. A hugely important, mostly unnoticed reason for the Royals success this year was that they were baseball’s best defensive team and it wasn’t even close. Their 79.9 team UZR dwarfed the second-place Diamondbacks (51.1) and third-place Orioles (39.9). Cain was one of the main contributors, playing elite defense at arguably the sport’s most difficult position. Ellsbury and Rasmus had great years as well – and were on the field more – but Cain was the best during his time in center, earning him the nod.

Right field – Shane Victorino

This offseason, the Red Sox took part in a current trend in the MLB by throwing away the idea of “corner outfielders” and simply trying to put the best possible athletes – usually natural center fielders – in the three outfield spots. Just a few examples being the Indians with Drew Stubbs (and Michael Brantley to an extent), the Pirates are with Starling Marte and now the Red Sox by signing Victorino to play right field. As you can see, it paid off, as Victorino had easily the best defensive season of any American League outfielder. Also, notice who snuck in at the third spot? David Lough, who racked up a full win’s worth of defensive value in just 577 innings for the, you guessed it, Kansas City Royals.

National League
Catcher – Russell Martin

I know, blasphemy, right? Yadier Molina has won five consecutive Gold Gloves and will probably make it six this year. He is incredible and one of the greatest defensive catchers of all-time. However, Russell Martin is pretty incredible himself and goes greatly unappreciated for his abilities behind the plate. He has a great catcher arm, in fact the most valuable in the MLB this season, and was the third-best pitch blocker in the MLB. While trying to concoct a way to cheat and give this award to Molina, I considered talking about pitch framing, the impact it has on a pitching staff and how that goes undetected in catcher’s defensive stats while Molina might be the best at it. But then I remembered that Martin is a pretty great pitch-framer, too which contributed a great deal to the success of Pirates pitching this year. Molina is a great catcher, but Martin was better this year and it would be pretty cool if he is rewarded for it.

First base – Anthony Rizzo

This was only one of two positions with the same three finalists as the three finalists chosen by the MLB. Good job MLB! Yonder Alonso and Brandon Belt are both pretty good with the glove for first basemen, but these three were clearly the best. Something tells me Gonzalez and his three Gold Gloves will end up winning another based on his reputation, but Rizzo was better across the board. Paul Goldschmidt also has a pretty nice showing, proving that he can do just about everything well and is already one of the league’s best players.

Second base – Darwin Barney

You can probably figure that Darwin Barney is a pretty great defender because otherwise why would he play every day for a Major League team. Part of that is probably because it’s the Cubs, but it’s mostly because Darwin Barney is a defensive wizard. You could probably say the same thing about DJ LeMahieu, too, though it doesn’t fully explain why Walt Weiss insisted on batting him second. There’s really not much else I can think to write about this one, besides maybe that the Cubs are kind of like the National League Royals in that we’ve had three positions and already three Cubs, except different in that it didn’t help lead them to any kind of success.

Third base – Juan Uribe

As I mentioned in the intro to this piece, Juan Uribe even being selected as a Gold Glove finalist shows a step in the right direction for the MLB and an even bigger one if he ends up winning it. By looking at him, you might not assess him as an elite defender on account of his, let’s say “shapely,” frame. However, he had a remarkable year at third base for the Dodgers, adding somewhere in the vicinity of two wins with his defense alone. This should not shock anyone, as he has a career UZR/150 of 19.7 at third base in a sample size of nearly 3,000 innings. In addition, he held his own at shortstop for nine years, logging close to 8,000 innings of above-average defense. Not to be lost in all of this is that Nolan Arendo appears to be exceptional at third base too, with a ridiculous 30 DRS in his rookie season that rivals Manny Machado. Also, hey, look. Another Cub!

Shortstop – Andrelton Simmons

It has been written on this site many times how ridiculous Andrelton Simmons is. He just had maybe the best defensive season ever. Basically, right now, he is to defense what Miguel Cabrera is to offense. He is going to win his first Gold Glove this year, which is a thing that, barring injury, will happen for many, many years to come. He has the potential to build a Hall of Fame career pretty much entirely with his glove, in the vein of guys like Ozzie Smith or Omar Vizquel. The Atlanta Braves are very lucky to have him, and you should watch him play shortstop with any chance you get. /gush

Left field – Starling Marte

As I wrote earlier, by playing Starling Marte in left field the Pirates are also taking part in the current trend of disregarding the preconceived notion of corner outfielders and just putting center fielders in the corners. Having two centerfielders in your outfield is very valuable defensively, and Marte is also an above-average hitter, making his role on the Pirates team a very valuable one. The MLB picked Eric Young Jr. over Carl Crawford, which isn’t a terrible selection as Young had the second highest RZR of any left fielder with 400+ innings and also edged Crawford out in DRS, 2-1. However, those two slight edges over Crawford didn’t make up for Crawford’s 8.6 – 3.9 edge in UZR.

Center field – Carlos Gomez

In addition to Carlos Gomez’s breakout year with the bat, he had an insane year with the glove in center field – one of the main reasons why, along with being one of the game’s elite baserunners, I picked him as my National League runner-up MVP on my Internet Baseball Awards ballot over on Baseball Propsectus. But I’d also really like to talk about that second name there. Some of you may have read Juan Lagares’ name and said, “Who?” My answer to “Who?” would be: “One of my favorite players in baseball after reading Jeff Sullivan’s piece on Lagares and his arm.” Uncovered in that piece, besides who is Juan Lagares, is that Lagares’ arm in center field this season was arguably the most effective arm since we began accumulating advanced fielding data in 2002. Dude has a great arm, but is even better at positioning and taking optimal routes to outfield ground balls by using his experience as an infielder. Lagares shows pretty great range in center, too, and the way he adds value with his arm makes him one of my biggest snubs in the MLB’s selections.

Right field – Gerardo Parra

Here’s the other position with the same three finalists as the three chosen by the MLB. Good job again MLB! Jason Heyward might have come out on top if he played a full season, but since he didn’t the award is probably Gerardo Parra’s to win. Parra has always been a phenomenal outfielder, but also has always been a part-time player due to his nasty platoon splits at the plate. This year, injuries forced him into the lineup on a nearly everyday basis and he was rewarded with recognition for his abilities in the field.

For a few years, it’s struck me as unusual that pitching and hitting metrics are asymmetric.  If the metrics we use to evaluate one group (FIP or wRC+) are so good, why don’t we use them for the other?

One issue is that we’re not used to evaluating pitchers on an OPS-type basis, and similarly we’re not used to evaluating hitters on an ERA basis.  Fine.  But there’s a bigger issue: Why do pitching metrics put so much more emphasis on the removal of luck?

While most sabermetricians are aware of BABIP, and recognize the pervasive impacts it can have on a batting line, attempts to (precisely) adjust hitter stats for BABIP are surprisingly uncommon.  While there do exist a few xBABIP calculators, these haven’t yet caught on en masse like FIP.  And xBABIP doesn’t appear on player pages in either FanGraphs or Baseball Prospectus.

xBABIP itself isn’t even the end goal.  What you probably really want is xAVG/xOBP/xSLG, etc.  Obtaining these is a bit cumbersome when you need to do the conversions yourself.

Moreover, it strikes me that xBABIP cannot be converted to xSLG without some ad hoc assumptions.  Let’s say you conclude a player would have gained or lost 4 hits under neutral BABIP luck.  What type of hits are those?  All singles?  2 singles and 2 doubles?  1 single, 2 doubles, 1 triple?  The exact composition of hits gained/lost affects SLG.  Or maybe you assume ISO is unaffected by BABIP, but this too is ad hoc.

At least to me, whenever a hitter performs better/worse than expected, we really care to know two things:

1. Is it driven by BABIP?
2. If so, what is the luck-neutral level of performance?

As I’ve attempted to illustrate, answering #2 is not so easy under existing methods.  (Nor do people always even attempt to answer it, really.)  Even answering #1 correctly takes a little bit of effort.  (“True talent” BABIP changes with hitting style, so it isn’t always enough just to compare current vs. career BABIP.  And then there are players with insufficient track record for career BABIP to be taken at face value.)

Compare this to pitchers.  When a pitcher posts a surprisingly good/bad ERA, we readily consult FIP/xFIP/SIERA.  Specific values, readily provided on the site.  So why not for hitters?

Here I attempt to help fill this gap.  The approach is to map a hitter’s peripheral performance to an entire distribution of hit outcomes.  These “expected” values of singles, doubles, triples, home runs, and outs, can then be used to computed “expected” versions of AVG, OBP, SLG, OPS, wOBA, etc.

Recovering xAVG and xOBP isn’t that different from current xBABIP-based approaches.  The main extension is that, unlike xBABIP, this provides an empirical basis to recover xSLG, and also xWOBA.

Steps:

1. Calculate players’ rates of singles, doubles, triples, home runs, and outs among balls in play.  (Unlike some other BABIP settings, I count home runs as “balls in play” to estimate an expected number.)
2. Regress each rate separately on a common set of peripherals.  You’ll now have predicted rates of each for each player.   (Keeping the explanatory variables common throughout ensures the rates sum to 100%.)
3. Multiply by the number of balls in play (again counting home runs) to get expected counts of singles, doubles, triples, home runs, and outs.
4. Use these to compute expected versions of your preferred statistics.

What explanatory peripherals are appropriate?  Initially I’ve used:

• Line drive rate, ground ball rate, flyball rate, popup rate
• Speed score
• Flyball distance (from BaseballHeatMaps.com), to approximate power
• Speed * ground ball rate
• Flyball distance * flyball rate

These explanatory variables differ somewhat from those in the xBABIP formula linked earlier.  The main distinctions are adding flyball distance (think Miguel Cabrera vs. Ben Revere) and using Speed score instead of IFH%.  (IFH% already embeds whether the ball went for a hit.  Certainly in-sample this will improve model fit, but it might not be good for out-of-sample use.)

Regression results:

Technical notes:

• These are rates among balls in play (including home runs)
• Each observation is a player-year (e.g. 2012 Mike Trout)
• I’ve used 2010-2012 data for these regressions
• Currently I’ve only grabbed flyball distance for players on the leaderboard at BaseballHeatMaps.  This is usually about 300 players per year, or most of the “everyday regulars.”  (Fear not, Ben Revere/Juan Pierre/etc. are included.)  The remaining cases get an indicator for ‘FB Dist missing.’
• LD%, GB%, FB%, and IFFB% are coded so that 50% = 50, not 0.50.
• Pitcher proxy = 1 if LD% + GB% + FB% = 0.  Initially I haven’t thrown out cases of pitcher hitting, nor other instances of limited PA.
• Notice the interaction terms.  The full impact of GB% depends both on GB% and Speed; the full impact of FB% depends on both FB% and FB distance; etc.  So don’t just look at Speed, GB%, FB%, or FB Distance in isolation.
• Don’t worry that the coefficients on pitcher proxy “look” a bit funny for HR rate and Outs rate.  (Remember that these cases also have LD%=0, GB%=0, and FB%=0.)  In total the average predicted HR rate for pitchers is 0.01% and their predicted outs rate is 94%.
• Strictly speaking, these are backwards-looking estimators (as are FIP and its variants), but they might well prove useful in forecasting.

I next calculate xAVG, xOBP, xSLG, xOPS, and xWOBA.  For now, I’ve simply taken BB and K rates as given.  (xBABIP-based approaches seem to do the same, often.)

Early results are promising, as “expected” versions of AVG, OBP, SLG, OPS, and wOBA all outperform their unadjusted versions in predicting next-year performance.  (At least for the years currently covered.)

Which players deviated most from their xWOBA?  Here are the leaders/laggards for 2012, along with their 2013 performance:

Is performance perfect?  Obviously not.  The model does quite well for some, medium-well for others, and not-so-well for some.  Obviously this is not the end-all solution for xHitting.

Some future work that I have in mind:

• A still more complete set of hitting peripherals.  I’m thinking of park factors, batted ball direction, and possibly others.
• Testing partial-season performance
• Comparing results against projection systems like ZiPS and Steamer

Otherwise, my main hope from this piece is to stimulate greater discussion of evaluating hitters on a luck-neutral basis.  Simply identifying certain players’ stats as being driven by BABIP is not enough; we really should give precise estimates of the underlying level of performance based on peripherals.  We do this for pitchers, after all, with good success.

Above I’ve contributed my two cents for a concrete method to do this.  A major extension to xBABIP-based approaches is that this offers an empirical basis to recover xSLG and xWOBA.  While the model is far from perfect, even in its current form it generates “expected” versions of AVG, OBP, SLG, OPS, and wOBA that outperform their unadjusted versions in predicting subsequent-year performance.  (Not just for leaders/laggards.)

Comments and suggestions are obviously welcome!

(Note: “Patience” here is really shorthand for “ability to get on base,” whether that’s via hits or walks. But it’s pithier and generally gets the point across as to what I’m trying to look at.)

In one of the Thursday chats on FanGraphs with Eno Sarris, I posed the following question, which he posted and the chatters answered collaboratively: Name the three players (minimum 3000 plate appearances) in the expansion era (since 1961) with a career on-base percentage above .400 and an isolated power number below .200. (Answers at the end of this post.)

In the entirety of baseball history, 36 players with 3000 plate appearances have achieved such numbers, and 24 since the beginning of the 20th century, but there are only three such players in the past 50 years. This is not particularly surprising; you won’t see many career lines such as Ty Cobb’s .366/.433/.512 anymore, or even Paul Waner’s .333/.404/.473.

But just how has the relationship between hitting for power and getting on base changed through the years?

Since we started at the individual level, let’s continue there. Let’s start with the last 20 years, from 1994-2013. Excluding pitchers, the league-wide on-base percentage was .338 and the league-wide ISO was .159. Over that time period, 761 players have had 1500+ plate appearances. How they break down on OBP and ISO lines:

Now, 1901-1920, during which time only 377 players had 1500+ plate appearances and the league averages were a .326 OBP and .082 ISO:

In either era, a substantial majority of players had either both an above average OBP and ISO, or both were below average. However, that majority is 59% in the last 20 years and was 68% in the deadball era. So one conclusion we can draw is that fewer players now sacrifice power to reach base or vice versa than they did in the olden days. (Whether they did so consciously or not.)

However, this breaks down if we go to extremes.*

From 1994-2013, 13 players had an OBP 10% above average and ISO 10% below average, while there were 15 players with an ISO 10% above average and OBP 10% below average. Overall, 3.7% of all players with 1500 PA are here.

From 1901-1920, 8 players had an OBP 10% above average and ISO 10% below average and 5 players had an ISO 10% above average and OBP 10% below average. Overall, 3.4% of the players with 1500 PA.

Players who get on base without power or hit for power without getting on base are basically as common now as they were in the dead ball era. But it’s also less common now for a player to sacrifice one or the other to any degree.

What about this power-patience relationship league-wide?

First, below are some league-wide stats over various time frames (excluding pitchers):

Time Frame	OBP	ISO	BB%	HR%
1901-present	.333	.130	8.7%	2.0%
1901-1920	.326	.082	7.6%	0.4%
1994-present	.338	.159	8.8%	2.8%
1901-1960	.341	.111	8.5%	1.2%
1961-present	.332	.142	8.8%	2.4%

The comparison between 1901-1920 and 1994-2013 really isn’t surprising. Most fans know that the dead ball era was not a time to hit for power, while the most recent times have generally been more offense-happy, especially the late 90s/early 00s.

In that chart we also see all of post-1900 baseball divided into two eras, divided along the Baseball Reference-identified beginning of the expansion era. OBP was actually higher before the Sixties while power was lower.

For now, I want to conclude with the year-by-year ratio of extra bases (2B+2*3B+3*HR) to bases reached (H+BB+HBP), graphically. I realize this might have some flaws similar to those of OPS, but a simple ISO/OBP ratio be even worse in that regard. I wanted to strip out total plate appearances or at-bats, and just look at the average number of extra bases that were earned each time a player reached base, which the selected method essentially does. The difference between ISO/OBP and the ratio selected is, on average, about 4%. At any rate this should do for a quick comparison:

A lot of famous seasons like 1930, 1968, and 1987 are identifiable on the chart. (The lowest ratio of the expansion era actually occurred in 1976, not 1968, however.) Also, it wouldn’t greatly surprise me if Babe Ruth is single-handedly responsible for the sharp increase from 1918 to 1921. (He got on base a lot, of course, but his power was the thing.) Most importantly, however, it’s clear that over time the ability of Major League player to hit for power has gone up relative to their ability to get on base. This too is not surprising to those familiar with baseball history.

And so all of this really only gives us a limited idea of the relationship between reaching base and hitting for power over time. Over the next few weeks, we’ll go further into things, both on the individual level and league level. Working backwards, next week will focus on the data underlying the above line chart.

Answers to the initial question:

Joe Mauer (.405 OBP, .145 ISO)
Rickey Henderson (.401 OBP, .140 ISO)
Wade Boggs (.415 OBP, .115 ISO)

*It’s not a Rickroll, it’s a Joelroll, which is even better because it rhymes.

Adam Wainwright has a great curveball. It’s probably the best curveball in baseball. Look at the curveball leaderboard, and you’ll find that he’s on top by a wide margin. Of course, if you’ve seen Wainwright, even in GIF form, you don’t need those numbers to tell you that. You know it’s a nasty pitch.

But, the curveball has always been a great pitch for Wainwright. While Wainwright has posted a career-best 2.55 FIP and 2.80 xFIP in 2013, his curveball has a slightly lower swinging strike rate than it did in 2012. Also, the curve hasn’t produced as many groundballs. Wainwright was solid, but not spectacular in 2013.

So, how has Wainwright been so much more successful in 2013 than in 2012?

Perhaps the biggest factor is that Wainwright has utilized his four-seam fastball much more frequently in 2013, throwing it on over 20 percent of his pitches. Before 2012, Wainwright didn’t feature a four-seam fastball. Even in 2012, he threw the pitch very sparingly.

The four-seamer has been a very effective pitch for Wainwright in 2013. He’s throwing the pitch for a strike 71% of the time, a higher rate than the two-seamer or sinker, whose usage has been curtailed. This helped Wainwright get ahead, and according to StatCorner he threw more pitches ahead in the count than ever before. As a consequence, Wainwright had a career-best 3.7% walk rate in 2013. Entering 2013, his walk rate sat at 6.7%.

Furthermore, the four-seamer produced swings and misses. The pitch had a 7.6% whiff rate. The sinker’s best rate was 4.2%. By run value, Wainwright’s four-seamer was the 8th best in baseball in 2013. I know, pitches exist in the context of repertoires, but consider that Wainwright’s two-seamer had a run value on par with the two-seamer of Jeremy Bonderman. That should tell you that it wasn’t his most effective pitch.

Even with the increased usage of the four-seam fastball, Wainwright has not sacrificed his groundball rate. At 49.1%, it is nearly equal to his career rate of 49.4%.

He’s throwing the pitch harder than ever. Maybe it took Wainwright more than a year to fully recover from the Tommy John injury he suffered before the 2011 season. When he threw the four-seamer in 2012, it averaged less than 90 miles per hour.

During the playoffs, the four-seamer has averaged nearly 94 miles per hour. Maybe the guns are juiced up, or maybe adrenaline is kicking in, but the pitch is up almost two miles from the regular season. Whatever the case, Wainwright is relying on his four-seamer even more during the playoffs. He’s thrown 23 innings, and surrendered only four runs, with 20 strikeouts and just a lone walk.

At age 32, and after throwing more than 240 innings during the regular season, Wainwright is looking stronger than ever. The addition of his four-seam fastball is proof that you can teach an old dog new tricks. Kudos to Cardinals pitching coach Derek Lilliquist and Wainwright for making the adjustment.