It’s been quite a week for the WAR stat. Since Jeff Passan dropped his highly controversial piece on the metric on Sunday night, the interwebs have been abuzz with arguments both for and against the all-encompassing value stat. One criticism in particular that caught my eye came from Mike Newman, who writes for ROTOscouting. Newman’s qualm had to do with a piece of WAR that’s often taken for granted: the positional adjustment. He made the argument that current WAR models underrate players who play premium defensive positions, pointing out that it would “laughable” for Jason Heyward to replace Andrelton Simmons at shortstop, but not at all hard to envision Simmons being an excellent right fielder.

This got me thinking about positional adjustments. Newman’s certainly right to question them, as they’re a pretty big piece of the WAR stat, and one most of us seem to take for granted. Plus, as far as I’m aware, none of the major baseball websites regularly update the amount they credit (or debit) a player for playing a certain position. They just keep the values constant over time. I’m sure that whoever created these adjustments took steps to ensure they accurately represented the value of a player’s position, but maybe they’ve since gone stale. It’s certainly not hard to imagine that the landscape of talent distribution by position may have changed over time. For example, perhaps the “true” replacement level for shortstops is much different than it was a decade or so ago when Alex Rodriguez Derek Jeter, Nomar Garciaparra, and Miguel Tejada were all in their primes.

I decided to try and figure out if something like this might be happening. If the current positional adjustments were in fact inaccurately misrepresenting replacement level at certain positions, we’d expect the number of players above replacement level to vary by position. For example, there might be something like 50 above-replacement third basemen, but only 35 shortstops. Luckily, the FanGraphs leaderboard gives you the ability to query player stats by position played, which proved especially useful for what I was trying to do. For each position, I counted the number of plate appearances accumulated by players with a positive WAR and then divided that number by the total plate appearances logged at that position. Here are the results broken out by position for all games since 2002.

Based on this data, it seems like the opposite of Newman’s hypothesis may be true. A significantly higher portion positive WAR plate appearances have come from players at the tougher end of the defensive spectrum, which implies that teams don’t have too difficult of a time finding shortstops and center fielders who are capable of logging WARs above zero. Less than 13% of all SS and CF plate appearances have gone to sub-replacement players. But finding a replacement-level designated hitter seems to be slightly more difficult, as teams have filled their DH with sub-replacement-level players nearly 30% of the time. Either teams are really bad at finding DH types (or at putting them in the lineup), or the positional adjustments aren’t quite right. The disparities are even more pronounced when you look at what’s taken place from 2002 to 2014.

The share of PAs logged by shortstops and center fielders hasn’t changed much over the years, but the numbers have plummeted for first basemen, corner outfielders, and DH’s. From Billy Butler and Eric Hosmer, to Jay Bruce and Domonic Brown, this year’s lineups have been riddled with sub-replacement hitters manning positions at the lower end of the defensive spectrum. Meanwhile, even low-end shortstops and center fielders, like Derek Jeter and Austin Jackson, have managed to clear the replacement level hurdle this season if we only count games at their primary positions.

The waning share of above-replacement PA’s coming from 1B, LF, RF, and DH has caused the overall share to drop as well, with a particularly big drop coming this year. Here’s a look at the overall trend.

And here it is broken down by position…

And just between this year and last…

Frankly I’m not sure what to make of all of this. I’m hesitant to call it evidence that the positional adjustments are broken. There could be some obvious flaw to my methodology that I’m not considering, but I find it extremely interesting that there’s been such a shift between this year and last. We’re talking an 8 percentage point jump in the number of PAs that have gone to sub-replacement-level players. Maybe its been spurred the rise of the shift or maybe year-round interleague play has something to do with it, but it seems to me that something’s going on here. And I’m interested to hear other people’s thoughts on these trends.

If you’ve been on the internet in the last few weeks (or within earshot of a Michigander) you may have heard about the Tigers. Specifically, you may have heard about how the odds in favor of a Detroit appearance in the 2014 ALDS dropped from 21-to-1 on July 25 to under break-even by August 23 before a slight rebound to finish out the month. Even more specifically, you may have read Mike Petriello’s article about that on this very website. Or at the very least, you may have heard their struggles described in a less quantitative fashion. Regardless, the month of August was not kind to the Bengals.

As Petriello pointed out, this has been less of a Tigers collapse than a Royals surge. But there’s still something to the idea that the Tigers were playing worse in August than they had been previously. Let’s start with the basics:

In August, the Tigers scored fewer runs, allowed more runs, and won fewer games than in the first half. On some level, that’s all that really matters. On another level, something else is different about August for these Tigers.

Back on July 14, Buster Olney and Jeff Sullivan both wrote articles about schedule strength. Olney called the Tigers’ schedule the second-most difficult of 17 “contending” teams (paywall), while Sullivan said it was the easiest in all of MLB. One of the key reasons for the discrepancy was that Sullivan was using projections to determine the difficulty of a particular opponent, while Olney was using actual results. Score one for Sullivan. Another key difference was that as of July 14, the Tigers were about to play 55 games in 56 days, which did not factor into Sullivan’s analysis.

A point for Olney? Perhaps. But first, what would we expect to see if this was a result of schedule fatigue? Or put another way, which groups of players might be hurt most or least by not having a day off? Based on conventional wisdom, the bullpen would probably be the most affected, and the starters the least. So how does this match up to the Tigers? Read the rest of this entry »

Last week I explored the strategic effect of seeing more pitchers per plate appearance. I love the ten-pitch walk as much as the next guy, but what I love even more is seeing a guy be able to change that approach to beat a scouting report. Let’s take a look at June 5, 2014, when the A’s went to see Masahiro Tanaka for the first time. The first batter is Coco Crisp:

So Crisp doesn’t get the best of Tanaka, but he makes Tanaka labor a bit through six pitches. If you’re going to make an out to start the game, it might as well be a long one. For the next batter, John Jaso, Tanaka decides to go right after him:

I may be looking too deeply into the narrative here, but I love to imagine Tanaka getting a bit frustrated here. Perhaps the scouting report said that both Coco is aggressive early, while Jaso’s running 15% walk rates in 2012 and 2013 suggest that he’s more patient.  Tanaka has to throw six pitches in order to get Crisp out, but after deciding to go right after Jaso, he gets taken deep.

So I wondered if there are players who are able to fulfill both ends of this spectrum. Are there any players that are capable of prolonging their time at the plate until they see the pitch they want, but are also aggressive and willing enough to hit the gas on the first pitch? I used FanGraphs for the pitches/plate appearance data, but used baseball-reference’s play index to look up all instances of first-pitch hits this season. Originally I was going to use first-pitch swings, but I decided to just stick to times when the pitcher gets punished for trying to get ahead early. After all, if your decision is to get ahead early in the count, and the guy swings but all he does is foul it off or hit into an out, then that doesn’t change your approach as a pitcher. I wanted to see guys whom the book isn’t written on yet.  Advance Warning: These stats will be about a week old by the time you see them, as I am a slow, slow man.

(For Reference: FPH% = First Pitch Hit Percentage, or how often a batter gets a hit on the first pitch they see.  P/PA = Pitches per Plate Appearance. FPHR = First Pitch Hit Ranking, or how they rank in this category compared to the rest of the league.  PPAR = Pitches per Plate Appearance Ranking.  FPHR + PPAR = The addition of these two numbers.)

I like this table!  I have wondered at times what has caused Scott Van Slyke‘s resurgence this year. Perhaps this table gives us a bit of a clue.  Van Slyke is the only person in the MLB to rank in the top 50 in both FPHR and PPAR.  That’s pretty neat.  Daniel Murphy is also quite balanced, but he’s been much more consistent over the last few years.  He’s particularly interesting in that he doesn’t have a particularly high walk rate or strikeout rate.  I guess he’s just selective at times.  Jesus Guzman’s presence on this list goes to show that a good approach doesn’t necessarily mean success; it just means that he may not head back to the bench in any predictable fashion.  I stretched out the table one spot to include Mark Reynolds, because his name on this table makes me feel better about drafting him in Fantasy Baseball for past five years.

I also wanted to look at the flip-side.  Who are the guys who don’t tend to take a lot of pitches, but also don’t tend to make any decent contact on first pitches?

Here we have a much less impressive list.  Joaquin Arias has been one of the worst hitter in the majors this year, and his dominance atop this leaderboard makes a bit of sense.  However, Conor Gillaspie is having an excellent season for the Pale Hose, despite the fact that he doesn’t seem to excel in either of the areas this article is interested in.  One pecuilar note is that this group is pretty poor at hitting for power in general; these 5 guys have 13 home runs between them on the year, and six of those are Gillaspie’s.

So now let’s look at the weird ones.  I would think that it stands that if there are certain players who tend to take a lot of pitches and who also never seem to square up the first pitch, then we know our game plan.  Get ahead early on these batters.  We can try to view that by simply looking at each players FPH Ranking minus their PPA ranking.  This is the same at looking at the absolute value of their PPAR minus their FPAR.  Here are the top five in that respect:

Golly; I’ve figured out Mike Trout!  Mike Trout ranks very highly on our list of PPAR but is unfortunately relatively average when it comes to the first-pitch punish.  All of these guys actually fit this mold.  We have three relatively poor hitters accompanied by the best player in baseball and an above average infielder on a winning team.  So we can tell that being patient isn’t necessarily a good or bad thing; it’s just that hitter’s style.  Now let’s take a look at the reverse:

It’s always satisfying when the data shows what you expect it to.  I imagined Jose Altuve as being among the more aggressive hitters, and this shows that at least.  Altuve ranks 5th in the league in FPH% and is rather mediocre in the PPA category.  Interesting to see that this top five is also sorted by wOBA; Altuve is the best hitter on the list, and Pierzynski is the worst.  So there’s nothing necessarily wrong with an aggressive approach, but it does give us a clue as to a possible plan of attack.

So all this is to say, like my last article, that no particular approach is best.  One can look to swing at the first pitch, or one can be patient and wait for their pitch to come.  That said, everybody does have an approach, and that means they’ve got something they’re not looking for.  Stats like FPH and PPAR may just give us more clues as fans as to what teams put together with scouting reports.

So to conclude by going back to our first example, perhaps Tanaka should have read this data before his start against the A’s.  Coco ranks 266th in the league in FPHR, but a respectable 76th in PPAR.  Conversely, Jaso ranks 80th in the league in FPHR, but just 225th in PPAR.  Tanaka might have been better served by going after the aging Crisp and saving his energy for the somewhat aggressive Jaso.

Baseball, more than any other major team sport, has the reputation for having the least athletic athletes. Jose Molina is obligated to, at times, sprint. Jorge de la Rosa must swing a baseball bat. David Ortiz sometimes has to play in the field. Having skills like catcher defense, pitching, and hitting with power will earn you playing time, and many players have such elite strengths that it’s worth it just to deal with those weaknesses. So many of baseball’s skills are unrelated that players have to spend a lot of time doing things they aren’t good at, at least relative to other MLB talent. A good way to make anyone look unathletic is to make them perform a long list of skills that have little to do with one another and compare them to the best in the world at those tasks.

I wanted to assemble a list of players who experienced something like this phenomenon the most frequently. Essentially, I wanted to see what players’ strengths and weaknesses were the farthest apart. To determine those players whose skills varied the most between themselves, I gathered what I consider to be the six stats that best describe what a player’s strengths and weaknesses are. BABIP and K% for contact, BB% for discipline, ISO for power, and Fielding and Baserunning values. I then gathered stats from 2011-2014 to better control for less reliable fielding metrics, assigned each player’s stats a percentile rank, and calculated the standard deviation of those six stats for each player.

For instance, Mike Trout’s attributes look like this:

His strikeout rate has been higher than MLB average, but he is otherwise an exceptionally well rounded player, as we know.

The most evenly talented player in baseball has been Kyle Seager, who is almost in the middle third at every stat.

Many players have much more severe strengths and weaknesses. Here are the 10 players whose stats show the greatest variation from one another.

10. Dexter Fowler

9. Ichiro Suzuki

8. Jose Altuve

7. Curtis Granderson

6. Mark Reynolds

5. Giancarlo Stanton

4. Miguel Cabrera

3. Darwin Barney

2. Adam Dunn

1. Ben Revere

The whole list is fun to look through and play around with, so feel free to click here and look through all the qualifying players.

It’s the bottom of the fourth. No outs. Your beloved Milwaukee Brewers are up to bat trailing the Dodgers 1-0, with Clayton Kershaw on the mound. They’ve picked up two scattered hits and drawn a walk over four innings, but the sentiment in the dugout and the stands seems to read if they haven’t scored yet, chances don’t look so good.

Consider the same situation, now, with one small change. Your Brewers are still down by a run. It’s still the bottom of the fourth. Kershaw is still dealing. But it’s 2-1 Los Angeles this time. Milwaukee has still only gotten two hits and drawn a single walk, but the timing has worked out such that a run scored. By the numbers, things are almost exactly the same. No question about it. The sentiment, though, is certainly different. We’ve broken through once already, think the players, manager, and fans. We can do it again. Well, of course the Brewers can do it again. But, statistically speaking, will they? That is: when trailing by one run as they enter a half-inning, is a team more likely to come back in a non-shutout than in a game in which they haven’t yet scored?

The answer is “yes,” although only by what initially appears to be a small margin. In 2013, 5705 half-innings began with the batting team trailing by a run. 11.4% (651) of those half-innings ended with the batting team tied or in the lead. The same year, 2915 half-innings began with the batting team trailing specifically by the score of 1 to 0. 11.1% (324) of those ended in a lead change or tie.

At first glance, a 0.3% difference between odds of scoring when down by a run versus the specific case of being down 1-0 seems minor. And it is, really. For years with complete-season data available since 1871, the percent of half-innings started where it’s a one-run game and the losing team up to bat which resulted in a lead change or tie (let’s call this %ORLC) averages out to 11.5% ± 1.3% (1 σ). The subset of these in which the batting team was being shutout (let’s call this %ORSLC) has an average of 10.6% ± 1.1% (1 σ). Middle-school statistics will tell you that while, yes, %ORSLC is on average nearly a percent lower than %ORLC, they fall within a standard deviation of each other and, thus, their difference is not statistically significant.

That’s true. But baseball isn’t middle-school statistics and two subsets whose error ranges overlap are not for all practical purposes equal. Quite remarkably, %ORLC has exceeded %ORSLC for each consecutive season of Major League Baseball since 1977 (when %ORSLC was 0.2% higher) and every year since 1871 except for five seasons (out of the 111 years of complete-season data that were available).

That is: in 106 out of the last 111 seasons for which box scores have been logged every game, a batting team behind in a one-run ballgame has successfully erased the deficit more often when not trailing 1-0. The margin isn’t huge, of course, but the trend is meaningful.

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Above: Percentage of one-run game situations and specific 1-0 game situations (%ORLC and %ORSLC, respectively) in which the team losing scores to tie or take the lead

After all, baseball is a game of small but meaningful margins. The 111-year average relative difference between these two metrics (10.6% vs 11.5%) is proportional to a .277 batting average versus .300, or 89 wins in a 162-game season instead of 97. The latter is perhaps a more relevant comparison, since it is gaining (and maintaining) a lead that is crucial to winning games.

Among teams in 2013, however, these differences aren’t so marginal. In %ORLC (percentage of half-innings in which a team trailing by a run ties it up or takes the lead) the Royals finished first at 16.7% and the Cubs finished last at 6.5%. In %ORSLC (same stat but for the score 1-0), the Rays finished first at 16.7% (same number, coincidentally) and the Red Sox finished last at 4.9%. Considering the Royals didn’t make the playoffs in 2013 and the Red Sox won the World Series, I wouldn’t use %ORLC and %ORSLC as indicators of a team’s ultimate success unless you’re looking to lose a lot of money in Vegas.

While one could theorize for hours on the meaning and utility of each made-up statistic, it sure doesn’t seem like %ORLC and %ORSLC are indicative of much on a team-by-team basis. But that doesn’t mean they’re useless. Let’s go back to the long-term trend of %ORLC and %ORSLC, where the former was higher than the latter 106 out of 111 times.

Some underlying process, it would seem, must be responsible for this impressive stat. If we are to believe that teams truly underperform, ever so slightly, when they’re losing 1-0 due only to the fact that they’re being shut out, shouldn’t we able to see the effect of psychology on performance somewhere else?

As it turns out, you don’t have to look far. Let’s consider the general situation of a team coming up to bat down by a run (not only the specifically 1-0 case), which is colloquially termed a “one-run game.” We’ll abbreviate any instance of this (a trailing team coming to bat in any half-inning) as OR. Now this situation could happen at any point in a game. A visiting team leads off with a run in the top of the 1st, the home team comes up to bat – that’s an OR. It’s all tied-up in the top of the 13th, the third baseman slugs a solo shot to left, three outs are recorded, the home team steps up the plate with one chance to stay alive – that’s an OR. So, in what inning on average does an OR occur?

In 2013, the answer was the 4.95th inning. In 2012 and also for the last 111 years of available records, the 4.91st inning. Baseball amazes us once again with its year-to-year consistency in obscure statistics. But this obscure stat isn’t all that meaningful on its own. Okay, so most one-run situations occur near the 5th inning – so what?

Well, let’s take a look now at the average inning in which a team scored in an OR to tie or take the lead. We’ll call this a one-run game situation where the lead changes, or ORLC. In 2013, of all the instances of ORLCs, the average time they occurred was the 5.18th inning. In 2012, the 5.10th inning. And for the same 111 seasons of recorded game data, the 5.20th inning. Once again, we see a marginal but nonetheless compelling deviation from the average, just as we saw with %ORSLC. Teams score in one-run situations about a third of an inning later than the one-run situations tend to occur themselves. That may not seem like a whole lot, but consider that in our 111-season dataset only two years – 1902 and 1912 – saw earlier ORLCs than ORs on average. Just two years in one-hundred eleven.

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Above: Average innings of occurrence for one-run game situations (OR) and one-run game situations in which the trailing team scores to tie or take the lead (ORLC)

So what’s going on? I like to think of average ORLC minus average OR as a league-wide statistic for urgency. Consider the following: if the inning number had no effect on the performance of a trailing team in a one-run situation, then we would see roughly the same average inning of occurrence for both OR and ORLC. Out of 111 years, we’d expect to see about 55 years in which OR occurred earlier on average than ORLC and around 55 in which it didn’t. But we don’t see this at all, which strongly suggests that inning number has an effect on how a team does at the plate when down by a run. This is the urgency statistic. It describes a trend that has rung true for the past 101 consecutive seasons of Major League Baseball – when time is running out and the 9th inning is rapidly approaching, teams in close games get their acts together and produce runs. Not every time, of course, but we’re speaking in averages of massive sample sizes here.

So, while your Brewers are likely to fare worse trailing Kershaw and the Dodgers 1-0 than 2-1, take solace in the fact that it’s the fourth inning. Statistically speaking, they’ll have a better chance breaking through as the game goes on and their need for a run becomes more urgent. The effect of team psychology has left its imprint on the records of baseball games since the sport’s earliest days.

I think I might be the biggest fan of the world of the Ten-Pitch Walk.  I don’t know why, but I get overly excited when I see a player really battle for a long time, against everything the pitcher has, only to win the battle through patience.  Perhaps it’s because it’s so contrary to the spirit of what’s actually exciting about baseball; seeing players run around and field a batted ball.  It’s wholly a battle of attrition.  It’s the baseball equivalent of watching somebody run a marathon; you may not think the act itself is exciting, but it’s certainly an impressive feat in a vacuum.

So this has also lead to a fascination with pitches seen per plate appearance.  I’ve long wondered if certain teams place an emphasis on teaching their players to see more pitches per plate appearance.  It seems fairly self-evident that seeing more pitches is, in a microcosm, better than seeing fewer pitches.  You tire the pitcher out quicker, you see more data for your next at-bat to work with, and you give your team a chance to see what the pitcher has, and how he’ll react in different situations.  I hypothesized, purely based on colloquial wisdom, that the A’s would be good at this and the Blue Jays would be bad at this.  That’s not to say that one approach is better than the other, but just that some teams seem more patient than others.

Fortunately, FanGraphs has data available per hitter as to how many pitches they see.  I pulled that data out and found out each player’s average pitch per at bat since the year 2003 (the earliest we have this data, from what I can tell) and restricted the findings to active players only.  Then I ran some regressions to see if there was any correlation between pitches per at bat and useful batting stats.  Here’s what I found:

We see a slightly positive correlation between P/PA and wOBA.  It’s not really anything to write home about, but it’s more than negative.  It doesn’t seem immediately that seeing more pitches relates heavily to overall performance at the plate.  What about on base percentage?

Slightly better here, but still not great.  Seeing more pitches does have a little more correlation to getting on base, but there are plenty of aggressive swingers that don’t follow that model, so it means the correlation is loose at best.  What if we talk just about taking walks?

Here we have a real correlation.  .59 is a fairly strong correlation, and that makes sense.  The more pitches you see, the more likely you are to take a walk.  If you can successfully foul off anything in the strike zone, you will eventually walk (or the pitcher will die of exhaustion, either way, you win).  This is reasonably useful.  If you’re trying to find a way to make your team walk more, maybe you can invest in some players that see more pitches per plate appearance than normal.  This strong of a correlation makes me think about strikeout percentage too, though, because every pitch you foul off makes you closer (or just one whiff away) from striking out.

There is a positive correlation here, but not nearly as strong as between BB% and P/PA.  It’s stronger than the other useful stats like wOBA, but it’s interesting to know that seeing more pitches relates much more strongly to taking a walk than it is to striking out, at least on a grand scale.  There is some research to be done here to see what the odds are of a plate appearance as the pitch count increases, but I’ll leave that for another day.  My next thought was to see if there are, in fact, any teams that are better at this than other teams.  Here’s what we’ve got on a team level:

Well, my original hypotheses were not great ones.  The A’s and the Blue Jays, at 11 and 13, are both decidedly middle of the road teams.  I find it most fun in times like this to look at the extremes; in this case, the Red Sox and the Brewers.  The difference in pitches seen per plate appearance between these two teams is 0.38.  That may seem small, but it adds up.  If we assume the average pitcher faces 4 batters per inning, that’s an additional 1.5 pitches per inning, and 9 pitches by the end of the sixth, just purely by the nature of the hitters.  In a tightly contested contest, that may mean the difference between getting to the bullpen in the 7th rather than the 8th, or even the 7th rather than the 6th.

It should be noted that I limited this data set to 2014 (in contrast to the earlier data which was 2003 onwards) just so we could get a realistic look at roster construction, and to see if any teams are, right now, putting any particular emphasis in this area. The BoSox are carried by the very patient eye of Mike Napoli (4.51 P/PA), but hurt by the rather hacky eye of AJ Pierzynski (3.42 P/PA). Even on one team, that’s more than a pitch per plate appearance, which is pretty startling. The Brewers don’t have nearly the same difference; their best is Mark Reynolds with 4.04 P/PA and their worst is Jean Segura with 3.42 P/PA. As an aside, Chone Figgins is by far the best in this with a whopping 4.99 P/PA, though it was in just 76 PA. Kevin Frandsen brings up the rear with 3.16 P/PA in 189 PA. A lineup of all Mike Napoli’s would see 24.3 more pitches than a lineup of Kevin Frandsens before the leadoff Napoli even comes up a third time. I would feel bad for that pitcher.

The talk about teams possibly emphasizing this data made me wonder if I could make a huge difference if I compiled a team solely to do this; just make sure the pitchers throw a ton of pitches.  With that, I present to you the 2014 All-Stars and Not-So-All-Stars in this area, with a PA minimum thrown in to eliminate Figgins-like outliers:

Despite the fact that there isn’t a strong correlation between wOBA and P/PA directly, it’s worth noting that the P/PA All-Stars are significantly better than the Not-So-All-Stars. Their difference in wOBA is .328 as compared to .314. The Not-So-All-Stars certainly present a fine lineup though; the All-Stars just have the benefit of having Mike Trout in their lineup. It’s nice to know that this is one other area that Mike Trout simply is amazing at, confirming the obvious. The All-Stars have a collective P/PA of 4.26, while their counterparts sit down at 3.43. That’s .83 pitches per plate appearance, which over the course of two turns through the lineup is 14.94 pitches; that’s definitely something notable.

So, it appears this is a demonstrable skill with some value, though not a ton. We can see that some teams are better at this than others, and we see some positive benefit from this, most notably in walk rate. While we see plenty of players on both sides of the scale who are excellent ballplayers, the data does seem to suggest that seeing more pitches is better than not doing so, though only marginally on a league wide scale. When we isolate leaders in this area vs. those more aggressive, we can see some startling differences though, suggesting that perhaps there is an advantage to be gained here.

I was listening to the Jonah Keri Podcast on Grantland recently, and he had Phillies beat writer Matt Gelb on the show. Gelb talked about all the sad things that Phillies fans are already tired of discussing, but he did make a statement that I found particularly poignant. He described Ben Revere’s season as something to the effect of “the emptiest batting average ever.” By empty, he means that while Revere is hitting above .300, an impressive feat in this offense-starved MLB landscape, he does so with almost no walks or extra-base hits. His value at the plate is almost entirely in the form of singles. This comment got me thinking: just how empty is his batting average?

As of this writing, Revere is hitting .314 with a .331 on-base percentage and a .371 slugging percentage. For comparison, the average player has a substantially worse batting average (think .240) but with a similar OBP and a substantially better SLG. To illustrate with normal stats, Revere has 27 total doubles, triples, homers, and walks this year. So far in 2014, there are 42 players with at least 27 doubles, 8 players with at least 27 homers, and 144 players with at least 27 walks.

But how rare is it to have this single-happy nature with such a high average? To look for players to compare to Revere historically, I looked for other player seasons since 2000 which had enough plate appearances to qualify for the batting title with a batting average at least as high as Revere’s but a walk rate and isolated slugging (slugging minus batting average) below his.

But there weren’t any, so I extended the search back to 1980.

Still nobody. 1960?

Nothing.

1900?

Zilch.

Now, to be fair, Ben Revere himself hasn’t completed a full season, so let’s use a more relaxed criterion of 400 plate appearances (Revere has 459).

OK, you get it.

In fact, since 1900 (it’s not worth going earlier because seasons were much shorter then), the only player with at least 400 plate appearances that had as high of a batting average with as little other hitting value is … Ben Revere. That’s it.

I’m not really sure that there’s much to be done with this information, but it’s a pretty shocking finding. As a member of a roster that’s overpaid and underperforming across the board, Revere’s limited skillset has been overshadowed by his more compensated counterparts. However, I was fascinated to discover that on a team that has had plenty of notable failings, Revere has had perhaps the most “unique” and “special” stats of any of them, as long as you’re not taking annual salary into account.

If you disregard his sub-par defense (especially compared to what you would expect from a guy with his speed), Revere really isn’t a terrible offensive player. If you took away all of his steals and instead turned that many singles into doubles, he’d have a slugging percentage around the league average. The problem is, a single followed by a steal isn’t as valuable as a double because it doesn’t advance runners on base, so his value would really be something less than that of a player with league-average slugging. Even if he posts a batting average way above the mean in any given season, he never walks or gets extra-base hits, so he has to sustain that mark against all kinds of luck and defensive factors in order to give the Phillies even passable offensive value. It’s a game that the Phillies seem interested in playing, and it’s defensible because of his obviously high average and stolen base totals, but I’m just not sure if they’re going to win that way.

The premise of this article is a very simple one: which hitter has been the most average in 2014? Considering this question led me through a very simple process, and to a very sad answer (I urge you not to look at the links until the end because suspense). To the leaderboards we go!

Seeing as we’re looking for the most average hitter (not considering defense), and wRC+ is a hitting statistic designed to compare hitters against the average, it seems like a natural starting place. Considering only players with wRC+ between 95 and 105 gives us a list of 24 players.

Next, let’s look at wRC+’s partner in crime: wOBA. League average for wOBA is .316, so this round we’ll be restricting our list of 24 even further, only looking at hitters with wOBA between .310 and .320. Doing so cut our list (almost) in half! We are now left with only 13 players, progress!

Now that we’ve condensed the list based on production, it’s now time to look at the composition of said production. Our average player should have a BB% of about 7.9, and a K% of 19.8. Adjusting our leaderboard leaves us with the three most average hitters in the league. One of these three is not a surprise. The other two are very sad surprises.

But we want 1 average player, not 3, so to narrow it down to the end, I have included another filter for ISO, because our most average hitter should hit for an average amount of power. This final filter leaves us with the single most average player in the major leagues, and fair warning, it will sadden you:

Evan Longoria: BB%: 8.8 / K%: 18.8 / ISO: .139 / BABIP: .287 / OBP: .324 / SLG: .390 / wOBA: .312 / wRC+: 102

League Average: BB%: 7.9 / K% 19.8 /ISO .140 / BABIP: .301 / OBP: .319 / SLG: .396 / wOBA: .316 / wRC+ 100

There was a time when Longoria was to baseball what Mike Trout is today (well maybe not quite on the same level). He came up in 2008 and was the the star of the Rays in their surprising march to the World Series. He showed off 100% not-fake, seemingly-superhuman powers. From 2008 to 2013, Longoria’s wRC+ was 15th in baseball, in a virtual tie with David Wright (who happens to be one of the other most average players). He was also the single most valuable position player by WAR (36.1) in that time. For the first 6 years of his career, Longoria was a model of offensive consistency.

2014 has been a different story though. I’m not the first to write about Longoria’s down year, so I’ll refer you to the works of Jeff Sullivan and James Krueger. The bottom line: Longoria’s bat speed is down, which is killing his power and his ability to hit inside fastballs. This can be seen in his power numbers: a .139 ISO is a far cry from his career ISO of .225 (for reference, David DeJesus has a career ISO of .140). Longoria’s only hitting 9.7% of his fly balls for home runs, compared to 15.5% for his career.

His power hasn’t fully disappeared, but it’s nowhere close to what it was. It’s this sort of sharp power decline that usually suggests some sort of injury à la Matt Kemp (.236 ISO in 2012, .125 in 2013 following a shoulder surgery). Longoria is not expected to miss much time with his latest foot injury, and as Krueger points out, Longoria himself has attributed these struggles with mechanical issues. However, if I were a betting man (or at least old enough to legally gamble in casinos), I would put money on the Rays’ third baseman undergoing some sort of procedure over the offseason.

Now the good news for the Rays is this: even as the league-average hitter, Longoria is still very valuable. Dave Cameron ranked him 9th in his trade value series, no doubt in large part due to his superb defense and very team-friendly contract. Projections have Longoria finishing 2014 with 4.0 WAR. If the cost of a win is approximately $6 million, then he’s worth about $24 million in 2014, but only being paid $7.5 million. Even if Longoria continues to be a league-average bat with excellent defense, he will be very underpaid and very valuable. Really goes to show how great that contract was, huh?

Even more fortunate for Rays’ fans is that given Longoria’s career history, this sort of drop off in offensive production likely is not representative of his true-talent level. While his days as a ~135 wRC+ hitter may be behind him, 119 games is not a huge sample size and Longoria is still just 28. It’s likely that Longoria’s production increases closer to his career averages (Oliver has him 126 wRC+ for next year, which definitely passes the sniff test). The fact remains: Evan Longoria, despite being the most average hitter in baseball, is still one of the most valuable. Now we’ll just have to see what happens to that other average-hitting third baseman.

Examining the foundations of batting analysis began in Part 1 with an historical examination of the earliest statistics designed to examine the performance of batters. In Part 2, I presented a new method for calculating basic averages reflecting the “real and indisputable” rate at which batters reached base. In Part 3, I examined the development of run estimation techniques over the last century, culminating with the linear weights system. I will employ that system now as I reconstruct run estimation from the bottom up.

We use statistics in baseball to tell stories. Statistics describe the action of the game or the performance of players over a period of time. Statistics inform us of how much value a player provided or how much skill a player showed in comparison to other players. To tell such stories successfully, we must understand how the statistics we use are constructed and what they actually represent.

A single, for instance, seems simple enough at first glance. However, there are details in its definition that we sometimes gloss over. In general, a single is any event in which the batter puts the ball into play without causing an out, while showing an accepted form of batting effectiveness (reaching on a hit), and ultimately advancing to first base due to the primary action of the event (before any secondary fielding errors or advancement on throws to other bases). Though this is specific in many regards, it is still quite a broad definition for a batting event. The event could occur in any inning, following any number of outs, and with any number of runners on the bases. The ball could be hit in any direction, with any speed and trajectory, and result in any number of baserunners advancing any number of bases.

These kinds of details form the contextual backdrop that characterizes all batting events. When we construct a statistic to evaluate these events, we choose what level of contextual detail we want to consider. These choices define our analysis and are critical in developing the story we want to tell. For instance, most statistics built to measure batting effectiveness—from the simple counting statistics like hits and walks, to advanced run estimators like Batter Runs or weighted On Base Average (wOBA)—are constructed to be independent of the “situational context” in which the events occur. That is, it doesn’t matter when during the game a hit is made or if there are any outs or any runners on the bases at the time it happens. As George Lindsey noted in 1963, “the measure of the batting effectiveness of an individual should not depend on the situations that faced him when he came to the plate.”

Situational context is the most commonly cited form of contextual detail. When a statistic is described as “context neutral,” the context being removed is very often the one describing the out/base state before and after the event and the inning in which it occurred. However, there are other contextual details that characterize the circumstances and conditions in which batting events occur that also tend to be removed from consideration when analyzing their value. Historically, where the ball was hit, as well as the speed and trajectory which it took to reach that location, have also not been considered when judging the effectiveness of batters. This has partly been due to the complexity of tracking such things, especially in the century of baseball recordkeeping before the advent of computers. Also, most historical batting analyses focus exclusively on the outcome for the batter, independent of the effect on other baserunners. If the batter hits the ball four feet or 400 feet but still only reaches first base, there is no difference in the personal outcome that he achieved.

If the value of a hit was limited to only how far the batter advances, then there would be no need to consider the “batted-ball context,” but as F.C. Lane observed in 1916, part of the value of making a hit is in the effect on the “runner who may already be upon the bases.” By removing the batted-ball context when considering types of events in which the ball is put into play, we’re assuming that a four-foot single and 400-foot single have the same general effect on other baserunners. For some analyses, this level of contextual detail describing an event may be irrelevant or insignificant, but for others—particularly when estimating run production—such a level of detail is paramount.

Let’s employ the linear weights method for estimating run production, but allow the estimation to vary from one completely independent of any contextual detail to one as detailed as we can make it. In this way, we’ll be able to observe how various details impact our valuation of events. Also, in situations where we are only given a limited amount of information about batting events, it will allow us to make cursory estimations of how much they caused their team’s run expectancy to change.

To begin, let’s define the run-scoring environment for 2013.[i] While we have focused on context concerning how events transpired on the field, the run scoring environment is another kind of contextual detail that characterizes how we evaluate those events. The exact same event in 2013 may not have caused the same change in run expectancy as it would have in 2000 when runs were scored at a different rate. We will define the run scoring environment for 2013 as the average number of runs that scored in an inning following a plate appearance in each of the 24 out/base states – a 2013-specific form of George Lindsey’s run expectancy matrix:

While we will focus on examining various levels of contextual detail concerning the events themselves, the run-scoring environment can also be varied based on contextual details concerning the scoring of runs. The matrix we will employ, as defined by Lindsey, reflects the average number of runs scored across the entire league. If we wanted, we could differentiate environments by league or park, among other things, to try and reflect a more specific estimate of the number of runs produced. As the work I’m going to present is meant to provide a general framework for run estimation, and these adjustments are not trivial, I’m going to stick with the basic model provided by Lindsey.

With Lindsey’s tool, we can define a pair of statistics for general analysis of run production. Expected Runs (xR) reflect the estimated change in a team’s run expectancy caused by a batter’s plate appearances independent of the situational context in which they occur. A batter’s expected Run Average (xRA) is the rate per plate appearance at which he produces xR.

xRA = Expected Runs / Plate Appearances = xR / PA

xR and xRA create a framework for estimating situation-neutral run production. Based on the contextual specificity that is used to describe the action of a plate appearance, xR and xRA will yield various estimations. The base case for calculating expected runs, xR₀, is calculated independently of any contextual detail, considering only that a plate appearance occurred. By definition, an average plate appearance will cause no change in a team’s run expectancy. Consequently, no matter a player’s total number of plate appearances, his xR₀ and, by extension, his xRA₀, will be 0.0.

This is completely uninformative of course, as base cases often are. So let’s add our first layer of contextual specificity by noting whether an out occurred due to the action of the plate appearance. This is the most significant contextual detail that we consider when evaluating batting events – it is the only factor that determines whether a plate appearance increases or decreases a team’s run expectancy. In 2013, 67.5 percent of all plate appearances resulted in at least one out occurring. On average, those events caused a team’s run expectancy to decrease by .252 runs. The 32.5 percent of plate appearances in which an out did not occur caused a team’s run expectancy to increase by .524 runs on average. We’ll define xR₁ as the estimated change in run expectancy based exclusively on whether the batter reached base without causing an out; xRA₁ is the rate at which a batter produced xR₁ per plate appearance.

You’ll notice that the components that construct xRA₁ can only take on two values—.524 and -.252—in the same way that the components that construct effective On Base Average (eOBA) (as defined in Part 2) can only take on two values—1 and 0. These statistics—xRA₁ and eOBA—have a direct linear correlation:

In effect, xRA₁ is a weighted version of eOBA, incorporating the same contextual details but on a different scale. This estimation provides us with an association between reaching base safely and producing runs. However, the lack of detail would suggest that all players that reach base at the same rate produce the same value, which is over simplified. It’s why you wouldn’t just use eOBA, or eBA, or any other basic statistic that reflects the rate which a batter reaches base, when judging the performance of a batter. Let’s add another layer of contextual detail to account for the different kinds of value a batter provides when he reaches base.

xR₂ will represent the estimated change in run expectancy based on whether the batter safely reached base and the number of bases to which he advanced due to the action of the plate appearance; xRA₂ will be the rate at which a batter produces xR₂ per plate appearance. While xR₁ and xRA₁ were built with just two components to estimate run production, xR₂ and xRA₂ require five components: one to define the value of an out, and four to define the value of safely reaching each base.

In 2013, a batter safely reaching first base during a plate appearance caused an average increase of .389 runs to his team’s run expectancy. Reaching second base was worth .748 runs, third base was worth 1.026 runs, and reaching home was worth 1.377 runs on average. Where xRA₁ provided a run estimation analog to eOBA, xRA₂ is built with very similar components to effective Total Bases Average (eTBA), though it’s not quite a direct linear correlation:

The reason xRA₂ and eTBA do not correlate with each other perfectly, like xRA₁ and eOBA, is because the way in which a batter advances bases is significant in determining how valuable his plate appearances were. Consider two players that each had two plate appearances: Player A hit a home run and made an out, Player B reached second base twice. Their eTBA would be identical—2.000—as they each reached four bases in two plate appearances. However, from the run values associated with reaching those bases, Player A would record 1.125 xR₂ from his home run and out, while Player B would record 1.496 xR₂ from the two plate appearances leaving him on second base. Consequently, Player A would have produced a lower xRA₂ (.5625) than Player B (.7480), despite their having the same eTBA. These effects tend to average out over a large enough sample of plate appearances, but they will still cause variations in xRA₂ among players with the same eTBA.

As stated in Part 2, the two main objectives of batters are to not cause an out and to advance as many bases as possible. If the only value that batters produced came from accomplishing these objectives, then we would be done – xR₂ and xRA₂ would reflect the perfect estimations of situation-neutral run production. As I hope is clear, though, the value of a batting event is dependent not only on the outcome for the batter but on the impact the event had on all other runners on base at the time it occurred. Different types of events that result in the batter reaching the same base can have different average effects on other baserunners. For instance, a single and a walk both leave the batter on first base, but the former creates the opportunity for baserunners to advance further on average than the latter. To address this, the next layer of contextual detail will bring the official scorer into the fray. xR₃ will represent the estimated change in run expectancy produced during a batter’s plate appearance based on:

(1)    whether the batter safely reached base,

(2)    the number of bases, if any, to which the batter advanced due to the action of the plate appearance, and

(3)    the type of event, as defined by the official scorer, that caused him to reach base or cause an out.

xRA₃ will, as always, be the rate at which a batter produces xR₃ per plate appearance.

Each of the run estimators that were examined in Part 3, from F.C. Lane’s methods through wOBA, are subsets of this level of xR. Expected runs incorporate estimations of the value produced during every event in which the batter was involved, including those which may be considered “unskilled.” The run estimators examined in Part 3 consider only those events that reflected a batter’s “effectiveness,” and either disregard the “ineffective” events or treat them as failures. xR₃ provides the total value produced by a batter, independent of the effectiveness he showed while producing it, based solely on how the official scorer defines the events. Consequently, some events, like strikeouts, sacrifice bunts, reaches on catcher’s interference, and failed fielder’s choices, among other more obscure occurrences, are examined independently in xR₃. From the two components of xR₂ and the five of xR₃, we build xR₄ with 18 components: five types of outs and 13 types of reaches.

To help illustrate how xR has progressed from level to level, here is a chart reflecting the run values for 2013 as estimated by xR based on the contextual detail provided thus far.

xR Progression

Beyond any consideration of skilled or unskilled production, xR₃ is the level at which most run estimators are constructed. It incorporates events that are well defined in the Official Rules of the game, and have been for at least the last few decades, and in some cases for over a century. While we still define most of a batter’s production by his accomplishing these events, we live in an era where we can differentiate between events on the field in more specific ways. Not all singles are identical events. We weaken our estimation of run production if we don’t account for the different kinds of singles, among other events, that can occur. xR₃ brought the official scorer into action; xR₄ will do the same with the stat stringer.

While the scorer is concerned with the result of an event, a stringer pays attention to the action in between the results. They chart the type, speed, and location of every pitch, and note the batted ball type (bunt, groundball, line drive, flyball, pop up) [ii] and the location to which the ball travels when put into play.While we don’t have this data as far back in time as we have result data, we do have decades worth of information concerning these details. By differentiating events based on these details, we will begin to unravel the “batted-ball context.” Ideally, we would know every detail of the flight of the ball, and use this to group together the most similar possible type of events for comparison.[iii] At present, we’re limited to what the scorers and stringers provide, but that’s still quite a lot of information.

xR₄ will represent the estimated change in run expectancy produced during a batter’s plate appearance based on:

(1)    whether the batter safely reached base,

(2)    the number of bases, if any, to which the batter advanced due to the action of the plate appearance,

(3)    the type of event, as defined by the official scorer, that caused him to reach base or make an out,

(4)    the type of batted ball, if there was one, as defined by the stat stringer, that resulted from the plate appearance,

(5)    the direction in which the ball travelled, and

(6)    whether the ball was fielded in the infield or outfield.

xRA₄ will be the rate at which a batter produces xR₄ per plate appearance.

There are 18 components in xR₃ which describe the assorted types of general events a batter can create.  When you add in these details concerning the batted-ball context, the number of components increases to 145 for xR₄. With such specific details being considered, we can no longer rely on a single season of data to accurately inform us on the average situation in which each type of event occurs; the sample sizes for some events are just too small. To address this, there are two steps required in evaluating events for xR₄. The first is to build a large sample of each event to build an accurate picture of their relative frequency in each out/base state. I’ve done this by using a sample covering the previous ten seasons to the one in which the estimations are being made. Once this step is completed, the run-scoring environment in the season being analyzed is applied to these frequencies, in the same way it is when looking at single season frequencies for basic events.

For instance, the single, which is traditionally treated as just one type of event, is broken into 24 parts based on the contextual details listed above. By observing the rate at which each of these 24 variations of singles occurred in each out/base state from 2004 through 2013, and applying the 2013 run-scoring environment, we get the following breakdown for the estimated value of singles in 2013:

This process is repeated for every type of batting event in which the ball is put into play. One of the ways we can use this information is to consider the run value based not on the result of the event, but on the batted-ball context that describes the event. Here are those values in the 2013 run-scoring environment:

Similarly, we can break down each player’s xR₄ by the value produced on each type of batted ball. Here are graphs for xR₄ produced on each of the four types of batted balls resulting from a swing, with respect to the number of batted balls of that type hit by the player. For simplicity, from this point on, when I drop the subscript when describing a batter’s expected run total, I’m referring to xR₄.

Line drives are the most optimal result for a batter. The first objective of batters is to reach base safely, and they did that on 67.0 percent of line drives last season. No batter who hit at least eight line drives in 2013 caused a net decrease in his team’s run expectancy during those events. For most batters, hitting the ball into the outfield in the air is the ideal way to produce value, as fly ball production tends to create a positive change in a team’s run expectancy. However, fly balls have the most variance of any of the batted ball types, and there are certainly batters who hurt their teams more when hitting the ball at a high launch angle than a low one. Here are the players to produce the lowest xRA on fly balls last season (minimum 50 fly balls):

For each of these batters, hitting the ball on the ground or on a line drive were far better results on average.

While groundballs may be a preferable result for some batters when compared to fly balls, they are still effectively batting failures for the team. There were 840 batters in 2013 to hit at least one groundball and only 44 produced a net positive change in their team’s run expectancy. Of those 44 players, only 11 hit more than 10 groundballs, and only two (Mike Trout and Juan Francisco) hit at least 100 groundballs. Here are the players with the highest xRA on groundballs in 2013 who hit at least 100 groundballs:

xR₄ allows us to tell the most detailed story concerning the type of value a batter produced, independent of the situational context at the time the plate appearance occurred. Because we gradually added layers of detail to our estimation, we can compare how each level of expected runs correlates to this most detailed level. In this way, we can judge how much information each level provides with respect to our most detailed estimation. Here is a graph that charts a batter’s xR₄ with respect to his xR₁, xR₂, and xR₃ estimations:

The line that cuts through the data reflects the xR₄ values charted against themselves. For each xR_n, we can calculate how well it correlates with xR₄ and, consequently, how much of xR₄ it can explain. Remember that we have already shown that xR₁ has a direct linear correlation with eOBA and xR₂ has a very high, though not quite direct, correlation with eTBA. For the xR₁ values, we observe a correlation, r, with xR₄ of .912, and an r² of .832, meaning that knowing the rate at which a batter reaches base explains over four-fifths of our estimation of xR₄. For the xR₂ values, r² increases to .986; for the xR₃ values, r² increases slightly higher to .990.[iv]

The takeaway from this is that when considering the whole population of players, there is little difference in a run estimator that considers the batted-ball context and one that does not; you can still explain 99 percent of the value estimated by xR₄ by stopping at xR₃. In fact, if all you know is the rate at which a batter accomplishes his two main objectives—reaching base and advancing as far as possible—you can explain well over 90 percent of the value estimated by xR₄. However, on an individual level, there is enough variation that observing the batted-ball context can be beneficial. Here are the five players with the largest positive and negative differences between their xR₃ and xR₄ estimations:

These changes are not massive, and these are the extreme cases for 2013, but they are certainly large enough that ignoring them will weaken specific analyses of batting production. Incorporating batted ball details into our analysis adds a significant layer of complexity to our calculation, but it must be considered if we want to tell the most accurate story of the value a batter produced.

If this work seems at all familiar, you may have read this article that I wrote last year on a statistic that I called Offensive Value Added (OVA). For all intents and purposes, OVA and xR are identical. I decided that the name change to xR would help me differentiate estimations more simply, as I could avoid naming four separate statistics for each level of contextual detail, but there was also a secondary reason for changing the presentation of the data. OVAr was the rate statistic associated with OVA, and it was scaled to look like a batting average, much in the same way that wOBA is scaled to look like an on base average. At the time, I choose to do this to make it easier to appreciate how a batter performed, since many baseball enthusiasts are comfortable interpreting the relative significant of a batting average.

After thinking on the subject, though, I came to decide that I prefer statistics that actually “mean” something to those that give a general, unit-less rating. For instance, try to explain what wOBA actually reflects. It starts as a run estimator, but then it’s transformed into a number that looks like a statistic with specific units (OBA), while not actually using those units. Once that transformation occurs, it no longer reflects anything specific and only serves as a way to rate batters. The same principle applies to other statistics as well, most notably OPS, which is arguably the most meaningless of all baseball statistics, perhaps all statistics ever (don’t get me started).

xR and xRA estimate the change in a team’s run expectancy caused by a batter’s plate appearances. They are measured in runs and runs per plate appearance, respectively. xRA may not look like a number you’ve seen before, and generally needs to be written out to four decimal places instead of three, unlike basic averages, but it’s linguistically very simple to use and understand. I’d rather sacrifice the comfort of having a statistic merely look familiar and instead have it actually reflect something tangible. This doesn’t take away from the value of a statistic like wOBA, which is a great run estimator no matter what scale it is on; a lack of meaning certainly does not imply a lack of value. Introducing an unscaled run average, xRA, will hopefully create a different perspective on how to talk about batting production.

There is one final expected run estimation that I want to consider that could easily cover an entire new part on its own, but I’ll limit myself to just a few paragraphs. The xR estimations we have built have been constructed independent of the situational context at the time of the batter’s plate appearance. Since we want to cover the entire spectrum of context-neutral run estimation to context-specific run estimation, we will conclude by considering xR_s, which is an estimate of the change in a team’s run expectancy based on the out/base state before and after the action of the plate appearance. This is very nearly the same thing as RE24 but it only considers runs produced due to the primary action of plate appearances and not baserunning events.

In many respects, xR_s is the simplest run estimator to construct of all that we have built thus far. There are only three pieces of information you need to know in a given plate appearance to construct xR_s: the run-scoring environment, the out/base state at the start of the action of the plate appearance, and the out/base state at the end of the action of the plate appearance. Next time you go to a baseball game, bring along a copy of a run expectancy matrix, like the one provided earlier. On a scorecard, at the start of every plate appearance, take note of the value assigned to the out/base state, making adjustments if any runners move while the batter is still in the batter’s box. Once the plate appearance is over, note the value of the new out/base state, separating out any advancement on secondary fielding errors or throws to other bases. Subtract the first value from the second value, and add in any RBIs on the play, and write the number in the box associated with the batter’s plate appearance; you just calculated xR_s. Do this for a whole game, and you will have a picture of the total value produced by every batter based on the out/base state context in which they performed.

The effective averages and expected run estimations provide a foundation on which batting analysis can be performed. They combine both “real and indisputable facts” with detailed estimations of the run produced in every event in which a batter participates. Any story that aims to describe the value that a batter provides to his team must consider these statistics, as they are the only ones which account for all value produced. 147 years ago, Henry Chadwick suggested that batters should be judged on whether they passed a “test of skill.” I think they should be judged on whether they passed a “test of value.”

Thanks to Benjamin H Byron for editorial assistance, as well as the staff at the Library of Congress for assistance in locating original copies of the 19^th century newspaper articles included in Part 1.

Here is data on eOBA, eTBA, and each level of xR and xRA estimation, for each batter in 2013.

Bibliography

[i] I’ll be focusing on 2013 because the full season is complete. All the work described here could easily be applied to 2014, or any other season, I just don’t want to use incomplete information.

[ii] While these terms are used a lot, there aren’t any specific definitions commonly accepted that differentiate each type of batted ball. For terms used so commonly, it doesn’t make much sense to me that they are not well defined. It won’t apply to the data used in this research, but here is my attempt at defining them.

A bunt is a batted ball not swung at but intentionally met with the bat. A groundball is a batted ball swung at that lands anywhere between home plate and the outer edge of the infield dirt and would be classified as a line drive if it made contact with a fielder in the air. A line drive is a batted ball swung at that leaves the bat at an angle of at most 20° above parallel to the ground (the launch angle), and either lands in the outfield or makes contact with any fielder before landing (generally through a catch, but sometimes a deflection). A fly ball is a batted ball swung at, with a launch angle between 20° and 60° above parallel (not inclusive), that either lands in the outfield or is caught in the air by a player in the outfield. A popup is a batted ball swung at that either (a) leaves the bat at an angle of 60° or greater above parallel and lands or is caught in the air in the outfield, or (b) leaves the bat at an angle greater than 30° and lands or is caught in the air in the  infield.

This would result in some balls being classified differently than they currently are, and not just because differentiating between a line drive and a fly ball is somewhat difficult with just a pair of eyes. If the defense were to play an infield shift, and the batter were to hit a line drive into the outfield grass into that shift, subsequently being thrown out at first base, it would likely be called a groundout by current standards. Batted balls should not be defined based on defensive success or failure, but by the general path which they take when leaving the bat. It may be unusual to credit a batter with making a line out despite the ball hitting the ground, but it more accurately reflects the type of ball put into play by the batter.

I don’t know that these are the “correct” ways to group together these events, but as we now are using technology that tracks the flight of the baseball from the moment it is released by the pitcher through the end of the play, we should probably have better definitions for types of batted balls than those currently provided by MLB. I don’t expect a human stringer to be able to differentiate between a ball hit with a 15° launch angle or a 25° launch angle, but that doesn’t mean we shouldn’t have some standard definition for which they should aim.

[iii] In theory, xR₅ would attempt to consider details that are even more specific, perhaps the initial velocity of the ball off the bat, the launch angle, and whatever other information can be gleaned from technology like HIT F/X. The xR framework leaves room to consider any further amount of detail that a researcher wants to consider.

[iv] Though not charted here, the r² value based on the correlation between wRAA, the “counting” version of wOBA, and xR₄ is .984. As wRAA is nearly identical to xR₃ but excludes a few of the more rare events from its calculation, it’s not surprising that the r² value between wRAA and xR₄ is just slightly smaller than the r² between xR₃ and xR₄.

Dear FanGraphs community,

This isn’t a post about baseball, per se, but rather about the way we talk about it. Lately, I’ve been thinking a lot about how to improve the quality of dialogue surrounding sabermetrics. Please excuse my rambling, as I tend to get rather emotional and philosophical when discussing this particular topic.

When reading posts and especially comments, I sometimes get the sense that we think we are right merely due to the fact that statistics are objective. In a sense, this is true. As long as the methodology is clearly laid out, stats really are just numbers. But people are biased. All language is persuasive in some sense, and the inherent neutrality of numbers is often hijacked by various human agendas. Sabermetrics are not exempt from this phenomenon.

Most modern discourse surrounding baseball analysis pits “old-school” vs. “new-school” in a largely arbitrary ideological cage fight. These sorts of polemical constructs make for good television, but slow progress. Its easy to get caught up in the excitement of a debate while completely missing out on what really matters. Baseball is a beautiful game and it brings people together. It’s America’s pastime for a reason! It transcends cultural differences, generation gaps, and even language itself.

Statistics help us to understand and evaluate how well this great game is being played. They act as a mental “handle” by which we can intellectually grasp the importance of each individual event and performance. Everyone, regardless of their stance on sabermetrics, wants statistics that are both intuitive and accurate. So let’s set aside our agendas for a minute and think about how to proactively bridge the gap between these two sides that have so much to offer!

For starters, we should minimize our implementation of hostile methodologies. Getting on a soapbox and proclaiming the evils of traditionalism simply doesn’t do anybody any good. It feeds our pride, as well as the opposition’s presumption that we care more about our statistics than we do about, you know, actual baseball. Over the last few years, I’ve begun to think of myself more as a teacher of sabermetrics than a defender of them. This approach has two important ramifications.

First, it dictates that we get along with those who disagree with us. In my experience, people are only open to new information in the context of a trusting relationship. As fellow baseball fanatics, we have an easy point of contact with traditionalists: we both like baseball. Duh! Focus on that first rather than stuffing a lecture on DIPS theory down their throats.

Second, a teaching disposition encourages us to refine and adapt our communication of sabermetric concepts. Next time you want to call someone a nincompoop on a message board, first ask yourself, “What could I have done to explain this idea more clearly.” Chances are, the person isn’t stupid, just unenlightened and/or overly argumentative. Over my next few posts, I’ll get into the nitty-gritty of how we might make this happen.

Contrary to popular belief, numbers aren’t evil. Baseball statistics in particular have come a long way toward being less deceptive. Let’s represent them well, shall we?

Sincerely yours,

KK-Swizzle