There are many arguments against the sacrifice bunt, by many sabermetricians and sports writers, all with the purpose of retiring its practice in baseball. The three main reasons not to bunt are that it gives away an out (out of only 27), the rate of scoring goes down (based on ERT by Tango), and that most bunters are unsuccessful.

For my argument, I will establish a more romantic approach and one I haven’t seen across the world of sabermetrics. With this approach, I will land on a conclusion that supports the sacrifice bunt and even speaks to the expansion of its practice.

Bunters can be successful

First, I’ll attack the last argument. If bunting is coached, bunters will be better. In my own research, as well as research done by others, I’ve found that there have been years when even the pitchers are able to bunt successfully over 90% of the time. Many people say that practice makes perfect, and while perfection might not be reached in the batters box, I wouldn’t be surprised if bunters were allowed to get close, or at least to their abilities in the 80’s.

Innings are more prosperous after bunt

The second argument is the main staple of this essay. In the world of analytics, general numbers are not good enough to explain why a phenomena is bad. Tom Tango’s famous Run Expectancy Matrix is used to make arguments against bunting across the Internet. Unfortunately, it’s assumed that the situations just exist rather than being set up the way that they are. It would be appropriate to use the table if a team were allowed to place a man, or men, on a base, or bases, and set the number of outs. However, as a strong believer in the principle of sufficient reason, I believe that there’s variability between a man on second with one out from a bunt and a man on second with one out from other situations.

For this reason, I set up my own analysis through the resource of Retrosheet play by play for the years of 2010-2013. To make things simple and not delve too deeply in varying circumstances, I will simply use larger data sets and noticeable differences to tell a story. First, I will look at only innings that start with men on base before the first out. Sacrifice bunts cannot happen when men are not on base, so it would be unfair to statistically compare innings with bunts to just innings without bunts. In line with Retrosheet’s system, I’m looking at all instances of SH, when they occur before (and usually result in) the first out.

To summarize, I’ll be looking at the percent chance that a team scores in an inning where they are able to get a man, or men, on base before the first out (as well as the average runs per inning when that situation is set up). I will compare this base situation to the percent chance that a team scores in an inning when they decide to sacrifice for that first out (as well as the average runs per inning when that situation is set up).

This data can be seen below with a total of about 53,000 innings across seasons where men were on base before the first out. In general, through the four years, teams score in about 26.8% of innings with about 0.478 runs per inning (RPI); when men get on base before the first out, they score 45.8% of innings with a .691 RPI. (In innings where a leadoff HR is hit, this does not count as men on base (nor will these runs count in calculation of either group, assuming men get on after the home run is hit, and before an out)).

Many managers, if not statisticians, understand this increase in the chance to score a run; after all, that’s why they do it. In 2010 and 2013, deciding to, and successfully laying down a sacrifice bunt resulted in a 13% increase in the ability to score that inning for the AL. And while it would make sense that the argument stops there, RPI also supports the sacrifice bunt (with data of the last four years). (Here, again, RPI = Runs scored after MOB B1O situation divided by number of innings of situation.)

This increase in RPI (seen as high as 0.137 Runs Per Inning larger than without bunting, 2012 AL) can contribute a decent number of runs over the course of a season. For example, in 2013, if the Oakland Athletics bunted a little less than once per series, they would have been on par with National League teams with number of bunts (in the 60’s). If they were able to bunt 47 more times (68, rather than 21), then their run total would have given them enough wins to have the best record in baseball (using Bill James adjusted pythagorean expected win percentage).

To summarize, an adjusted estimated runs table with respect to sacrifice bunt set up positioning and outs would produce more runs than the average table that does not take into concern how outs or players arrived at their position. This argument was suggested at the end of an essay by Dan Levitt, with earlier data in a more complex and subtle manner. RPI and the probability of scoring a run increase with a sacrifice bunt.

Bunting is symbolic of the greater good

The first and final argument to discuss is the idea that a sacrifice bunt throws away an out. In baseball, if a player bats out of order, or does not run out an error (among other mental mistakes), then that is giving away an out. And I believe that if a coach tells a player that he can’t hit, and to bunt because he can’t hit, then I wouldn’t argue that in those cases, you are giving away an out (knowingly removing the opportunity from the player to get a hit). So unless you believe that’s how coaches interact with their players prior to calling for the bunt, I will disagree with that notion.

The dictionary definition of sacrifice is “an act of giving up something valued for the sake of something else regarded as more important or worthy.” It’s the biggest theme in religious studies, the coolest way to die in movies, and the plot for heroic stories in the nightly news. Eliminating the psychological effects of a sacrifice, where they’re common place in our culture, seems slightly irresponsible after seeing the data.

This idea lends nicely to the discrepancy between American and National Leagues. Articles can be found, research has been done, and the common thought among those surrounding the game is that pitchers should bunt because they won’t do much else (in appropriate situations). In fact, an article by James Click gives the opinion that the lower the average, the more advantageous it is to bunt. However, my argument is the opposite. The amount they sacrifice, if they’re unable to hit is not valuable to those involved. If the pitcher is respected as a hitter, then their sacrifice is meaningful. Mentally as a leadoff man, if your pitcher is hitting sub .100, and there’s a man on base, he’s bunting because he cannot hit. That’s not a teamwork inspired motive, that’s a picking poison motive. The chart below shows data from the last four years when men get on base before the first out, it distinguishes that the National League is better than either league that doesn’t bunt, but far from as effective as AL bunters.

The argument can be made that the AL contains better hitters, and while I believe this, there would be a larger separation of the % scoring without bunting as well as the RPI of the innings where players get on before the first out.

Because of this separation, I feel that bunting is not giving away an out, but sacrificing for something greater. Simply put, if my teammate sets me up to knock in a run with a hit, that’s easier that having to find a gap, or doing something greater. In many cases, I might need to just find a hole in the infield. Also, I know that my team, and coach, believes in me to be successful. Professional athletes can’t possibly feel pressure and confidence that emanates from teammates with the hopes of greater success, that idea would be ridiculous, right? Those ideas are practiced and taught in business places and self-help books around the world.

Opposition

The data that I used was from Retrosheet, and while this data lists a lot of SH’s (sacrifice bunts) from where errors occur, to double plays, the main output is the standard sacrifice bunt. That being said, it does not include instances where the batter was bunting for a base hit (regardless of number of men on base), or other strange incidents of sacrifice failures (places where the scoring did not distinguish that an SH was in play). After recreating the analysis to include all bunts, the values of RPI and % scoring assuming men on base before the first out, values were still larger than without the bunt, but not as large as the sacrifice representation. This argument falls with the established idea that bunting could be more successful than most people think (especially when the bunt is a sacrifice). For instance, if the numbers above are reduced by as much as 85% in some cases, it still produces more successful results.

The next piece of opposition is that different circumstances have different weights in these situations, and that my case is too general to provide an advantage to a staff trying to decide whether to bunt. My argument is that upon analyzing circumstances, the most important element is the sacrifice bunt. In most situations, I feel that it will boost the team’s ability (and desire) to have success. With four years of data, my goal was to be able to refute the reliance on the simple Tango Run Expectancy Matrix, and how it is used, not to recreate one. In my opinion, in order for people to understand how historically successful situations have been, there should be hundreds of Run Expectancy Matrices highlighting how runners came to be where they are, as well as what batters follow.

The final piece of opposition has been created by myself during the generation of this essay or idea. The Heisenberg Uncertainty Principle relates to the ability to study the speed and position of a microscopic particle. Simply put, by studying one, you’re unable to observe the other. The act of observation limits the ability to fully observe. Because my argument is set up in a romantic sense, it could be argued that this principle relates. If coaches and teams start bunting every other inning, the act of giving oneself away for the greater good of the team will diminish and its advantage psychologically will wither away. In other words, the knowledge of how something effects one emotionally can limit one from being emotionally affected. I present this as an opposition because I feel that this might already be the case where if a pitcher is repeatedly bunting, teams will not think much of it as a quest for the greater good. However, when players are seen as an asset in the box, this advantage still exists; so teammates can still be sold on the relevance of the opportunity.

If these ideas spread, will this essay result in more bunts, especially when there are no outs? Probably not, because statisticians are stubborn. But it definitely provides an outlet for coaches who support the old school, traditional game of baseball.

Anytime a sports piece starts making claims that so and so is the best player ever, it’s best to check assumptions being made.  And the sooner those assumptions are made, the better.  So let’s get the big assumption out of the way early.

Felix now has a legitimate claim to being the best Mariner pitcher ever.  Considering that he has 8 full seasons under his belt and 2 half seasons, all the while sitting atop the Mariner rotation, this claim hardly seems surprising, but for one thing…

Randy Johnson pitched 8 full seasons and 2 half seasons for the Mariners, too.

And for anyone following baseball during the 1990’s, it’s hard to believe any pitcher could usurp the title of best ever from the Big Unit, whose left arm terrified hitters, as a Mariner, from 1989 to 1998.  Nevertheless, here we are:

Johnson has very few peers, through history, in his ability to strike out hitters.  But it’s clear that Felix is proportionally better than the Unit in his ability to limit base on balls.  Felix’s superior FIP is mostly a function of playing his home games at Safeco while Johnson had to pitch in the hitter friendly Kingdome.  As WAR is park-adjusted, we can see that Felix has come to match Johnson’s 45 WAR accumulation, as of this date.  From this point on in Felix’s career, his WAR total will likely increase beyond Randy’s static Mariner total of 45, and probably rapidly so.

One could take the position that Randy’s playoff totals in 1995 and 1997 still keep him ahead of Felix.  But that would be crediting Randy’s better supporting cast for having gotten him to that position in the first place.  Hardly an individual achievement.

The amazing thing about Felix is he’s putting up performances that are the best of his career.  Felix came into his own by winning the Cy Young Award in 2010.  He followed up that season in 2011 by essentially matching those award winning stats.  His encore has been to better the stats in each successive year, to where he’s matching his best K-rate and beating his best BB-rate, ever, in 2014.

And in case you were wondering, here’s where Felix ranks for pitchers between the ages of 16 and 28, over the last 50 years:

And by the way, if you’re curious who Felix will need to measure up to for the rest of his career, from his age 29 season onward; well, there’s really only one name: Randy Johnson, who accumulated 101.2 WAR, from the age of 29 to 45.

As a long-time Mariners fan, I never thought I’d see the likes of Randy Johnson, ever again.

Then came the King.

This title is slightly misleading, and may be best put as “What is Not Quite Right with Trevor Rosenthal?”  His ERA is below 4.00 and his FIP is much better than his ERA, thanks in large part to his high strikeout rate and low home run rate. Yet, Rosenthal is not dominating in the same way that he did last year when he struck out 108 batters in 75 1/3 innings and compiled a miniscule 1.91 FIP. So, what is different about Rosenthal that has led to a 1.36 increase in ERA and .83 spike in FIP? As I said, Rosenthal is in the midst of a very respectable season, by many metrics, but he is not supposed to be “just” respectable. Rosenthal should be able to dominate the league, just as he did last year when he ranked 5^th among relievers in FIP and WAR. Naturally, I turned to the numbers to determine what is holding Rosenthal back from being one of the best closers in the league.

With such a significant jump in his ERA, I expected to see that Rosenthal was being hit much harder, but that is not what I found. Not only is his opponents’ SLG% down, but so is his opponents’ AVG. So, Rosenthal is allowing fewer hits compared to last year and also fewer extra base hits, which certainly seems like a great formula for success. However, based on the type of contact Rosenthal is letting up this year, I would expect to see the opposite trend. For the second straight season, Rosenthal’s GB% has decreased, and this year, his Line Drive % (LD%) ballooned 10% up to 30%. Despite allowing more hard contact, Rosenthal has decreased his BABIP, which suggests he has actually been lucky to this point in the season. Rosenthal has also done a nice job limiting home runs, even while allowing more balls to be put in the air. His GB/FB ratio has dropped all the way to .85 from 1.23 just a year ago. Fortunately, he has still managed to drop his HR/9 to 0.3 thanks to a miniscule HR/FB ratio of .037.

In an attempt to understand why he was letting up more solid contact, I looked at his fastball velocity, but it was right where it was last year. Rosenthal has not lost any velocity from where he was last year, which means it his stuff is not to blame for his increased FB and LD rates this year. Yet, even with his upper-90s heat, Rosenthal has struggled to get ahead in the count. He has thrown the first pitch of the at-bat for a strike just 57.1% of the time this year, which is a 6% drop from last season. Anytime you fall behind a hitter, you give them a much better chance to make solid contact, even when you can touch triple digits. As a pitcher with as much stuff as he has, Rosenthal must be aggressive and work ahead in the count in order to maximize his lights out repertoire.

More concerning than the fact that he is falling behind more hitters than last year, is where Rosenthal is missing. Of all the pitches Rosenthal has thrown outside the strike zone, 44% have missed up above the zone, compared to just 28% below the zone. This is compared to last year when he missed above the zone just 34% of the time and below the zone with 35% of his pitches outside the zone. While this may not seem significant since these balls are outside the zone, so they are unlikely to be hit, it is always concerning to see a pitcher consistently throwing up in the zone. Rosenthal’s propensity to miss with pitches up has certainly contributed to his increased LD% and FB%, as it is easier to elevate a pitch that is already up. This could be a strategy for Rosenthal, as it is harder to catch up to fastballs up in the zone, but it has yet to materialize into positive results, as his performance is worse than in 2013.

Also, based off the times I have seen him throw, this does not seem to be a strategy, as he has also missed up in the zone with his changeup, which is never intended by any pitcher. Despite some issues keeping it down in the zone, Rosenthal’s changeup has been his best pitch by far this season. This is particularly surprising for a pitcher that throws as hard as he does, but his changeup has compiled an astounding 5.71 runs above average per every 100 pitches, which has likely contributed to his increased use of the pitch (up to 15% from 6% in 2013). On a more concerning note though, his fastball is registering a career low .21 runs above average per every 100 pitches, down .77 runs from last year. It isn’t surprising the fastball is not worth as much as the changeup on average because the changeup is often used in higher leverage situations and also with less frequency. However, with Rosenthal’s struggles to get ahead in the count, it is not shocking that his fastball is less effective this year.

While Rosenthal has allowed harder contact this year, it has yet to materialize into better statistics for his opponents, in terms of batting average and slugging percentage. Where Rosenthal has been hurt this season is with his walks, which is among the few things he can fully control. He has already walked 17 batters this season, after walking just 20 all of last season in 45 more innings. Rosenthal’s BB/9 has actually more than doubled from it 2.39 mark in 2013, as it sits at 4.99 thus far in 2014. As a result of his lost control, Rosenthal’s opponent’s OBP has shot up from .289 last year to .321 this season, despite a lower opponent’s batting average. Rosenthal also tends to lose his control at the wrong times, as he has walked 10 of his 17 batters in high leverage situations, while pitching just 2/3 of an inning more in those situations than low and medium leverage situations.

Even more concerning, he has walked 11 batters with men on base, leading to an opponent’s OBP of .409 with men already on base. Rosenthal’s struggles from the stretch seem to be related to his rushing to the plate. Based purely on the times I have seen him throw, he has a propensity to rush to the plate when pitching from the stretch, which does not give his throwing arm time to get up into position. This tendency for his arm to lag leaves him susceptible to throw the ball up, which is where most of his pitches are missing. With his struggles from the stretch, it is no wonder Rosenthal’s Left on Base% has dropped 5.3% from last season.

This is not an article to criticize Rosenthal and call for his removal from the closer role, but rather to point out where Rosenthal needs to improve. His ERA is certainly high for a closer, but because he is not allowing many hits, he can easily improve his season by being more aggressive in the strike zone. A pitcher with as much stuff as Rosenthal should not be afraid to pitch within the zone. Working ahead in the count will also work to prevent the solid contact that has increased this year. Rosenthal shows the importance of throwing strikes, as he has gone from one of the premier late-inning arms in the game to a pitcher with the 114^th best ERA of qualified relievers. Even in terms of FIP, Rosenthal ranks 51^st among qualified relievers. While these are certainly discouraging trends, if he can return to throwing strikes the way he did in his previous two opportunities in the Majors, he will be able to reverse these trends.

Tip: Don’t understand an acronym? Just click on it and it will take you to the corresponding FanGraphs glossary of terms.

Watching the final game of the Yankees – A’s series last week, which featured one of the game’s finest pitchers in Masahiro Tanaka, I had a thought during Josh Donaldson’s final at-bat against the Japanese hurler. After he struck out to finish 0-3 against Tanaka, my mind traveled back to the ALDS game 5s of the past two years. It’s no secret the A’s crashed out against a dominant Verlander in both 2012 & 2013, just like it’s no secret that Josh Donaldson was almost entirely absent in both of those very important games: 1-7, 0 BB, 3 K (with all 3 of those Ks coming in 2013′s game 5). 7 at-bats is obviously an incredibly small sample size, especially for an up-and-coming player getting his first taste of the postseason. However, for what Donaldson means to the A’s, there were certainly quiet rumblings of disappointment among the fan base.

Verlander is very good; it seems he’s especially good in high leverage situations when his team needs him. Josh Donaldson is also very good, posting 7.7 WAR last year in 158 games. This year, Donaldson has been even better, posting 3.4 WAR through just 62 games and asserting himself in the conversation of the best overall players in baseball. A sizable portion of that WAR comes from the plus defense he plays, but his bat is what he’s known for: since getting called up from the minors on August 14th, 2012 (the point at which his consensus “breakout” started), he’s batted .291/.377/.509 with a wRC+ of 148 (which means that Donaldson has created 48% more runs than a league average player). Only one player has higher WAR in 2013 and 2014 combined (Mike Trout), and only nine other players have higher wRC+. Josh Donaldson is an elite defensive and offensive player by many metrics.

After watching Donaldson’s at-bats against Tanaka, I started wondering how he fares against other elite pitchers in the game, having an unproven hunch he might struggle against them. We know that most everyone struggles against elite pitching, as that is generally the very definition of elite pitching; however, there’s the larger question of just how much impact elite pitching has on hitting statistics, and how elite hitters fare against elite pitching. One might assume that elite hitters are better able to succeed against elite pitching. Looking at Donaldson’s statistics, you wouldn’t think that is the case.

Pulling data from the start of the 2013 season, I’ve identified some of the “elite” pitching that Donaldson has gone up against. I’ve tried to identify pitchers he has faced most often in terms of plate appearances – fortunately (for our sake at least), those pitchers he’s seen most often are also elite arms in his division, like Felix Hernandez, Yu Darvish, and Hisashi Iwakuma. All pitchers on this list are ranked in the top 15 for xFIP for 2013-2014 (minimum 160 innings pitched) with the exception of Verlander (77th) & Lester (41st). I’ve included them as their FIP rankings are in the top 40, and because I’ve already used Verlander as a benchmark above. Here are Donaldson’s statistics for 2013 & 2014 against some of the best arms in the game, with his total statistics overall in the final line for reference:

These figures don’t include the 2012 and 2013 postseason series against the Tigers, which actually helps Donaldson’s case. However, let’s get the small sample size disclaimer out of the way before we continue. 113 plate appearances is about a month’s worth of full-time hitting statistics, which is not a tremendous sample to draw from, but not insubstantial either. What’s clear from these numbers is that Donaldson really struggles against elite arms, posting awful strikeout and walk rates and severely depressed average, on base, and power numbers (just 7 extra base hits in 104 at-bats).

One larger question we have to answer is whether Donaldson’s drop in production vs. elite pitching is congruent with the standard drop of production any hitter would expect when going up against this level of competition. To find that out, I combined all of the batting-against statistics for these 12 pitchers for all of 2013 & 2014, a total of 12,534 plate appearances, which gives us a “league average” line vs. these pitchers. The findings? These elite arms are really good. Big surprise, right? In fact, the league strikeout and walk rates against these pitchers is very close to Donaldson’s rates, with the walk rate exactly the same. Here are Donaldson’s numbers vs. the elite pitchers, his overall numbers vs. all competition, and then the league average line vs. the elite arms:

Even though we’re looking at the best pitchers in baseball, these statistics were still a bit surprising to me, as these league-wide walk and strikeout rates are abysmal from a hitter’s perspective. How does Donaldson’s slash line compare to the league average? Again, let’s take a look:

We know that Donaldson’s poor BB and K rates fit tidily within the standards of the league line, as seen in the first graph, but his slash lines tell us that he’s been far worse than the rest of the league against these elite pitchers in the limited plate appearances we’re looking at. Shouldn’t we expect a player of his offensive caliber to fare better than league average against this level of competition?

The answer is not necessarily. Donaldson’s approach at the plate has a large bearing on the fact that he struggles against elite pitching. He is not a contact hitter, posting below average marks in swinging strike percentage, contact percentage, and Z-Contact percentage. In fact, he has changed his approach over the past calendar year specifically to try to hit more home runs, resulting in an almost 5% spike in his strikeout rate from 2013 to 2014 (16.5% to 21.1%), but also increasing his home run per fly ball rate by almost 7 points to 17.3%, an elite mark for someone who plays half of their games in one of the most pitching friendly ballparks in baseball. Coupled with an increase in his walk rate, Donaldson’s run creation output has benefited from Chili Davis’ hitting instruction, sitting on pitches he is more likely to drive and swinging hard at the expense of a lower average and higher strikeout rate. Donaldson batted .301 in 2013 with an inflated BABIP (.333), but with his change of approach, he projects somewhere in the .270 range moving forward.

Donaldson is the profile of a hitter that may be more apt to struggle against the elite pitching in the league due to the simple fact that elite pitchers tend to have makeups consisting of low walks and high strikeouts. For example, against “Power” pitchers (pitchers that are in the top third of the league in strikeouts plus walks), Donaldson has a career line of .210/.316/.356, showing that he struggles with pitchers who have strikeout potential, whether elite or not. He’s not alone in being a top offensive player that struggles against power pitching in relation to his overall performance: the benevolent baseball god Mike Trout slashes a fairly pedestrian (for him) .269/.379/.473 against the high strikeout arms.

The most important point to remember when looking at these statistics is that Josh Donaldson is currently one of the best players in baseball, regardless of his past performance versus elite pitching. He is a player that has enjoyed only a year and a half of sustained high-level performance and is continuing to make adjustments in hopes of greater success, which could completely alter his future at bats versus these elite arms I’ve highlighted. However, my gut tells me he may always struggle with these pitchers due to his approach at the plate, which trades contact for power – an Oakland A’s team-wide trait. It bears further scrutiny in the future for his potential playoff success, as he will obviously face more elite pitching in October when the average arms have gone home for the offseason. Will Donaldson and the Oakland A’s home run-centric approach carry them to a deep playoff run against the best arms in the game? Fortunately for us, it looks like we’re going to find out.

Wondering about the two home runs he hit off of Bumgarner and Sale? EXTRA CREDIT BONUS FREE BASEBALL GIFS!

Off Madison Bumgarner: May 27, 2013, 2-0, no out, 1 on, 4-seam fastball:

Off Chris Sale: June 8th, 2013, 1-1, 1 out, 3 on (oppo taco all the way), 2-seam fastball:

Right now Eric Hosmer is the worst base runner of 2014 by a decent margin over Adam Dunn.  This makes very little sense, well not the Adam Dunn part, but Eric Hosmer is an athletic player and not your traditional base clogging oaf.  For his career, Hosmer’s Spd rating is 4.4, which says he is right at average for speed overall.  Last year he was 11 of 15 on stolen base attempts and the year before he stole 16 bags in 17 tries.  You expect that the best base runners are fast and the worst are slow, and generally that seems to be true.  When it is not true though, there is an interesting difference in the groups.

I went out to look for two groups.  The first was a group of really fast players who had bad years on the base paths.  The cut-offs for them were an Spd rating of 7 or higher, considered excellent speed, and a negative Bsr and were therefore a liability on the bases despite their speed.  For Spd below average is 4.0, so for the second group I looked for players below that who managed to have great base running years, anything above 5 Bsr.

The total sample went back through the 1980 season for batting title qualified players, which included 5049 player years.  The group of fast players who had bad base running looks like this:

There are a lot of good players in there, and one legitimate superstar in Sammy Sosa.  You will notice that none of them repeated the feat either.  Only once in their careers did they manage to have the combo of excellent speed with negative base running value.  Most of them were just not very good base runners consistently and happened to have an especially bad year to get on the list.  Luis Castillo and Lance Johnson were decent on the base paths most years and had a few really good seasons.  Rudy Law had a Bsr of 10.6 the year before, by far the best season of any of these players, so I don’t know what happened in 1984.

Now to the group of over achieving base runners.  It is a small and accomplished list:

Again, no players repeated the feat, but this time the caliber of player jumps up.  Albert Pujols is an all time great.  Scott Rolen is a likely Hall of Famer, and Joe Mauer will probably get there.  The only one that isn’t likely to get to Cooperstown is Ryan Zimmerman, but it isn’t inconceivable that he could get there if he can get healthy and put some good seasons up through his 30s.  Even when they were young, none of these guys were particularly fast though Rolen managed to get a Spd of 6.1 once.  For all of these guys you can Google and quickly find things about their great work ethic and/or leadership qualities, so maybe only the truly diligent can make up for their lack of speed by being hard working students of the game.

Madison Bumgarner has pitched like a top tier starter since he appeared on a big league mound in 2009. While his strikeout rate—8.46 career K/9—has always been above average, something has clicked with the big lefty this season, launching him into legitimate No. 1 starter territory. Through 13 starts this season, Bumgarner has a K/9 of 10.04, ranking third in the NL behind only Stephen Strasburg and Zack Greinke.

What’s most fascinating about Bumgarner is that he’s dominating hitters basically with two pitches, both of which—the fourseamer and the cutter—are high velocity pitches. PITCHf/x has Bumgarner throwing a fourseamer 41.19% of the time and a cutter—which FanGraphs lists as a slider—37.22% of the time. For the sake of simplicity, I will refer to the latter pitch as a cutter.

This season, the fourseamer has been especially effective for Bumgarner. Batters are swinging at the pitch at a higher rate (45%) than any previous season, and they are making contact with less frequency, as the 29.50% whiffs per swing shows. In 2013 batters whiffed at the pitch 26.69% of the time when swinging; between 2009-2012, the rate was never higher than 19.81%.

The cutter, of which the usage rate has dropped almost 2% since 2012, has seen similar results as the fourseamer. Hitters swing at the cutter 57.25% of the time and whiff with 24.33% of those swings.

A big reason for the diminished contact rate is the fact that Bumgarner is throwing his pitches in strike zone less often than in years past. His in-zone rate is just 39.63%, the only time in his career that it’s been under 40%. When hitters swing at pitches out of the strike zone—which they do 36.01% of the time, a career high—they whiff 37.7% of the time. When swinging at pitches in the zone, the whiff rate is 16.75—a rate that surpasses those in any of his previous seasons.

When Bumgarner gets hitters into two-strike counts, his approach stays the same for the most part. In those counts, he throws his fourseamer 41.41% of the time and his cutter 37.5% of the time, both numbers just slightly above the overall usage in any count. The one aspect that changes in two-strike counts is Bumgarner’s usage of his curveball. Overall, he throws the pitch 11.93% of the time. In two-strike counts, the usage rate jumps up to 17.5% and batters swing at it 55.84% of the time. The result is a 20.78% whiff rate, highest of all Bumgarners pitches in two-strike counts (16.23% fourseamer, 14.55% cutter).

Another aspect of Bumgarner’s dominance this year has been his ability to fight back and limit damage when behind in the count. His fourseamer and cutter have been the main reason for this. When behind in the count 1-0, Bumgarner has thrown the cutter 43.57% of the time and the fourseamer 35.71%. Here’s what happens with those pitches in 1-0 counts:

Between the two pitches, over half of the swings result in a foul ball. Add in the whiff rates and Bumgarner finds himself back in the drivers seat more often than not after falling behind.

What about the 1-0 counts that get to 2-0? More often than not—62.22% of the time—he throws the cutter while throwing the fourseamer 31.11% of the time. Here are the results:

Again, more often than not, Bumgarner is able to fight through being in an unfavorable count. Once he gets to 2-1, he continues to attack hitters with the fourseamer (35.71%) and the cutter (54.29%). Here’s what happens:

In addition to these numbers, Bumgarner’s current walk rate of 2.01 BB/9 further shows that he doesn’t often lose hitters when falling behind. Rather, he uses his fourseamer and cutter to get himself back into a favorable count and is thus putting hitters away at a career-high rate.

On February 13, 2012, the Oakland A’s shocked the baseball world by signing Cuban outfielder, Yoenis Cespedes. They never make big money signings but this time they did, signing him to a four year, $36 million deal. That season, he seemingly led the Oakland A’s to their surprising division title and was thought to be a major candidate for the MVP award for leading the A’s offensive charge. Had it not been for some player on the Los Angeles Angels, I think his name is Mike Trout, winning the Rookie of the Year, Cespedes would have been an easy pick for that award.

During that same season, another Cuban outfielder was signed by a Major League team. This time it was the Los Angeles Dodgers on June 28, 2012 signing 21 year old Yasiel Puig to a seven year, $42 million contract. Puig played in rookie ball and A ball in 2012 before making his Major League debut with the Dodgers in 2013. From that moment on, Cespedes was seemingly forgotten and the birth of “Puigmania” began. Puig, like Cespedes did for the Athletics, led the Los Angeles Dodgers offense in his 104 games with them to a division title. Puig too, lost out on Rookie of the Year but he certainly did provide a strong case for that award.

And this year, Puigmania rolls on but another Cuban slugger has come in as well. Jose Abreu of the Chicago White Sox (on a six year, $68 million contract) has burst onto the scene, making the White Sox one of the story teams this year. And while it is likely that the White Sox won’t make a run like the A’s or Dodgers did, Abreu certainly will make his strong case for Rookie of the Year.

Each of these players are great, all of them with phenomenal talent. One question that has been brought up with the recent emergence of Abreu is which Cuban player is better. Judging everyone based on the stats that they have put up and seeing how each one stacks up by the common scouting method called, “the five tools,” (the five tools being hitting for power, hitting for contact, speed, arm strength, and fielding ability). I will try to present a case for which one of them is truly the best. Now granted, both Cespedes and Puig have had more playing time than Abreu, but that will be taken into account when judging them.

Hitting for Power:

This, to me, is one of the most interesting of the five tools to compare the players because each of them has quite a lot of power. Cespedes has yet to post up a Major League season where he has not hit at least 20 homers (he looks to be on pace for that number this year again with his 12 homers in 55 games so far), Puig hit 19 home runs in only 104 games last year, and Jose Abreu has done nothing but knock the cover off the ball so far this year hitting 17 homers in a mere 47 games. But as many people who go on this website I’m sure know, there is more to power than just hitting home runs. Extra bases count. Doubles, triples, home runs, all contribute to one’s ability to hit for power.

Looking at ISO, Abreu is far and away the leader in this category. His .353 ISO leads Cespedes (.218) and Puig (.232) by a very wide margin. But since his .353 ISO is in a limited playing time of only 47 games, I have decided to measure the ISO through the first 47 games of both the careers of Cespedes and Puig. Cespedes’ ISO through his first 47 games was .341 and Puig’s was .310. While I can see Abreu’s power diminishing somewhat from this extraordinary power number, I can’t see Puig and Cespedes quite matching his power hitting ability (even though Cespedes really punished the baseball in the 2013 Home Run Derby).

Edge: Jose Abreu

Hitting for Contact:

This too is an interesting statistic to judge because there are so many numbers to indicate contact hitting ability. One could look at batting average to see who the best is but of course that could easily be countered by BABIP. For example, Puig has the highest batting average of the three, hitting .327 but his BABIP (.385) is over .100 points higher than both of the other two. The other two players have BABIP numbers that are remarkably close to their actual batting average. Cespedes’ batting average is at .262 with a .261 BABIP while Abreu’s batting average is at .266 but his BABIP is at .276. But those numbers are just how good someone is at letting the ball hit the ground and reach base with a hit, not necessarily making contact with the ball.

Each player is good at making contact with the baseball. One would think that because Puig has the highest batting average, he is the best at making contact but that is actually not true. In fact, of the three players, he makes contact the least of all of the players. He just happens to hit the ball in such a way that he gets a hit more often than the other two do. In terms of overall contact%, Cespedes makes the most contact with his 74.8% contact rate, Abreu comes after him with 70.9% contact, and Puig is third with 69.9%. When the ball is inside the strike zone, Abreu is slightly better than Cespedes with his 83.3% vs. Cespedes 82.5% (Puig is also fairly close at making contact with the ball 81.6% of the time when it is in the strike zone). When the ball is outside the strike zone, Cespedes is once again the contact king with a contact rate of 64%, Abreu is trailing far behind with only 55.5%, and Puig is again in third with 53.3%. Now granted, Puig’s numbers are improving, but so are Cespedes’ numbers and Abreu is still only in his first season with plenty of time to improve.

Edge: Yoenis Cespedes

Speed (Base running ability):

If anyone is expecting Abreu to be the best in terms of speed and overall base running ability, I’m going to tell you right now to not get your hopes up. Abreu isn’t awful in terms of base running but he is far from great. This is basically between Cespedes and Puig. With more time under his belt, Cespedes does have more stolen bases but they are both equal in caught stealing. Cespedes has stolen a total of 23 bases and been thrown out 12 times (a 66% success rate) while Puig has stolen 16 bases and been thrown out 12 times (57% success rate). Abreu has not attempted a steal yet. Then when looking at actual speed in terms of miles per hour, Cespedes has been clocked at a high of 19.4 mph while Puig has been clocked around 20 mph so Puig has a slight edge in terms of raw speed but not necessarily an overwhelming advantage. To settle the divide, a look at the sabermetrics should settle who is better.

To say the least, Yasiel Puig is reckless running on the bases. He runs very fast but he often runs into outs. So needless to say his BsR is hurting. He has a career -5.2 BsR with his low being in 2013 when he had a -4.2 number and his high being this year at -0.9. Yoenis Cespedes is much smarter on the bases. He doesn’t run himself into outs as frequently as Puig does and so his BsR career number sits at 2.9 with a low of 0.6 in 2013 and a high of 1.4 in 2012. And if that isn’t enough to show that Cespedes is better, his career Spd sits at 5.3 while Puig’s is at 4.8. For the record, Abreu’s Spd is at 2.8 and his BsR is at -0.7 so like I said, he isn’t bad but he just isn’t a very fast guy.

Edge: Yoenis Cespedes

Fielding Ability:

Defensive ability is always thought to be one of the toughest things to measure because there is no real perfect way to calculate it. Another thing making it difficult is that while outfielders Puig and Cespedes basically play the same position, Abreu does not. Since he is the only first baseman in this mix of players, we will look at his numbers first.

When stacking him up with the other first basemen, Abreu really doesn’t seem half bad. In terms of UZR, Abreu is 7th among all first basemen with at least 300 innings played with his 2.2 UZR which is slightly above average. In terms of Defensive Runs Saved, Abreu is 24th among all first basemen with at least 300 innings played with his -4 which is deemed below average. So by no means is he bad, he just isn’t great. Now in the outfield, Puig and Cespedes are different stories.

Puig and Cespedes are both very good defensive outfielders. In his career, Puig has been better defensively posting up a career UZR of 3.5 while Cespedes has put up a 2.7 number. When it comes to Defensive Runs Saved, Puig again holds an advantage with his +7 mark to Cespedes -1. All in all, while Abreu is a decent first baseman, Puig is a very good defensive outfielder (not deserving of a gold glove but none the less is the best defensive player of these three).

Edge: Yasiel Puig

Arm Strength:

Defensive ability isn’t just catching and fielding the ball, it is also having the arm to make big plays. But it is tough to tell who is best because there aren’t many numbers to point to actual arm strength. Puig has some of the more highlight reel arm throws, in terms of both good throws and bad throws, and so his arm has garnered the most attention of the three. Abreu, being a first baseman generally just has to do underhand flips to the pitcher covering the bag at first and occasionally start a double play feed so his arm is really not tested as much. So again, Abreu is eliminated from the conversation almost before it started. It is again between Puig and Cespedes.

Like I said, Puig has made some of the more highlight reel throws but him being in Los Angeles and in the center of a massive media hub might have some effect on that. Cespedes has made some very strong throws but being in Oakland where not much media attention is seen, he doesn’t get as much time on the highlight reels. Still, the arm of Cespedes is not to be denied. Again, he has played in more innings than Puig has so it would be expected that he would have more outfield assists than Puig, and he does. He has 25 assists, 13 more assists than Puig’s 12. He also has two more throwing errors with three compared to Puig’s 1. But the numbers show that in spite of those throwing errors, Cespedes rARM (Outfield Arms Runs Saved) is much higher, being a 12 as opposed to Puig’s 4. The other statistic to rate an outfielder’s arm is the ARM (Outfield Arm Runs), another stat designed to show runs saved based on throwing ability, that still has Cespedes higher with 13.8 to Puig’s 4.1. So sure Puig has made some good throws, but his arm is not better than that of Yoenis Cespedes.

Edge: Yoenis Cespedes

By judging each player by the scouting five tools, Cespedes does have an edge both in actual scouting reports and by the numbers. Cespedes has the best arm, base running ability, and contact ability while Puig is the best fielding and Abreu is the best power hitter. If only judging by the five tools, Cespedes appears to be the better player but when looking in terms of actual production, Puig has done the best over his career to this point. Posting a 7.2 WAR, Puig matches Cespedes’ exact same WAR in 160 fewer games. Puig also has the highest wOBA of them all (Puig has .415, Cespedes has .344, and Abreu has .396) and the highest wRC+ of the three (Puig with 172, Cespedes with 120, and Abreu with 151). Puig is also the youngest of the three at only age 23 while Cespedes is 28 and Abreu is 27 so there is more time and room for improvement.

And in conclusion, this article would not be complete if I also did not compare the bat flips of the three. So here they are:

Puig:

Cespedes:

And Abreu’s bat drop (I’m sure that he is working on his bat flip though):

Before his June 6th appearance, Dellin Betances had thrown his knuckle curve 255 times, and it had amassed a value of 8 runs above average(according to FanGraphs), but that is not the point of this post. Betances throws the knuckle curve a lot (48% of the time), batters can’t hit it (74% zone contact, 20% out of zone contact!, for a total contact rate of 42%), and when they do it’s very weakly (15% line drives, 55% ground balls, 10% popups, 0 home runs). It’s impressive  but not what I’m interested in.

Here’s a hint, in gif form

Batters take the pitch for a called strike all the time. They swing at the curve in the strike zone a measly 29.3% of the time. This is where it gets really crazy, they swing at it out of the strike zone 36% of the time! I’ll let that sink in. This may sound hyperbolic (it’s actually hypergeometric) but a literal blind person would be expected to do better than these pros have.  There is an 83.96% chance swinging at random would beat current major league performance.

For a little math aside, you can think of this like one of those marble problems. You have a jar filled with 116 red marbles (pitches in the strike zone) and 139 green marbles (pitches outside the zone), and you pick 84 (swing at) at random. What are the chances that out of the 84 marble you chose more than 34 are red (in the strike zone)?  You can determine the probability of picking more than 34 red marbles using a hypergeometric distribution.

How is it even possible to make major league players look so confounded (see gif above)?

The worst approach at the plate (other than sabotaging yourself) is just swinging at random.  There is an 84% chance that the approach of  these players is worse than random. A possible explanation is hitters are actually trying to swing at more of the pitches outside the strike zone. This sounds like a really stupid strategy, because it is. The only reason hitters should do this is if they were able to crush the knuckle curve when it’s outside the strike zone. Hitters haven’t crushed any of the knuckle curves (an anemic .029 ISO), and they are barely ever hitting it when it’s outside the zone. It makes you wonder if Betances is using Jedi mind tricks.

Assuming that Betances is not a Jedi (if he was wouldn’t he use his powers on his fastball as well?), then something else has to be going on. From the batter’s reaction you can tell that the batter thought the pitch was going to hit him. So, maybe the batters are just so worried about the 95MPH heater that they are getting surprised by the knuckle curve? Still Betances threw the pitch 48% of the time; it’s not a surprise pitch.  Whatever it Betances is doing is definitely making hitters look dumbfounded. I don’t know of any other pitch that gets a higher swing rate out of the zone than in it (if you can think of a pitch that gets more swings out of the zone than in leave it in the comments).

Thanks to Pitcher Gifs for this great gif.

Also and unrelated useless fact, hitter have exactly a .000 wOBA on plate appearances ending with DB’s knuckle curve.

This is definitely something to keep an eye on and look into further.  What makes a pitch look like a ball to the batter when its in the strike zone and look like its going to be a strike when it is out of the zone. This is the only pitch I know of that can do both.

I challenge any reader to find a pitch thrown more than 200 times that has a higher O-Swing% than Z-swing%, and leave the name of the pitcher and the pitch in the comments.

All stats are from FanGraphs PITCHf/x

This article was originally posted at GWRamblings.

The MLB draft is coming up and with any luck I’ll get this posted by Thursday and take advantage of web traffic. I can hope! (ed. note: nope) Anyway, Tuesday on FanGraphs I read a fascinating portrayal of the draft process, laying out the nuts and bolts of how organizations scout for the draft. The piece, written by Tony Blengino (whose essays are rapidly becoming one of my favorite parts of this overall terrific baseball site), describes all the behind the scenes work that happens to prepare a major league organization for the Rule 4 draft. Blengino described the dedication scouts show in following up on all kinds of prospects at the college and high school levels, what they do, how much they need to travel, and especially how much ground they often need to cover to try and lay eyes on every kid in their area.

One neat insight for me was Blengino’s one-word description of most scouts as entrepreneurs. You could think of them almost as founders of a startup, with the kids they scout as the product the scouts are trying to sell to upper layers of management in the organization. As such, everything they can do to get a better handle on a kid’s potential can feed into the pitch to the scouting director.

I respect and envy scouts’ drive to keep looking for the next big thing, the next Jason Heyward or Mike Trout. As Blengino puts it, scouts play “one of the most vital, underrated, and underpaid roles in the game.” While one might make the argument that in MLB, unlike the NFL or NBA, draft picks typically are years away from making a contribution and therefore how important can draft picks be?, numerous studies have shown that the draft presents an incredible opportunity for teams in building and sustaining success. In fact, given that so much of an organization’s success hinges on figuring out which raw kids will be able to translate tools and potential into talent, one could (and others have)  made the argument that scouting is a huge potential market inefficiency for teams to exploit. Although I’ll have a caveat later. But in any case, for a minor league system every team wants to optimize their incoming quality because, like we say in genomic data analysis, “garbage in, garbage out.”

As I was reading this piece, I started thinking about ways to try and create more efficiencies. And I started thinking about Big Data.  Read the rest of this entry »

I’ve decided to break this final section in half and address the early development of run estimation statistics first, and then examine new ways to make these estimations next week. In Part 1, we examined the early development of batting statistics. In Part 2, we broke down the weaknesses of these statistics and introduced new averages based on “real and indisputable facts.” In Part 3, we will examine methods used to estimate the value of batting events in terms of their fundamental purpose: run creation.

The two main objectives of batters are to not cause an out and to advance as many bases as possible. These objectives exist as a way for batters to accomplish the most fundamental purpose of all players on offense: to create runs. The basic effective averages presented in Part 2 provide a simple way to observe the rate at which batters succeed at their main objectives, but they do not inform us on how those successes lead to the creation of runs. To gather this information, we’ll apply a method of estimating the run values of events that can trace its roots back nearly a century.

The earliest attempt to estimate the run value of batting events came in the March 1916 issue of Baseball Magazine. F.C. Lane, editor of the magazine, discussed the weakness of batting average as a measure of batting effectiveness in an article titled “Why the System of Batting Averages Should be Changed”:

“The system of keeping batting averages…gives the comparative number of times a player makes a hit without paying any attention to the importance of that hit. Home runs and scratch singles are all bulged together on the same footing, when everybody knows that one is vastly more important than the other.”

To address this issue, Lane considered the fundamental purpose of making hits.

“Hits are not made as mere spectacular displays of batting ability; they are made for a purpose, namely, to assist in the all-important labor of scoring runs. Their entire value lies in their value as run producers.”

In order to measure the “comparative ability” of batters, Lane suggests a general rule for evaluating hits:

“It would be grossly inaccurate to claim that a hit should be rated in value solely upon its direct and immediate effect in producing runs. The only rule to be applied is the average value of a hit in terms of runs produced under average conditions throughout a season.”

He then proposed a method to estimate the value of each type of hit based on the number of bases that the batter and all baserunners advanced on average during each type of hit. Lane’s premise was that each base was worth one-fourth of a run, as it takes the advancement through four bases for a player to secure a run. By accounting for all of the bases advanced by a batter and the baserunners due to a hit, he could determine the number of runs that the hit created. However, as the data necessary to actually implement this method did not exist in March 1916, the work done in this article was little more than a back-of-the-envelope calculation built on assumptions concerning how often baserunners were on base during hits and how far they tended to advance because of those hits.

As he wanted to conduct a rigorous analysis with this method, Lane spent the summer of 1916 compiling data on 1,000 hits from “a little over sixty-two games”[i] to aid him in this work. During these games, he would note “how far the man making the hit advanced, whether or not he scored, and also how far he advanced other runners, if any, who were occupying the bases at the time.” Additionally, in any instance when a batter who had made a hit was removed from the base paths due to a subsequent fielder’s choice, he would note how far the replacement baserunner advanced.

Lane presented this data in the January 1917 issue of Baseball Magazine in an article titled similarly to his earlier work: “Why the System of Batting Averages Should be Reformed.” Using the collected data, Lane developed two methods for estimating the run value that each type of hit provided for a team on average. The first method, the one he initially presented in March 1916, which I’ll call the “advancement” method,[ii] counted the total number of bases that the batter and the baserunners advanced during a hit, and any bases that were advanced to by batters on a fielder’s choice following a hit (an addition not included in the first article). For example, of the 1,000 hits Lane observed, 789 were singles. Those singles resulted in the batter advancing 789 bases, runners on base at the time of the singles advancing 603 bases, and batters on fielder’s choice plays following the singles advancing to 154 bases – a total of 1,546 bases. With each base estimated as being worth one-fourth of a run, these 1,546 bases yielded 386.5 runs – an average value of .490 runs per single. Lane repeated this process for doubles (.772 runs), triples (1.150 runs), and home runs (1.258 runs).

This was the method Lane first developed in his March 1916 article, but at some point during his research he decided that a second method, which I’ll call the “instrumentality” method, was more preferable.[iii] In this method, Lane considered the number of runs that were scored because of each hit (RBI), the runs scored by the batters that made each hit, and the runs scored by baserunners that reached on a fielder’s choice following a hit. For instance, of the 789 singles that Lane observed, there were 163 runs batted in, 182 runs scored by the batters that hit the singles, and 16 runs scored by runners that reached on a fielder’s choice following a single. The 361 runs “created” by the 789 singles yielded an average value of .457 runs per single. This method was repeated for doubles (.786 runs), triples (1.150), and home runs (1.551 runs).

In March 1917, Lane went one step further. In an article titled “The Base on Balls,” Lane decried the treatment of walks by the official statisticians and aimed to estimate their value. In 1887, the National League had counted walks as hits in an effort to reward batters for safely reaching base, but the sudden rise in batting averages was so off-putting that the method was quickly abandoned following the season. As Lane put it:

“…the same potent intellects who had been responsible for this wild orgy of batting reversed their august decision and declared that a base on balls was of no account, generally worthless and henceforth even forever should not redound to the credit of the batter who was responsible for such free transportation to first base.

The magnates of that far distant date evidently had never heard of such a thing as a happy medium…‘Whole hog or none’ was the noble slogan of the magnates of ’87. Having tried the ‘whole’ they decreed the ‘none’ and ‘none’ it has been ever since…

‘The easiest way’ might be adopted as a motto in baseball. It was simpler to say a base on balls was valueless than to find out what its value was.”

Lane attempted to correct this disservice by applying his instrumentality method to walks. Over the same sample of 63 games in which he collected information on the 1,000 hits, he observed 283 walks. Those walks yielded six runs batted in, 64 runs scored by the batter, and two runs scored by runners that replaced the initial batter due to a fielder’s choice. Through this method, Lane calculated the average value of a walk as .254 runs.[iv]

Each method Lane used was certainly affected by his limited sample of data. The proportions of each type of hit that he observed were similar to the annual rates in 1916, but the examination of only 1,000 hits made it easy for randomness to affect the calculation, particularly for the low-frequency events. Had five fewer runners been on first base at the time of the 29 home runs observed by Lane, the average value of a home run would have dropped from 1.258 runs to 1.129 runs using the advancement method and from 1.551 runs to 1.379 runs using the instrumentality method. It’s hard to trust values that are that so easily affected by a slight change in circumstances.

Lane was well aware of these limitations, but treated the work more as an exercise to prove the merit of his rationale, rather than an official calculation of the run values. In an article in the February 1917 issue of Baseball Magazine titled, “A Brand New System of Batting Averages,” he notes:

“Our sample home runs, which numbered but 29, were of course less accurate. But we did not even suggest that the values which were derived from the 1,000 hits should be incorporated as they stand in the batting averages. Our labors were undertaken merely to show what might be done by keeping a sufficiently comprehensive record of the various hits…our data on home runs, though less complete than we could wish, probably wouldn’t vary a great deal from the general averages.”

In the same article, Lane applied the values calculated with the instrumentality method to the batting statistics of players from the 1916 season, creating a statistic he called Batting Effectiveness, which measured the number of runs per at-bat that a player created through hits. The leaderboard he included is the first example of batters being ranked with a run average since runs per game in the 1870s.

Lane didn’t have a wide audience ready to appreciate a run estimation of this kind, and it gained little notoriety going forward. In his March 1916 article, Lane referenced an exchange he had with the Secretary of the National League, John Heydler, concerning how batting average treats all hits equally. Heydler responded:

“…the system of giving as much credit to singles as to home runs is inaccurate…But it has never seemed practicable to use any other system. How, for instance, are you going to give the comparative values of home runs and singles?”

Seven years later, by which point Heydler had become President of the National League, the method to address this issue was chosen. In 1923, the National League adopted the slugging average—total bases on hits per at-bat—as its second official average.

While Lane’s work on run estimation faded away, another method to estimate the run value of individual batting events was introduced nearly five decades later in the July/August 1963 issue of Operations Research. A Canadian military strategist, with a passion for baseball, named George R. Lindsey wrote an article for the journal titled, “An Investigation of Strategies in Baseball.” In this article, Lindsey proposed a novel approach to measure the value of any event in baseball, including batting events.

The construction of Lindsey’s method began by observing all or parts of 373 games from 1959 through 1960 by radio, television, or personal attendance, compiling 6,399 half-innings of play-by-play data. With this information, he calculated P(r|T,B), “the probability that, between the time that a batter comes to the plate with T men out and the bases in state B,[v] and the end of the half-inning, the team will score exactly r runs.” For example, P(0|0,0), that is, the probability of exactly zero runs being scored from the time a batter comes to the plate with zero outs and the bases empty through the end of the half-inning, was found to be 74.7 percent; P(1|0,0) was 13.6 percent, P(2|0,0) was 6.8 percent, etc.

Lindsey used these probabilities to calculate the average number of runs a team could expect to score following the start of a plate appearance in each of the 24 out/base states: E(T,B).[vi] The table that Lindsey produced including these expected run averages reflects the earliest example of what we now call a run expectancy matrix.

With this tool in hand, Lindsey began tackling assorted questions in his paper, culminating with a section on “A Measure of Batting Effectiveness.” He suggested an approach to assessing batting effectiveness based on three assumptions:

“(a) that the ultimate purpose of the batter is to cause runs to be scored

(b) that the measure of the batting effectiveness of an individual should not depend on the situations that faced him when he came to the plate (since they were not brought about by his own actions), and

(c) that the probability of the batter making different kinds of hits is independent of the situation on the bases.”

Lindsey focused his measurement of batting effectiveness on hits. To estimate the run values of each type of hit, Lindsey observed that “a hit which converts situation {T,B} into {T,B′} increases the expected number of runs by E(T,B′) – E(T,B).” For example, a single hit in out/base state {0,0} will yield out/base state {0,1}. If you consult the table that I linked above, you’ll note that this creates a change in run expectancy, as calculated by Lindsey, of .352 runs (.813 – .461). By repeating this process for each of the 24 out/base states, and weighting the values based on the relative frequency in which each out/base state occurred, the average value of a single was found to be 0.41 runs.[vii] This was repeated for doubles (0.82 runs), triples (1.06 runs), and home runs (1.42 runs). By applying these weights to a player’s seasonal statistics, Lindsey created a measurement of batting effectiveness in terms of “equivalent runs” per time at bat.

Like with Lane’s methods, the work done by Lindsey was not widely appreciated at first. However, 21 years after his article was published in Operations Research, his system was repurposed and presented in The Hidden Game of Baseball by John Thorn and Pete Palmer—the man who helped make on base average an official statistic just a few years earlier. Using play-by-play accounts of 34 World Series games from 1956 through 1960,[viii] and simulations of games based on data from 1901 through 1977, Palmer rebuilt the run expectancy matrix that Lindsey introduced two decades earlier.

In addition to measuring the average value of singles (.46 runs), doubles (.80 runs), triples (1.02 runs), and home runs (1.40 runs) as Lindsey had done, Palmer also measured the value of walks and times hit by the pitcher (0.33 runs), as well as at-bats that ended with a batting “failure,” i.e. outs and reaches on an error (-0.25 runs). While I’ve already addressed issues with counting times reached on an error as a failure in Part 2, the principle of acknowledging the value produced when the batter failed was an important step forward from Lindsey’s work, and Lane’s before him. When an out occurs in a batter’s plate appearance, the batting team’s expected run total for the remainder of the half-inning decreases. When the batter fails to reach base safely, he not only doesn’t produce runs for his team, he takes away potential run production that was expected to occur. In this way, we can say that the batter created negative value—a decrease in expected runs—for the batting team.

Palmer applied these weights to a player’s seasonal totals, as Lindsey had done, and formed a statistic called Batter Runs reflecting the number of runs above average that a player produced in a season. Palmer’s work came during a significant period for the advancement of baseball statistics. Bill James had gained a wide audience with his annual Baseball Abstract by the early-1980s and The Hidden Game of Baseball was published in the midst of this new appreciation for complex analysis of baseball systems. While Lindsey and Lane’s work had been cast aside, there was finally an audience ready to acknowledge the value of run estimation.

Perhaps the most important effect of this new era of baseball analysis was the massive collection of data that began to occur in the background. Beginning in the 1980s, play-by-play accounts were being constructed to cover entire seasons of games. Lane had tracked 1,000 hits, Lindsey had observed 6,399 half-innings, and Palmer had used just 34 games (along with computer simulations) to estimate the run values of batting events. By the 2000s, play-by-play accounts of tens of thousands of games were publically available online.

Gone were the days of estimations weakened by small sample sizes. With complete play-by-play data available for every game over a given time period, the construction of a run expectancy matrix was effectively no longer an estimation. Rather, it could now reflect, over that period of games, the average number of runs that scored between a given out/base state and the end of the half-inning, with near absolute accuracy.[ix] Similarly, assumptions about how baserunners moved around the bases during batting events were no longer necessary. Information concerning the specific effects on the out/base state caused by every event in every baseball game over many seasons could be found with relative ease.

In 2007, Tom M. Tango,[x] Mitchel G. Lichtman, and Andrew E. Dolphin took advantage of this gluttony of information and reconstructed Lindsey’s “linear weights” method (as named by Palmer) in The Book: Playing the Percentages in Baseball. Tango et al. used data from every game from 1999 through 2002 to build an updated run expectancy matrix. Using it, along with the play-by-play data from the same period, they calculated the average value of a variety of events, most notably eight batting events: singles (.475 runs), doubles (.776 runs), triples (1.070 runs), home runs (1.397 runs), non-intentional walks (.323 runs), times hit by the pitcher (.352 runs), times reached on an error (.508 runs). and outs (-.299 runs). These events were isolated to form an estimate of a player’s general batting effectiveness called weighted On Base Average (wOBA).

Across 90 years, here were five different attempts to estimate the number of runs that batters created, with varying amounts of data, using varying methods of analysis, in varying run scoring environments, and yet the estimations all end up looking quite similar.

Beyond the general goal of measuring the run value of certain batting events, each of these methods had another thing in common: each method was designed to measure the effectiveness of batters. Lane and Lindsey focused exclusively on hits,  the traditional measures of batting effectiveness.[xi] Palmer added in the “on base” statistics of walks and times hit by the pitcher, while also accounting for the value of those times the batter showed ineffectiveness. Tango et al. threw away intentional walks as irrelevant events when it came to testing a batter’s skill, while crediting the positive value created by batters when reaching on an error.

The same inconsistencies present in the traditional averages for deciding when to reward batters for succeeding and when to punish them for failing are present in these run estimators. In the same way we created the basic effective averages in Part 2, we should establish a baseline for the total production in terms of runs caused by a batter’s plate appearances, independent of whether that production occurred due to batting effectiveness. We can later judge how much of that value we believe was caused by outside forces, but we should begin with this foundation. This will be the goal of the final part of this paper.

[i] In his article the next month, Lane says explicitly that he observed 63 games, but I prefer his unnecessarily roundabout description in the January 1917 article.

[ii] I’ve named these methods because Lane didn’t, and it can get confusing to keep going back and forth between the two methods without using distinguishing names.

[iii] Lane never explains why exactly he prefers this method, and just states that it “may be safely employed as the more exact value of the two.” He continues, “the better method of determining the value of a hit is…in the number of runs which score through its instrumentality than through the number of bases piled-up for the team which made it.” This may be true, but he never proves it explicitly. Nevertheless, the “instrumentality” method was the only one he used going forward.

[iv] This value has often been misrepresented as .164 runs in past research due to a separate table from Lane’s article. That table reflected the value of each hit, and walks, with respect to the value of a home run. Walks were worth 16.4 percent of the value a home run (.254 / 1.551), but this is obviously not the same as the run value of a base on balls.

[v] The base states, B, are the various arrangements of runners on the bases: bases empty (0), man-on-first (1), man-on-second (2), man-on-third (3), men-on-first-and-second (12), men-on-first-and-third (13), men-on-second-and-third (23), and the bases loaded (123).

[vi] The calculation of these expected run averages involved an infinite summation of each possible number of runs that could score (0, 1, 2, 3,…) with respect to the probability that that number of runs would score. For instance,  here are some of the terms for E(0,0):

E(0,0) = (0 runs * P(0|0,0)) + (1 run * P(1|0,0)) + (2 runs * P(2|0,0)) + … + (∞ runs * P(∞|0,0))

E(0,0) = (0 runs * .747) + (1 run * .136) + (2 runs* .068) + … + (∞ runs * .000)

E(0,0) = .461 runs

Lindsey could have just as easily found E(T,B) by finding the total number of runs that scored following the beginning of all plate appearances in a given out/base state through the end of the inning, R(T,B), and dividing that by the number of plate appearances to occur in that out/base state, N(T,B), as follows:

E(T,B) = Total Runs (T,B) / Plate Appearances (T,B) = R(T,B) / N(T,B)

This is the method generally used today to construct run expectancy matrices, but Lindsey’s approach works just as well.

[vii] To simplify his estimations, Lindsey made certain assumptions about how baserunners tend to move during hits, similar to the assumptions Lane made in his initial March 1916 article. Specifically, he assumed that “runners always score from second or third base on any safe hit, score from first on a triple, go from first to third on 50 per cent of doubles, and score from first on the other 50 per cent of doubles.” While he did not track the movement of players in the same detail which Lane eventually employed, the total error caused by these assumptions did not have a significant effect on his results.

[viii] In The Hidden Game of Baseball, Thorn wrote that Palmer used data from “over 100 World Series contests,” but in the foreword to The Book: Playing the Percentages in Baseball, Palmer wrote that “the data I used which ended up in The Hidden Game of Baseball in the 1980s was obtained from the play-by-play accounts of thirty-five World Series games from 1956 to 1960 in the annual Sporting News Baseball Guides.” I’ll lean towards Palmer’s own words, though I’ve adjusted “thirty-five” down to 34 since there were only 34 World Series games over the period Palmer referenced.

[ix] The only limiting factor in the accuracy of a run expectancy matrix in the modern “big data” era is in the accuracy of those who record the play-by-play information and in the quality of the programs written to interpret the data. Additionally, the standard practice when building these matrices is to exclude all data from the home halves of the ninth inning or later, and any other partial innings. These innings do not follow the standard rules observed in every other half-inning, namely that they must end with three outs, and thus introduce bias into the data if included.

[x] The only nom de plume I’ve included in this history, as far as I’m aware.

[xi] Lane didn’t include walks in his Batting Effectiveness statistic, despite eventually calculating their value.