For those of you who don’t know, I’ve been a Washington Nationals fan since the team moved to D.C. in 2005. One of my favorite players to watch—though he was with the team for just two seasons—was Adam Dunn. The 6’6, 250 pound lefty masher was an incredible physical specimen who could hit home runs like nobody’s business. Unfortunately, the only thing he did better than hit homers was strike out. He’s 36th on the MLB all-time home run list with 462, and 3^{rd} on the all-time strikeout list with 2,379. Because of his high strikeout numbers and sub par batting average on balls in play, he sported a lifetime batting average of just .237.

I bring up Adam Dunn because he’s a prime example of the baseball truism that I’ll be investigating today: Do power hitters tend to strike out more often?

This claim is deceptively tough to evaluate because there’s no one clear way to tell if, and to what degree, a player is a power hitter. I came up with as many rational ways to measure power as I could and compared each with strikeout rates. I’ll let you decide for yourself exactly how well each metric relates to power.

Let’s start with the most obvious measure of a power hitter: Home Run Hitting

Here’s the correlation between a player’s home run rate (HRs/AB) and strikeout rate (Ks/AB)

**r = 0.527**

A correlation coefficient of 0.527 isn’t bad, and you can see a clear upward trend in the data, but let’s keep going.

Home runs obviously aren’t the only way to measure power. Let’s see what happens when we expand our study from home runs to all extra base hits.

**r = 0.427**

So it turns out there’s actually even less of a correlation with extra base hit rate than with home run rate.

There is a flaw to evaluating power using per at-bat rates. If a player has a high strikeout rate his rate of any type of hit will be lower. Here’s what happens when we redo the previous two graphs using home runs and extra base hits *per hit* instead of per at-bat.

**r = 0.609**

**r = 0.627**

Much higher correlation. Correlation in the .600 range isn’t the goal—but it’s definitely an indication that something’s there. Since non-per at-bat rates seem promising, let’s try per ball in play as opposed to per hit.

**r = 0.634**

**r = 0.669**

Even stronger correlation. Let’s move on now to a classic measure of power: Isolated Power (ISO).

**r = 0.508**

Good correlation, but not as strong as we just saw with HRs and EBHs per hit and per BIP. But when you look at what ISO actually is, it’s a per at-bat rate statistic.

Why don’t we redo ISO as per hit or and per ball in play instead of per at-bat?

**r = 0.642**

**r = 0.673**

So it turns out reworking ISO as per ball in play actually gave us our strongest correlation yet at 0.673.

Side note: I tried adjusting the ISO coefficients a couple of different ways since valuing a triple twice as much as a double and a home run three times as much as a double but just 1.5 times as much a triple seemed odd to me. As it turned out, the correlation didn’t get any better. Touché sabermetrics community, touché.

One of the great things about doing this study in 2016 is that we aren’t limited to traditional outcome-based stats. That being said, one of the less great things about doing this study in 2016 is there’s only one full season of publicly available statcast data. As a result, I’m lowering my minimum observations per player from 1000 plate appearances to 100 at-bats. For context Manny Machado led the league in plate appearances in 2015 with 713. So we’re clearly going to see decreased correlation because of poor sample size. To give you an idea of what that looks like, here’s a few of the correlations from the previous section compared with what they would have been had I used 2015 statcast data instead:

Stat |
1000 Plate Appearance Correlation |
100 At-Bat Correlation |

HR per BIP | 0.634 | 0.457 |

EBH per AB | 0.427 | 0.133 |

ISO per BIP | 0.673 | 0.495 |

HR per AB | 0.527 | 0.302 |

What you should take from this is that the strength of pretty much all of the correlations we’re going to look at will be diluted. Many stats that appear to have rather weak correlation could have a real relationship given more data, we just can’t know. It’s unlikely we’ll see some really indicting evidence that a specific measure of power implies a higher strikeout rate, but it could give us a good clue of where to look in the future. So with that out of the way, let’s crunch some numbers.

One obvious way to use statcast to measure power is to look at exit velocity. If you tend to hit the ball hard, chances are you’re a power hitter. Here’s how average exit velocity correlates with strikeout rate.

**r = 0.338**

There’s some correlation, albeit pretty weak. Perhaps power isn’t best represented by whose hits on average are the hardest but rather who has the highest rate of very hard-hit balls. Home runs tend to be hit at least 95 mph, so let’s check the correlation between rate of 95+ mph balls in play and strikeout rate.

**r = 0.393**

There’s better correlation, but it’s still rather weak. Let’s move on.

Next up is Launch Angle. Power hitters hit more fly balls because that’s the only way to get a ball out of the park and a common way to hit a double.

**r = 0.260**

There’s even less correlation than with exit velocity, and when I looked at the rate of “home run launch angles” (25˚ – 30˚) the correlation went down even further to 0.093. While we’re on the subject, I checked the correlation for the rate of balls in play that both had an exit velocity of at least 95 mph and a launch angle between 25˚ and 30˚ and got 0.323—lower than both exit velocity-only correlations.

Perhaps distance will yield better results. Below is the correlation between average ball in play distance and strikeout rate.

**r = 0.353**

Still not much correlation, but as with exit velocity it would make sense for the true sign of power to be high rates of balls in the 300 feet range rather than the exact distribution of balls hit 100/200 feet.

**r = 0.398**

So we see improved correlation, but 300 feet was a rather arbitrary number. Let’s try 350 feet.

**r = 0.481**

There’s some decent correlation here, but maybe we’ve made a mistake in lumping together distances to all parts of the field. Here’s what happens when we redo the previous two graphs but only count balls hit to center field that went an extra 50 feet.

**r = 0.416**

**r = 0.463**

The correlation went up from 300 to 300/350 and down from 350 to 350/400 (interestingly both by .018). This brings up an interesting question: Does power manifest itself more or less on balls in play in different parts of the field? In looking at this I organized players by their handedness—dividing balls in play by pull/center/opposite field not LF/CF/RF. (I omitted switch hitters from this part and looked only at balls hit to the outfield.) Rather than show 21 graphs, I made a table below with the correlation coefficients.__ __

Location |
Avg. Exit Velocity |
Avg. Launch Angle |
Avg. Distance |
HR Range Exit Velocities |
300+ ft. |
350+ ft. |
400+ ft. |

Pull |
.306 | .433 | .399 | .327 | .386 | .442 | .293 |

Center |
.410 | .148 | .270 | .379 | .267 | .353 | .388 |

Oppo |
.336 | -.147 | 0.021 | .293 | .028 | .054 | .215 |

__The last stat I’m going to look at is Arc Angle. Arc Angle is a stat I created to evaluate a batted ball’s trajectory. You can find out more about it in my Hardball Times article. Just note that it’s only for balls hit in the air and lower angles are fly balls while higher angles are line drives.__

**r = -0.474**

So none of the statcast stats yielded a correlation coefficient of 0.5 or more. As I said at the top this is likely—at least in part—a sample size issue. I’ll update these numbers after the season to see what difference that makes.

That was a lot, so here’s a table of all the correlation coefficients and increase in strikeout rate per unit of the stat for the comparisons we made.

Stat |
Correlation Coefficient |
Increase in K Rate per 1 Unit of Stat |

Home Runs per AB | .527 | 2.16 |

Extra Base Hits per AB | .427 | 1.40 |

Home Runs per Hit | .609 | 0.63 |

Extra Base Hits per Hit | .627 | 0.53 |

Home Runs per Ball in Play | .634 | 1.85 |

Extra Base Hits per Ball in Play | .669 | 1.44 |

Isolated Power | .508 | 0.67 |

Isolated Power per Hit | .642 | 0.21 |

Isolated Power per Ball in Play | .673 | 0.61 |

Average Exit Velocity | .338 | 0.01 |

Home Run Exit Velocity Rate | .393 | 0.32 |

Average Launch Angle | .260 | 0.01 |

Average Ball in Play Distance | .353 | 0.002 |

300 + ft. Balls in Play Rate | .398 | 0.49 |

350 + ft. Balls in Play Rate | .481 | 0.77 |

300 + ft. LF/RF 350 + ft. CF Rate | .416 | 0.72 |

350 + ft. LF/RF 400 + ft. CF Rate | .463 | 1.12 |

Average Arc Angle | -.474 | -0.01 |

Location |
Avg. Exit Velocity |
Avg. Launch Angle |
Avg. Distance |
HR Range Exit Velocities |
300+ ft. |
350+ ft. |
400+ ft. |

Pull |
.306 | .433 | .399 | .327 | .386 | .442 | .293 |

Center |
.410 | .148 | .270 | .379 | .267 | .353 | .388 |

Oppo |
.336 | -.147 | 0.021 | .293 | .028 | .054 | .215 |

As to our initial question: Does power correlate with strikeouts? I think it’s pretty clear that yes, power correlates with strikeouts in some capacity. As for how much it correlates and what exactly power is? That’s not clear. Hopefully additional seasons of statcast data will help.

]]>The final term, C, is a constant that ensures FIP is on the same scale as Earned Run Average (ERA).

Based on the knowledge that ERA and FIP are on the same scale with the only difference being ERA’s inclusion of balls in play, I thought I would compare the ERAs and FIPS of last year’s pitchers to see who got lucky, who didn’t, and how the CY Young award did (or didn’t) take this into account. This is also a good predictive study because pitchers whose ERA varied greatly from their FIP will likely see regression to the mean this season. Analysts who aren’t sabermetrically savvy will be amazed by these so-called comeback seasons or shocking deteriorations, but it will all be a result of their luck on balls in play.

For a full list of players’ FIPs and ERAs from last season click here. Note that I only took into account pitchers who threw at least 100 innings.

Below is a look at the luckiest, and unluckiest pitchers from last season. 25 of 70 AL Pitchers and 19 of 71 NL Pitchers (min 100 IP) had a FIP that was 0.5 or more different from their ERA. I also included a column at the end of the table that gave their Batting Average on Balls in Play (BABIP), which should explain the FIP-ERA discrepancies.

** ^{† }**Indicates CY Young finalists

^{‡ }Indicates CY Young Winner

**Lucky**

**Unlucky**

**Lucky**

**Unlucky**

There are many reasons for players to experience changes in performance other than chance, but analysts often mistake simple BABIP regression to the mean for a more far-fetched explanation. Don’t be surprised if this year’s story lines include players under the “unlucky” column making an amazing comeback because they started drinking fortified smoothies before games and regressions from players under the lucky column for other irrational reasons.

^{*}A quick note about R.A. Dickey: One of the known exceptions to the DIPS theory is knuckleball pitchers. They are thought to regularly induce more outs on balls in play than normal as a result of their knuckleballs—which players roll over or pop up. I wouldn’t classify R.A. Dickey as lucky and would assume his ERA is actually a better indicator of his performance.

No love for Clay Buchholz who had the best FIP in the American League but didn’t receive a single CY Young vote. Unsurprisingly, he was the 11^{th} unluckiest pitcher in the American League, sporting a BABIP of .329 which was 36 points above the league average.

While it isn’t exactly pertinent to this post, I compiled a list of the worst FIP performers from last year. Click here to see it.

*Ranks are out of 70 with 1 being best/luckiest and 70 being worst/most unlucky*

Look at the top 3 AL finishers: Keuchel, Price, and Gray had very good years. That said, they all had worse FIPs than Chris Sale and yet better ERAs. Archer also had a better FIP than the top 3. Yet, he too had the highest ERA of the bunch.

*Ranks are out of 71 with 1 being best/luckiest and 71 being worst/most unlucky*

Now look at the top 2 NL finishers. Arrieta and Greinke both pitched very well, but they also both got really lucky. Kershaw outdid both of them in FIP. Greinke was even outdone by Cole and deGrom—the latter of whom received less than 5% as many voting points.

^{**}Wade Davis and Mark Melancon both pitched fewer than 100 innings last season so they do not have a FIP or Luck rank.

You may be skeptical of DIPS and think these players performed better on balls in play because they’re better pitchers. Have a look at how the lucky CY Young finalists we just discussed performed just a year earlier on balls in play. Players go from left to right as given in the upper left box.

Every single player performed worse the year before and two (three if you round Keuchel up 0.001) even performed worse than the league average in 2014.

Expect strong seasons from players who had low FIPs. Also expect many if not most of the players who had very good or very bad luck to reverse that. This doesn’t mean lucky players should be unlucky and vice versa, but rather their BABIPs should be closer to the league average.

When it comes to the Cy Young, players with low FIPs should be finalists. However, winning the award may have as much to do with luck as with skill. In that regard, maybe it is better to be lucky than good.

]]>Arguing with couch-mates about what a National Football League team should do on fourth down has become a nearly equivalent staple to football Sundays as nachos. I analyzed data from 2010 to 2014 to make statistical predictions of the results of the three potential play types—Punt, Field Goal, and Run a Play From Scrimmage (“Go For It”)—as an alternative to the hindsight and anecdotally based arguments that are most frequently used. I divided my research based on where the offense is on the field using the five-yard demarcations drawn on all fields. Overall, the results of the research indicated overwhelming evidence in favor of “Going For It” on fourth down. The advantage to “Going For It” rather than punting ranged from 2.618 to 3.384 average net points resulting from the decision. The advantage to attempting a field goal ranged from 2.702 to -0.193 average net points (potential explanations for negative value explained within).

Click here for full research.

]]>My strategy in trying to figure this out was not overly complex and can be explained in three steps. First, I compiled data from all players who had an at-bat in a 3-0 count (ie. they put a 3-0 pitch in play, as walks are not considered official at-bats) since 1988—the first year this data was available. I divided the data into two groups, those with at least 10 at-bats and those with fewer. I did this to ensure that sample size did not skew my results for the 10+ at-bat group, but still see how the less than 10 AB group stacked up. I also compiled data for these players’ performances after a 3-0 count, or in other words, the outcome of all plate appearances in which the count was 3-0 at one point but did not end with the 3-0 pitch.

*Note: I adjusted this data to not include intentional walks, hit by pitches, and reach on errors since those don’t reflect the ability of the hitter.

My next step was assessing value to three different categories of outcomes, 3-0 at-bats (balls put in play in a 3-0 count), 3-0 walks, and post 3-0 plate appearances. To do this I used run values from Tom Tango’s *The Book: Playing the Percentages in Baseball*. Run values give the average number of additional runs scored in an inning after a given event (eg. a single or a stolen base). One issue I ran into was not having a run value for sacrifice flies or ground into double plays. Exactly how I got around this is not extremely relevant, but I went ahead and explained it at the end if you are interested.

The last step in this process was to compare each player’s performance with the green light to their projected performance had they not had the green light. I added the run value amassed from all 3-0 plate appearances under investigation (ie. not intentional walks, hit by pitches, and reach on errors) to the run value amassed in post 3-0 plate appearances. This sum constituted the player’s performance with the green light.

Calculating each player’s projected performance without the green light required a few steps. I added all 3-0 walks and post 3-0 plate appearances together, leaving just 3-0 at-bats unaccounted for. I multiplied the number of 3-0 at-bats by the average run value of a post 3-0 plate appearance and added this product to the previous sum of 3-0 walks and post 3-0 plate appearances.

This entire projection hinges on the following assumption: that no Major League player would swing at a pitch outside the strike zone with a 3-0 count. I’ll go into more detail on this later, but the important part of this assumption is that it means that all 3-0 at-bats, had the player not had the green light, would have resulted in a strike and a subsequent 3-1 count. This situation would be the exact same as all the other post 3-0 plate appearances these players had, so I can accurately project how the player would have done overall in those plate appearances without the green light by substituting a post 3-0 plate appearance for each 3-0 at-bat.

Finally, I subtracted the projected performance of a player with the red light from their actual performance and divided this difference by the total number of at-bats they had in a 3-0 count (the total number of times the plate appearance was changed by the fact that they had the green light). I call this value the Green Light Effect.

*To green light or not to green light:*

The beauty of this study is it’s incredibly easy to read. Each player’s Green Light Effect is the average increase in runs that can be expected by a player getting the green light. I should clarify that this number is for each time a batter utilizes the green light—puts a ball in play with a 3-0 count—not just when he gets the green light and has the opportunity to swing. So in theory, any player with a positive value should get the green light, as doing so would increase the number of runs his team is expected to score.

*Who are the best (and the worst) players with the green light: *

There are two different ways to assess a player’s green light ability, how a player performed when swinging on a 3-0 count and how much better or worse that player did than if they instead had the red light. To figure out just how good or bad these players are I used standard deviations. Below are all the players that who are two or more standard deviations from the mean in either direction.

This first set of data deals strictly with the run value of each player’s 3-0 at-bats, without taking into account how much better or worse this is than their expected performance with the red light. The mean of the data for players with at least 10 3-0 at-bats was 0.0959 runs and the standard deviation was 0.155 runs. The middle column is the average number of additional runs that the player’s team is expected to score after their 3-0 at-bat. The right column shows how many standard deviations each player was from the mean.

**Cumulative Run Value of 3-0 At-Bats**

**Best**

__Player__ __Green Light Runs__ __Standard Deviations__

Nelson Cruz………………. 0.765 ………………………… 4.31

Jose Hernandez…………. 0.550 ………………………… 2.93

Ben Broussard……………. 0.511 ………………………… 2.67

Nomar Garciaparra……… 0.463 ………………………… 2.36

Eduardo Perez…………….. 0.459 ………………………… 2.34

Matt Wieters………………. 0.438 ………………………… 2.20

**Worst**

__Player__ __Green Light Runs__ __Standard Deviations__

Casey McGehee…………… -0.352 ………………………… 2.89

J.J. Hardy………………….. -0.299 ………………………… 2.55

Adrian Gonzalez…………. -0.281 ………………………… 2.43

Andruw Jones……………. -0.269 …………………………. 2.36

Gerald Perry……………… -0.269 …………………………. 2.36

James Loney……………. -0.258 ………………………… 2.28

Charlie Hayes……………. -0.241 ………………………… 2.17

Manny Machado………… -0.229 …………………………. 2.09

This next set of data deals with the advantage/disadvantage that the green light presents, that is, the difference in runs that is expected from having the green light. The mean of this data was -0.156 runs and the standard deviation was 0.150 runs.

** **

**Run Value Compared to Expected Run Value with Red Light**

**Best**

__Player__ __Green Light Effect__ __Standard Deviations__

Nelson Cruz………………… 0.479 ……………………….. 4.22

Jose Hernandez……………. 0.326 ……………………….. 3.21

Ben Broussard……………… 0.256 ………………………… 2.74

Nomar Garciaparra……….. 0.185 ……………………….. 2.27

Eduardo Perez……………… 0.175 ……………………….. 2.20

Matt Wieters……………….. 0.162 .………………………. 2.12

Mike Napoli………………… 0.158 .………………………. 2.09

Paul Konerko………………. 0.151 ……………………….. 2.04

** **

**Worst**

__Player__ __Green Light Effect__ __Standard Deviations__

Adrian Gonzalez…………. -0.569 ……………………….. 2.76

Casey McGehee…………. -0.514 …………………………. 2.39

Vladimir Guerrero……. -0.492 …………………………. 2.24

Ichiro Suzuki……………. -0.477 …………………………. 2.14

Andruw Jones…………… -0.476 …………………………. 2.13

James Loney…………….. -0.473 …………………………. 2.12

Charlie Hayes…………… -0.471 …………………………. 2.10

Gene Larkin……………… -0.462 …………………………. 2.04

These are the 3-0 at-bats of the top 3 best and worst hitters based on both Green Light Runs and Green Light Effect:

Player |
AB |
H |
2B |
3B |
HR |
GIDP |
SF |

N. Cruz | 10 | 9 | 3 | 0 | 3 | 0 | 0 |

J. Hernandez | 17 | 12 | 4 | 0 | 5 | 0 | 1 |

B. Broussard | 15 | 9 | 3 | 1 | 4 | 0 | 0 |

C. McGehee | 11 | 0 | 0 | 0 | 0 | 1 | 0 |

J.J. Hardy | 10 | 0 | 0 | 0 | 0 | 0 | 0 |

A. Gonzalez | 11 | 1 | 0 | 0 | 0 | 1 | 0 |

V. Guerrero | 35 | 11 | 4 | 0 | 1 | 2 | 0 |

* *

*The big assumption:*

As I explained my process I made a passing reference to the crucial assumption that I made. I assumed that no Major League players swung at 3-0 pitches outside the strike zone. This assumption is necessary because my study assumes that all 3-0 pitches that are swung at would have resulted in a 3-1 count anyways if the player did not have the green light. Under this assumption, each player drew the maximum number of 3-0 walks possible (either with the red light or by taking all 3-0 pitches outside the strike zone with the green light). Thus, swinging on 3-0 did not give up the opportunity to walk *on that pitch*. As a result, it’s possible to project how each plate appearance would have gone without the green light by substituting the average result of that player’s plate appearances after a 3-0 count. Thus, swing and misses and foul balls don’t need to be accounted for because whether the player took the pitch or amassed a strike by swinging, the count would be 3-1. By no means can I guarantee that this assumption is correct, but it makes intuitive sense because Major Leaguers are extremely selective with 3-0 pitches—even 3-0 strikes—so I have to image they are disciplined enough to not swing at ball four on a 3-0 count. It actually turns out that there is a PITCHF/x metric called O-Swing % that measures the percentage of pitches outside the strike zone that are swung at. The problem is there is not public O-Swing % data (to my knowledge) for batters as opposed to pitchers, nor is there data for specific counts. With this data I could easily replace the generic projection value originally given for any 3-0 pitches outside the strike zone with the walk run value when calculating Overall Expected Red Light Performance.

* *

*Sac Fly and Double Play Run Values: *

There were two events that I wanted to account for that did not have a given run value—sacrifice flies and ground into double plays. These don’t make up a very big part of the outcomes under investigation, so I came up with a makeshift solution for each without worrying too much about it. For sacrifice flies I took a weighted average of the change in run expectancy when an out is made and a runner on third base scores (assuming, somewhat arbitrarily, no advancement by trailing baserunners) weighted by the frequency of each scenario. For ground into double plays I added the run value of an out to the run value of a pickoff. My rationale was that the outcome of a double play, two outs and the loss of a baserunner, is the same as combining a pickoff, which results in an out and the loss of a baserunner, with an additional out. Furthermore, in both scenarios the majority of the eliminated baserunners were on first base before the pickoff/GIDP.

* *

*The survivor effect: *

One of the questions I had going into this study was whether the survivor effect was a factor, in other words, whether players with more 3-0 at-bats performed disproportionately better with the green light. It would have made sense for players who performed well swinging on a 3-0 count to do so more often, and those who had poor 3-0 results early on to do so less. This would have affected results, as it would look like everyone did well with the green light, while in fact only those who did well had the minimum number of 3-0 at-bats to be studied. To check this I plotted all of the data, regardless of number of 3-0 at-bats, on the same graph. On this graph the independent variable was 3-0 at-bats and the dependent variable was Green Light Effect. A general upward trend would indicate that players with more 3-0 at-bats typically did better and the survivor effect was a factor. As it turned out there was no real sign of an upward trend.

This is a graph of every player with a 3-0 at-bat. The red line is the mean value for all players with fewer than 10 at-bats (-0.172). The majority of points with an x value of 10 or greater would need to be above that line to indicate the presence of the survivor effect.

I recopied the same graph, limiting the x-axis to 50 at-bats to make it easier to see.

]]>Nearly every aspect of baseball has been quantified by a sophisticated modern statistic. I took an underrepresented aspect, the baserunning allowed by the battery (pitcher and catcher), and quantified the performance of each team’s battery in this area. The statistic I created, which I title Battery Allowed Baserunning (BAB), melds the ability of the battery to prevent runners from stealing bases with their ability to prevent runners from advancing on pitches that get by the catcher. I combined these two disciplines by weighting each by their respective run value (the average change in runs scored by the opposition as a result of the given event). I found each team’s resulting BAB value for each season from 2003 to 2014, as well as their values for each of the two disciplines I referenced (preventing stealing and preventing advancement on balls that get by the catcher).

Click here for full research.

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