Here’s a hint, in gif form
Batter’s 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.
On May 20^{th} Peter O’Brien hit a massive home run to straight away center clearing the 32 foot tall batter’s eye at Arm & Hammer Park more the 400 feet from home plate. O’Brien is currently 1 home run behind Joey Gallo, in what looks to be an exciting competition for the minor league home run title. O’Brien isn’t as highly touted a prospect as Gallo, but he still has some of the most impressive power in the minor leagues. Reggie Jackson saw O’Brien’s home run and said it was one of hardest hit balls in the minor leagues that he had ever seen (and Reggie knows a thing or two about tape measure home runs).
How hard was that ball actually hit? It is impossible to figure out exactly how hard and how far the ball was hit from the available information. You can however use basic physics to make a reasonable estimation.
Below I explain the assumptions and thought process I used to get to an estimate of how hard the ball was hit. If that does not interest you, then just skip to the end to find out what it takes to impress Reggie Jackson. But, if you’re curios or skeptical stick around.
OBSERVATIONS
I started off by watching the video to see what information I could gather (O’Brien’s at bat starts at the 37 second mark in the video).
TIME OF FLIGHT From the crack of the bat, to the ball leaving the park – it appears to take 5 seconds. If you watched the video, you can tell this is not a perfect measurement since the camera doesn’t track the ball very closely. If you think you have a better estimation, let me know and I’ll rework the numbers.
LOCATION LEAVING THE PARK The ball was hit to straight away center. From the park dimensions we know when it left the park it was 407 feet from home plate and at least 32 feet in the air to clear the batter’s eye.
ASSUMPTIONS
COEFFICIENTS OF DRAG (Cd) – The Cd determines how much a ball will slow down as it moves through the air. I chose 0.35 for the Cd because it is right in the middle of the most frequently inferred Cd values for the home runs that Alan Nathan was looking at in this paper.In looking at the Cds of baseballs, Alan Nathan showed there is reason to believe that there is some significant (meaning greater than what can be explained by random measurement error) variation in Cd from one baseball to another.
ORIGIN OF BALL I assume the ball was 3.5 feet off the ground and 2 feet in front of home plate when it was hit. These are the standard parameters in Dr. Nathan’strajectory calculator. But what if the location is off by a foot? The effects of the origin on the trajectory are translational. One foot up, one foot higher. One foot down, one foot lower. The other observations and assumptions are more significant in determining the trajectory of the home run.
Using these assumptions and the trajectory calculator, I was able to determine the minimum speed and backspin a ball would need in order to clear the 32 foot batter’s eye 5 seconds after being hit at different launch angles. The table below shows the vertical launch angle (in degrees), the back spin (in RMPs) and the speed of the balled ball (in MPH).
Vertical launch angle | Back spin | Speed off Bat |
19 | 14121 | 101 |
21 | 6817 | 101.9 |
23 | 4155 | 102.75 |
25 | 2779 | 103.69 |
27 | 1940 | 104.7 |
29 | 1375 | 105.89 |
30 | 1156 | 106.5 |
32 | 805 | 107.88 |
34 | 536 | 109.4 |
36 | 322 | 111.1 |
38 | 149 | 112.99 |
40 | 4 | 115.1 |
The graph shows a more visual representation of the trajectories in the table above (with the batter’s eye added in for reference).
Looking at the graph you will notice that all of these balls would be scraping the top of the batter’s eye. This makes sense because the table shows the minimum velocities and back spins needed for the ball to exactly clear the batter’s eye.
What is the slowest O’Brien could have hit the ball?
If you were in a rush, looking at the table you would think the slowest O’Brien could have hit the ball would be 101 MPH at 19^{o}. But, not so fast! The amount of backspin required for the ball to travel at that trajectory is humanly impossible.
What is a reasonable backspin?
I am highly skeptical of backspin values greater than 4,000 rpm based on the Baseball Prospectus article by Alan Nathan “How Far Did That Fly Ball Travel?.” The backspin on home runs Nathan examined ranged from 500 to 3,500 rpm, with most falling in around 2,000. The first 3 entries in the table have backspins of over 4,000 and can be eliminated as possibilities. If the ball with the 19^{o}launch angle only had 3,500 rpm of back spin it would have hit the batter’s eye less than 11 feet off the ground instead of clearing it. Maybe you’re skeptical that I eliminated the 3^{rd} entry because it’s close to the 4,000 rpm cut off. Think about it this way, if a player was able to hit a ball with over 4,000 rpm of back spin, they would have to be hitting at a much higher launch angle than 23^{o} (Higher launch angles generate greater spin while lower launch angles generate less spin).
The high launch angle trajectories with very little back spin (like the bottom three in the table) are also not very likely. A ball hit with a 40^{o} launch angle would almost certainly have more than 4 rpm of back spin. If the ball hit with the 40^{o} launch angle had 1,000 rmp of back spin (instead of 4) it would have been 70 feet off the ground, easily clearing the 32 foot batter’s eye.
Accounting for reasonable back spin, the slowest O’Brien could have hit the ball is 103.69 MPH at 25^{o} with 2,779rpm of backspin.
So what do all these observations and assumptions get us?
We can say that the ball was likely hit 103.69 MPH or harder, with a launch angle of 25^{o} or greater. 103.69 MPH launch velocity is not that impressive, it is essentially the league average launch velocity for a home run. Distance wise, how impressive of a home runs was it? Unobstructed the ball would have landed at least 440 feet from home plate (assuming the 25^{o} scenario). The ball probably went further than 440 because it did not scrape the batter’s eye. So, how rare is a 440+ foot home run? Last year during the regular season there were 160 home runs that went 440 feet or further, there were a total of 4661 home runs that season, meaning only 3.4% of all home runs were hit at least that far.
For those of you who wanted to just skip to the end. My educated guess is that the ball went at least 440 feet and left the bat at at least 103.69 MPH.
Update * Greg Rybarczyk was kind enough to run my numbers through the hit tracker model for comparison. The results are a 442 true distance, 25 degree vertical launch angle, and 107 MPH speed off bat. *
Article originally posted at www.fangraphs.com/community
None of this would have been possible without Alan Nathan’s great work on the physics of baseball. I used his trajectory calculator to do this, and I referenced his articles frequently to make sure I wasn’t way making stupid assumptions. The information on major league home run distance is based off of hittrackeronline.com
Also big thanks to Greg Rybarczyk of hit tracker, for
Middlebrooks’s glaring flaw last season was his sub .300 OBP (.271), which was driven in large part by his low walk rate (5.3%) and high strikeout rate (26.2%). Believing that Middlebrooks can improve those numbers is central to any hope that he will have a breakout season. Alex Speier showed that it’s not unprecedented for young power hitters with sub .300 OBPs to see a large improvement in the OBP area, but it’s also not guaranteed. Of the players Speier looked at only 18% saw their OBP increase by 30 points or more (which is what it would take to get Will over .300), so why does the Boston media believe that Middlebrooks will experience this rare transformation?
The main driving narrative behind this optimism is that Middlebrooks was over aggressive and had terrible plate discipline last year, and this allowed pitchers to dominate him. But now that he has worked on his approach at the plate during spring training everything will come together.
This “Willpower” narrative goes all the way to the top
Red Sox manager John Farrell told reporters “I think last year we saw some at-bats where maybe he was pressing a little bit, maybe trying to make up for some previous at-bats where it would cause him to be a little overaggressive or expand the strike zone, That willingness to swing, pitchers didn’t have to challenge him all that much” when explaining Middlebrooks past struggles. We are led to believe that this former Achilles heel is no more after his successful spring training, as Middlebrooks told reporters “The one thing that sticks out to me is I’ve swung at one pitch outside of the zone this spring.”
Will Middlebrooks had a great spring training ( .353/.389/.667) but spring training stats are useless for predicting regular season success. And, as it turns out, are far from the only problems with this “Willpower” narrative. The idea that Will Middlebrooks was overly aggressive and had bad plate discipline is something that can be checked very easily by looking at Middlebrooks’s plate discipline stats vs the league average for last season.
Did Middlebrooks have poor plate discipline last season?
2013 |
pitches/PA | Swing% | 1stP Swing | Contact | O-Swing% | Z-Swing% | Z-Contact | Zone% | Swstr% |
Will |
4.11 |
46.6% |
26.2% |
75% |
30.8% |
64.5% |
81.4% |
47% |
11.5% |
Lg ave |
3.86 |
46.4% |
25.3% |
79.5% |
30.9% |
65.8% |
87.2% |
44.5% |
9.2% |
Will Middlebrooks plate discipline compared to the average major leaguer.
Checking the number reveals the surprising fact that Will Middlebrooks’s plate discipline was not terrible but surprisingly average. He appeared to be a little bit aggressive, swinging a bit more at the first pitch but those 0.9 percentage points translated three more plate appearances with Will swinging at the first pitch hardly enough to ruin his triple slash line. The next surprising thing that the numbers reveal is that pitchers were actually throwing Middlebrooks more strikes than the average hitter (and more compared to what he saw the previous season), so while pitcher might not have had to challenge him, they didn’t shy away from throwing him pitches in the zone. Middlebrooks actually saw a lot more pitches in the strike zone than other power hitters. For players with at least a 0.190 ISO and at least 350 PA only Jayson Werth saw more pitches in the strike zone . These facts throw the whole premise of this “Willpower” out the window.
How does the image of Will Middlebrooks the aggressive hacker persist when it’s clearly untrue?
Well whenever you see such a low walk rate coupled with such a high strike out rate the easy first assumption is that the player swings at everything, this is a fare guess if didn’t have better data, but we do. But what about some on who watched every single Middlebrooks plate appearance such as his manager, how could they have such a distorted view. Well everything is relative, relative to an average major-leaguer Middlebrooks’s plate discipline and his approach were average but compared to other players on the Red Sox Middlebrooks was aggressive and undisciplined. The Red Sox as a team swung at the first pitch less often than any other team in the majors. So when not watching Middlebrooks, John Farrell was watching some of the most patient and disciplined hitters in baseball so this is an understandable bias.
The highly improbable feat of chasing only one pitch out of the strike zone over 26 plate appearances.
Now let’s look at Will’s assertion that he only chased one pitch out of the strike zone over his first 26 plate appearances (that’s the number he had prior to his quote). This would be incredible and might even be meaningful if it were true. We don’t have spring training plate discipline numbers so we will do a Gedankenexperiment (what Einstein called thought experiments because he was German) and assume the Will saw 100 pitches over those 26 plate appearances (lower than his career average rate and a bit below league average) and half of those were out of the strike zone (also generous considering that usually more than half of pitches are out of the strike zone and in spring pitcher are rusty and of a lower talent pool) this would give Will Middlebrooks a 2% chase rate ( chances are it would have to be lower than that for him to only chase one pitch over 26 plate appearances but we are giving him the benefit of the doubt). This would be really impressive for a guy who normally chased around 30% of pitches (it would actually be impressive for anyone), and it’s a number that no one has ever sustained for a full season.
How rare is 2% chase rate over that short a time frame? It’s so rare that no one even came close to it last year. The closest was Shane Robinson, when last year in the month of June he had 27 plate appearances and only swung at 7.7% of pitches outside the strike zone, that was the lowest chase rate any player had during any month last season (assuming they had at least 20 plate appearances).
Given our prior knowledge about Will Middlebrooks and major-league hitters in general I will go out on a limb and say that I believe Middlebrooks swung at more than one pitch out of the zone. I bet Middlebrooks believes he only swung at one pitch out of the zone, and this more than anything might point to a flawed understanding of the strike zone. So while any player can improve by improving their plate discipline (case in point that Joey Votto can still benefit from it) its not a cure-all for baseball problems, and Will Middlebrooks’s problems extend beyond his plate discipline.
If plate discipline wasn’t the reason Middlebrooks was terrible last year then what was the problem?
Part of Middlebrooks’s problem was his abysmal .263 BABIP, this will likely be closer to league average in 2014 and is probably one of the best reasons to believe that Middlebrooks will be better than he was last year. Unfortunately it sounds much better to say you are working on your plate discipline in spring training than to say you are hope your BABIP will regress towards the mean. But BABIP is only part of the picture it doesn’t explain his 5.3% walk rate and 26.2% strikeout rate (the low BABIP and therefore production might have led pitcher to throw Will more strikes thus diminishing his walk rate, but this would only be a small effect).
Middlebrooks’s real problem seems to be with making contact, especially when it comes to pitches in the strike zone. He was 212th out of the 237 players with at least 350 PA last year in terms of zone contact (that means 89% of players are better than him), making contact only 81.4% of the time when he swung at a pitch in the strike zone. This low zone contact rate is probably a large part of the reason pitchers felt comfortable throwing him so many pitches in the zone. This issue was further compounded by the fact that when Will did make contact the ball went foul slightly more than half of the time (50.4% compared to the league average of 48.1%). This leads to his high strike out rate.
Look at it this way:
a) when Middlebrooks swung his chance of making contact with the ball was below average, and
b) when he did make contact the chance of that ball going in fair territory was below average, and
c) if that ball was put in play the chance of it being a hit was well below average.
These issues meant pitchers could throw Will lots of strikes, and if a player with average discipline sees fewer balls than average then they are going to walk less than average.
Will Middlebrooks will most likely be better than he was last season (more of a bounce-back than a breakout), and he might even have a breakout season but it will take more than improved plate discipline for that to happen.
All stats are from FanGraphs (used the regular plate discipline stats not the pitch f/x ones) with the exceptions of pitches per PA, 1^{st} pitch swing%, and foul ball stats which are all from baseball-reference.com
Also the quotes are from the Alex Speier article, although I believe they were given to the media in general.
Article originally posted at www.fangraphs.com/community
A few more active players look like they are about to join the club
Three favorites are Giancarlo Stanton, Mike Trout and Bryce Harper. According to the Oliver five year projection system, each of these players will reach over 150 home runs by the end of his age 25 season.
This chart shows each player’s current home run totals, the seasons played through so far, the number of additional home runs Oliver projects through the 25 season, the projected total runs by the age of 25 (Career HR + Oliver projected), and finally what each player would need to average to hit 150 runs by the age of 25. This last measure is interesting because it gives you an idea of what level each player would need to fall below to miss the mark.
Minor league players might knock out A-Rod for #1
Miguel Sano, Joey Gallo and Javier Baez make up a trio of minor leaguers who Oliver believes could also make the list. Not only does Oliver project these three players will to fly past 150 home runs, he predicts Sano and Gallo could pass A-Rod for the most home runs by age 25.
*the Gallo projections are only through his age 24 season so if he kept up the home run pace he would be in the 270s at the age of 25
While Sano, Gallo and Baez have a high number of projected home runs, they also have a high number of projected strikeouts. Adam Dunn shows that you can be very successful as a player who strikes out & hits home runs frequently. But the three minor league players could be even more extreme. Dunn struck out 26% of the time and homered 5.7% of the time through his age 25 season. The minor league trio are predicted to strike out between 32 and 43% of the time and homer between 7 and 8% of the time. Could these three players redefine the all or nothing hitter, or are they somehow breaking projection systems?
Reasons to be skeptical
The Oliver model is complex and would take a long time to completely dissect, but from what I can tell it has the following limitations (these limitations are intentional because they add other value to the projections system):
#1 The Assumption of Games – Oliver projections assume a player gets 600 major-league plate appearances every year. This is not necessarily a given because top minor league players will likely spend part of a season in the minors before moving up to the majors, or in Sano’s case miss games rehabbing an injury.
#2 Inherent Uncertainty – First, projections based off minor league numbers have more uncertainty than those based off major league numbers. Second, each additional year projected in the future adds more uncertainty because each year you go out you are guessing what happened the previous year – vs. knowing what happened the previous year. Compounded, these two stated effects create a good deal of inherent uncertainty.
So, what does this all mean?
If the projections are anywhere close to correct, it looks like we are going to see a new breed of power hitter in the major league soon. Although the projections are far from foregone conclusions, it’s another great reason why we watch the game of baseball.
Article originally posted at www.fangraphs.com/community
There are several reasons the Earth’s gravity as we experience it is not constant. First, the Earth is not a perfectly uniform sphere. When mathematically approximating gravity we make the assumption that the Earth is a perfectly uniform sphere. But, since the Earth is not perfectly round and uniform, this assumption leads to a small error in the approximations and does not account for gravitational variations in different locations.
Second, gravity is dependent on your distance from the center of the Earth. Gravity is inversely proportional to the square of the distance between two objects, say between you and the Earth. The further away from the Earth you are, the weaker gravity is, g = g_{0} (r_{e }/(r_{e}+h))^{2 } where r_{e} is the radius of the Earth, g_{0} is gravity at sea level, and h is how high you are above sea level. For example, at Coors Field g=g_{0}(20,925,524.9/(20,925,524.9+5,219.82))^{2 } this equation tells us that gravity is 32.157913 ft/s^{2} at Coors Field, or 0.05% less than gravity at sea level (32.1740 ft/s^{2}).
The third reason why the Earth’s gravity as we experience it is not constant is related to the centrifugal forces caused by the Earth spinning. The fact that the Earth is rotating does not actually change gravity (well this is a lie according to relativity there will be some rotational frame dragging but this effect is extremely hard to detect and surely won’t have a measurable effect on baseball). Centrifugal forces appose gravity and make items feel lighter. These forces are strongest near the equator (where you are the furthest from the Earth’s axis and therefore moving the fastest) and weakest near the poles (where you are closer to the Earth’s axis and rotating more slowly). An easy way to remember this is gravity will be weaker the closer you are to the equator.
Let’s take a break from all this math for a bit. Here is the juicy part, the table below shows the gravity at all the different major league ballparks and the percent increase or decrease in gravity compared to the average gravity at all the ballparks (this is based on EGM2008, made easily available thorough wolfram alpha). Negative percentages indicate a decrease in gravity, while positive percentages indicate an increase in gravity.
Team | g (ft/s2) | % change |
Miami Marlins |
32.11348 |
-0.126% |
Tampa Bay Rays |
32.11936 |
-0.108% |
Houston Astros |
32.12558 |
-0.088% |
Texas Rangers |
32.13392 |
-0.062% |
Arizona Diamondbacks |
32.13474 |
-0.060% |
San Diego Padres |
32.13553 |
-0.057% |
Atlanta Braves |
32.13608 |
-0.056% |
Los Angeles Dodgers |
32.13887 |
-0.047% |
Angeles |
32.14466 |
-0.029% |
Colorado Rockies |
32.14466 |
-0.029% |
Oakland Athletics |
32.15333 |
-0.002% |
Giants |
32.15341 |
-0.002% |
Average |
32.15395 |
0.000% |
St. Louis Cardinals |
32.15517 |
0.004% |
Kansas City Royals |
32.15538 |
0.004% |
Cincinnati Reds |
32.15677 |
0.009% |
Washington Nationals |
32.15742 |
0.011% |
Baltimore Orioles |
32.15886 |
0.015% |
Pittsburgh Pirates |
32.16099 |
0.022% |
Philadelphia Phillies |
32.16119 |
0.023% |
New York Mets |
32.16435 |
0.032% |
New York Yankees |
32.16442 |
0.033% |
Cleveland Indians |
32.16511 |
0.035% |
Chicago White Sox |
32.16655 |
0.039% |
Chicago Cubs |
32.16697 |
0.041% |
Detroit Tigers |
32.1684 |
0.045% |
Boston Red Sox |
32.17023 |
0.051% |
Milwaukee Brewers |
32.17096 |
0.053% |
Toronto Blue Jays |
32.1744 |
0.064% |
Minnesota Twins |
32.17764 |
0.074% |
Seattle Mariners |
32.18997 |
0.112% |
(If you are paying close attention: 1) you might have noticed the average gravity in the table is lower than our conventional constant for gravity, 32.1740 ft/s^{2}. The average gravity in the table above is the average gravity at major-league ballparks only, not the average gravity of all points around the world. 2) The table value for gravity at Coors Field does not exactly match what we calculated earlier. This is because the measure we calculated earlier did not account for centrifugal force or the effects of a non-uniform Earth. The gravity for Coors Field in this table allows for those factors.
The difference between the two most extreme ballparks is 0.07649 ft/s^{2}. Alone this number seems small and is hard to conceptualize. I’ve gone ahead and explored a few different baseball scenarios to illustrate its effects.
So, what does 0.07649 ft/s^{2 }really mean for the game of baseball?
1. Players are measurably lighter at lower gravity ballparks.
CC Sabathia feels just a little lighter while pitching in Miami than when in Seattle, a whole whopping 0.69 lbs lighter! (Perhaps this is why when so many players travel to Florida for Spring Training they report feeling in the best shape of their life…)
2. An outfielder will have slightly longer to catch a fly ball in a lower gravity ballpark.
A fly ball with 4.5 second hang time at an average park would stay in the air 5.7 milliseconds longer in Miami, and in Seattle it would be in the air for 5 fewer milliseconds. That almost 11 millisecond difference in hang time between Miami and Seattle would mean that a running out fielder might cover 2 more inches in Miami, not enough to make any reel difference but interesting nonetheless.
3. Pitches will sink less in a lower gravity ballpark.
Pitches will sink less in Miami than they will in Seattle, but how much less? On a 65 mph slow curve it takes the ball about 0.650 seconds to reach the plate. This ball will drop 0.2 inches lower in Seattle vs. Miami. An average pitch taking 0.45 seconds to reach home plate, will only drop an addition 0.09 inches in Seattle vs. Miami. For comparison the diameter of a baseball bat is 2.6 inches or less. A 0.2 inch difference is 1/13 the diameter of a baseball bat, which is too small of a difference to turn a hit into a swing and miss.
4. Home runs will travel farther in a lower gravity ballpark.
When it comes to home runs one would think differences in gravity would start to play a bigger role. Because home runs are in the air longer, gravity is bound to have a greater effect on them than it does on pitched balls. The hang time of a home run is usually a full order of magnitude longer than that of a pitch. Assuming identical weather conditions, a baseball hit 120 MPH at a 26^{o} angle would travel 13 inches (THAT’S MORE THAN 1 FOOT!) farther in Miami than it would in Seattle. That could make a difference, not in the actual score, but in what seat in the bleachers the ball would land. Although a foot is the largest difference we have talked about so far, practically it doesn’t really matter much for a no-doubt home run that’s traveling over 460 feet.
5. Just for Fun…
On the surface of the Earth if we wanted to look for extremes we would see the highest gravity at the South Pole, which would be 32.26174 ft/s^{2} or 0.335% higher than the average gravity at a major league ball park (this and a few other factors would lead me to believe that playing in the South Pole would really suppress home runs). The other extreme would probably be in Quito, the capital of Ecuador (there is actually a volcano in Ecuador with slightly lower gravity but let’s look at one plausible hypothetical) where gravity is 32.04248 ft/s^{2} or -0.347% below average. In Quito Sabathia would be 1lb lighter than he would at an average ball park and 1.3 pounds lighter than he would in Seattle. That same hypothetical 120 mph home run would go 0.9 feet farther in Quito than it would a an average ball park, and 1.3 feet shorter at the South Pole. This is of course completely hypothetical because we are assuming all other conditions are the same at these two ball parks such as air density and temperature, and this definitely not the case.
Thanks to
National Geospatial-Intelligence Agency for publicly releasing the Earth Gravitational Model EGM2008
Alan Nathan for providing the trajectory calculator tool, which I used to calculate difference in batted ball distances, the calculator can be found on his websitehttp://baseball.physics.illinois.edu/trajectory-calculator.html
Article originally posted at www.fangraphs.com/community
Glavine’s reputation alone likely influenced a batter’s behavior at the plate, encouraging batters who were behind the count to swing at questionable pitches. Batters believed if they did not swing these pitches would be called strikes for Glavine (when a batter swings at a pitch out of the zone when the batter is ahead of the count that has more to do with a pitchers stuff than the batter giving the pitcher an expanded zone). So, what would we expect from a pitcher who is getting batters to expand the strike zone? You would expect batters to make poor contact, yielding a lower BABIP. The batter would most likely swing at pitches outside the zone when the batter is behind the count.
Based on this reasoning, I hypothesize that Tom Glavine will see a greater reduction in quality of contact when he gets ahead of the count than a league-average pitcher. I’m going to look at the time span from 1991 to 2002 because that was the time span Jeff looked at and because I like palindromes.
To measure quality of contact I will be looking at BACON (batting average on contact). BACON is slightly different than BABIP because BACON includes home runs. If batters are expanding the strike zone when Glavine is ahead in the count we should see the quality of contact decrease. To measure the decrease in quality of contact, I will look at the ratio of BACON when Glavine is ahead to BACON to when Glavine is behind (the lower the number the greater improvement the pitcher experiences by getting ahead in the count). I will refer to this measure as EXP (a lower EXP shows a greater decrease in quality of contact, an EXP above 100 shows an increase in quality of contact). The graph below compares Glavine’s EXP to the league average EXP for each season during the 11-year span.
The league-average EXP is consistent year to year, hovering around 91, which suggests batters expand the strike zone for most pitchers when batters are behind in the count. Glavine’s EXP is not always better than the league-average EXP. In ‘94 and ‘96 Glavine was actually worse when ahead in the count than when he was behind. This is to be expected because BACON takes a while to stabilize. Looking at Glavine’s data for a single season is subject to a fair amount of random noise because you have a relatively small sample of data. One season for Glavine gives us about 170 fair balls with Glavine ahead and 280 fair balls with Glavine behind. However, over a larger sample BACON stabilizes. At around 2,000 fair balls (more than in a single season for Glavine) BACON stabilizes. For example, when looking at the league-average EXP for a full year BACON is stable — with 3,500 fair balls with the pitcher ahead of the count and 4,600 fair balls with pitcher behind the count.
To make sure we are not just attributing skill to some random variation we need to look at a larger sample for Glavine. Over the 11 year span form 1991-2002 Glavine induced weaker contact (lower BACON) than the league average both when he was ahead of the count and behind the count. This is not surprising as we would expect a good pitcher to be better than average ahead and behind the count. What’s interesting is Glavine has better than league-average EXP (87 vs. 92) which suggests Glavine is better at expanding the strike zone than league-average pitchers. This comes with the caveat that while we have 3,056 fair balls when Glavine is behind the count, we only have 1,853 fair balls when Glavine is ahead — just shy of the 2000 at which the measure should stabilize. Even so, the difference between Glavine’s EXP and the league-average EXP is very convincing.
To stabilize BACON, I increased the sample by looking at all the balls put in play. I compared balls put in play when the pitcher had two strikes to balls put in play when the pitcher had fewer than two strikes, which led to EXP2: the ratio of BACON when a pitcher has two strikes, to when he has fewer than two strikes. The table bellow shows a comparison of the quality of contact in two strike counts to non-two strike counts.
Even with this larger sample size Glavine’s BACON is still lower than the league average in respective counts. More importantly, his EXP2 is still better than league average (although higher than his EXP). Pitchers in general try to induce weaker contact when they are ahead of the count, but the data shows Glavine is doing something special to induce even weaker contact.
Is Glavine getting batters to give him a wider strike zone? We cannot definitively say what is causing this pattern in the data, but we are seeing the type of numbers we would expect to see if the batter was giving him a wider strike zone.
All splits number are from Baseball-Reference.
Article originally posted at www.fangraphs.com/community
The obvious answer to this question is yes, but I was interested in how much a pitcher’s success was dependent on velocity. Bill Pettit wrote a great piece about CC Sabathia’s fastball, and I hope to shed more light on this interesting question.
(The following pitch f/x number come from Brooks Baseball, and on a technical note I believe that because Brooks Baseball uses a Y_{0} of 55 feet instead of 50 the fastball release speeds are slightly higher than those reported from other pitch/fx sites since they measure speed 5 feet later, so while FanGraphs says CC topped out at 96.3 mph in 2012 Brooks baseball shows him hitting 97.)
I decided to look at all the fastballs CC threw in 2012 to see how well velocity correlated with pitch value. (One more technical note; these are my own pitch value calculations. They differ from FanGraphs in that they treat all balls in play as being worth the same. I did this to try to remove some of the effects of defense. Also note that the scale I’m using is runs- per- pitch and that a negative value is good for the pitcher while a positive value is good for the hitter.) Now according to pitch f/x CC throws a four-seamer and a sinker; because pitch classifications are not perfect I looked at both four-seamers and sinkers together and then looked at them each individually to minimize any artifacts from the classification system. [see the three graphs below]
The first thing that jumps out at me when looking at this is how miniscule the R^{2} values are. Normally any correlation this weak would be ignored but because we know velocity does in fact play a role we can take these R^{2} values to show us how small a role velocity actually plays and how it is just a speck of the big picture. I am not saying that velocity doesn’t matter; I’m just saying that there are a lot of other factors that matter as much or more than velocity. Looking at the plot of all of CC’s fastballs there is no obvious trend (as you would expect with an R^{2} of 0.0002) but the best fit line does have a distinctly negative slope. This means that the faster the pitch the less likely it is to give up runs. A slope of -0.0017 does not seem like much but this is on a per pitch basis so this means that a 1 mph difference would be worth an additional 2.89 runs over CC’s 2012 season (1701 fastballs times .0017 runs per fastball) This may not sound like much but that’s $1.4 million of value so not chump change!
The best fit line for CC’s sinker actually had a positive slope of 0.0056 which would imply that the harder he threw his sinker the worse it did. This seem counter intuitive; a slower pitch is better?, This could be just noise but it does make me believe that Sabathia’s sinker relies less on velocity than his four-seamer does (CC only had 551 pitches classified as sinkers so this is a much smaller sample size so one or two home runs off fast sinkers could throw this off as well). There is a possibility that this is due to a pitch classification artifact but when limiting the regression to only looking at the 100 sinkers with the highest pitch classification confidence the trend actually grows stronger as both the R^{2} and the slope increase.
The four-seam fastball showed the greatest dependence on velocity with the best fit line having a slope of -.0033, which is roughly double that of the slope for all of his fastballs. Another way to look at it, is CC’s loss of four-seamer velocity from 2011 to 2012 cost him about half a win.
Now all these run values have to be taken with several grains of salt because they are based off fit lines with such low R^{2} values and there are many other factors that could be confounding the results, and obviously correlation does not imply causation (also the assumption that the effect of velocity is linear and independent from other pitch characteristics is false but necessary for simplifying this complex problem). It is really impossible to say how much better or worse CC Sabathia would be if his velocity were x instead of y, the values based of the best fit lines are really just educated guesses the only way to find out if CC can continue to be a dominant pitcher with a slower fastball is to wait and see.
All that can be said for sure is that velocity can only explain a fraction of a percent of the variance between good and bad fastballs. This means that there are definitely ways in which a pitcher can adjust to more than make up for the loss of fastball velocity. Now what these adjustments may be is a whole new question. A pitcher can only adjust what they can control, which brings up the question how much control does a pitcher have over the different characteristics of their pitches? Is there something CC can control to make his four-seamer effective at lower velocities? I would say yes based on his ability to throw a sinker that does not rely on velocity for its success.
So does velocity matter? Yes, but so do lots of other things. It’s not clear how much control a pitcher has over these other things that matter; anyone can by mistake throw a pitch on the outside edge of the strike zone, but really, how repeatable is that skill? I’ve never heard of someone throwing 95 by mistake. That’s what nice about velocity, there is no luck involved.
Lou Gehrig famously won the Triple Crown in 1934 (but not the MPV) and even more famously in 1939 Lou stated that he considered himself “the luckiest man on the face of the earth.” Miguel Cabrera has won the Triple Crown; he is the first winner since 1967. While it may be hyperbolic to say that Miguel Cabrera is the luckiest man on the face of the earth, it is in no way hyperbolic to suggest that luck factored significantly with him winning the Triple Crown. Baseball is a game of luck and skill, and whenever a player puts up fantastic numbers (like Cabrera did this year); despite how skilled the player might be there is usually some component of good luck contributing to those numbers.
There are numerous ways in which luck can contribute to Triple Crown stats (BA, RBI, and HR). RBIs for example are greatly dependent on the number of RBI opportunities that a player gets and a lot of the variance in BABIP is due to luck. I am not going to look at RBIs or batting average; although Miguel Cabrera actually had a lower BABIP than Mike Trout and fewer runners on base when he batted than Josh Willingham, I will look at the role of luck and home run totals. Greg Rybarczyk in collaboration with ESPN Stats & Information Group has done a fantastic job tracking MLB home runs over at hittrackeronline.com. Hit tracker does not just calculate how far a home run was hit; it also calculates what effect atmospheric conditions had on the ball. If a home run would have not cleared the fence in normal weather conditions (a 70-degree no wind day) it is classified as a lucky home run. Miguel Cabrera had 7 lucky home runs this season, the most of any player this season and the second highest single season lucky home run total since Hit tracker began tracking home runs in 2006. Without these 7 lucky home runs Cabrera would not have won the Triple Crown; he would not have even been that close. He would have finished with a batting average in the low .320s, good for second in the league, and a home run total of 37 which would be good for fifth in the league. Without those 7 home runs Miguel Cabrera’s season would look eerily similar to Adrian Beltre’s, except with worse defense (no more MVP contention). The fact that 7 of Cabrera’s home runs need a little luck to help them clear the fence should in no way be counted against him because those lucky home runs are just as valuable as the rest of his home runs.
Miguel Cabrera is hardly the only player to benefit from lucky home runs; there were 248 lucky home runs hit this season and 2232 hit in the regular season since 2006. While many players have benefitted from lucky home runs other may have gotten the short end of the stick and lost a few home runs due to weather conditions (this unfortunately is not tracked). Cabrera still did most of the work, hitting deep fly balls that the weather turned into lucky home runs. So I am going to look at what percent of potential lucky home runs actually clear the fence. I defined potential lucky home runs as all out field fly balls that did not clear the fence and all lucky home runs. The chart below shows the number of potential lucky home runs, lucky home runs and the percent of potential lucky home runs that actually cleared the fence (I used Fangraphs Fly ball split to find the number of outfield fly balls that were not home runs).
year | AL lucky HR | NL lucky HR | total lucky HR | AL potential | NL potential | total potential | AL luck% | NL luck% | total luck% |
2006 | 193 | 249 | 442 | 19009 | 20989 | 39998 | 1.015% | 1.186% | 1.105% |
2007 | 170 | 179 | 349 | 19636 | 22344 | 41980 | 0.866% | 0.801% | 0.831% |
2008 | 155 | 207 | 362 | 18906 | 20168 | 39074 | 0.820% | 1.026% | 0.926% |
2009 | 150 | 168 | 318 | 19702 | 20967 | 40669 | 0.761% | 0.801% | 0.782% |
2010 | 128 | 153 | 281 | 19474 | 20932 | 40406 | 0.657% | 0.731% | 0.695% |
2011 | 122 | 110 | 232 | 18248 | 19934 | 38182 | 0.669% | 0.552% | 0.608% |
2012 | 126 | 122 | 248 | 16722 | 18335 | 35057 | 0.753% | 0.665% | 0.707% |
2006-2012 | 1044 | 1188 | 2232 | 131697 | 143669 | 275366 | 0.793% | 0.827% | 0.811% |
Now that we have an ideas of what amount of good luck is normal let’s look at Miguel Cabrera. The table below shows Miguel’s luck number for this year and his expected number based on league average levels of luck.
hr | lucky | potential lucky | Luck% | relative luck | |
Cabrera ’12 | 44 | 7 | 148 | 4.730% | 1 |
AL ’12 | 38.11 | 1.11 | 148 | 0.753% | 6.281182 |
MLB ’12 | 38.20 | 1.20028 | 148 | 0.811% | 5.831973 |
NL ’06 | 38.76 | 1.75528 | 148 | 1.186% | 3.987968 |
Cabrera’s luck percentage% of 4.7% is pretty darn lucky; he was just more than 6 times as lucky as the average AL player this year, and even those lucky NL hitter in ‘06 aren’t close to Cabrera who had 4 times as much luck. So if Cabrera does win the MVP this year he should consider himself one of the luckiest men on the face of the earth.