Thursday, January 7, 2016

How far can a major leaguer hit a baseball?

The discussion has to begin with a definition of terms. We don't mean "off the top of Mt Everest" or "on the Moon" or even "in Denver." If you were to go take Giancarlo Stanton out to an open field in Denver and let him hit with an aluminum bat on an 70-degree day with a 40 mph tailwind, he could probably blast some monumental homers. But that's not what we mean.

We are trying to determine how far a very powerful man can drive an official baseball with a legal wooden bat, assuming that the ball lands at field level, there is no wind, the park is at sea level, the temperature is 75 degrees, the barometer is steady at 29.92, and the relative humidity is 50%. Given those parameters, we can use physics to make the determination. All we need is the exit velocity of the ball from the bat, and then we can determine the optimal flight angle necessary to maximize the carry, using a downloadable Excel spreadsheet created by a physicist.

We can obtain that exit velocity. Home Run Tracker charted every major league home run for more than a decade, and the highest exit velocity they have ever recorded or estimated for a ball leaving a wooden bat is 122.4 mph. Note that there were nearly 1.5 million batted balls in MLB in that period, and only 18 homers were produced by a ball velocity of at least 120 mph off the bat. It is such a rarity that in 2014 and 2011, there were none at all. But we'll assume 122.4 mph as the human limit for our model, since it has been done once, when Giancarlo Stanton hit a grand slam off Jamie Moyer in that ageless pitcher's second-last game in May of 2012. Making all the standard assumptions I listed above, a ball with an exit velocity of 122.4 mph, stroked at the optimal angle for carry, will land a bit less than 515 feet away.

That's it.

515 feet is the very limit for human beings as we know them today.

Mind you, that distance is highly unlikely to be achieved in reality, since only one batted ball out of a million is hit with that velocity, and on that one time in a decade when it happens, there is no guarantee that it will be launched at the optimal angle with the optimal spin (severe topspin would decrease its flight distance, as in any ball sport). Let's look at a more realistic possibility. How often can we expect to see a ball hit 500 feet?

If we drop the exit velocity on the model to 120 mph, we see that a 500 foot homer can be produced within a certain range of lift angles. A quick look at Giancarlo Stanton's home run history shows that he hits about a third of his homers within that range. Let's assume that he is typical in that regard, and that about half of the homers launched at the right angle also spin appropriately. Based on those assumptions, the 18 balls which reached that velocity in the past decade should have produced six homers capable of exceeding 500 feet, of which perhaps three would have the correct spin to actually reach that distance. 502 feet would be the maximum distance achievable from a launch velocity of 120 mph. According to Home Run Tracker, there were five homers in the range of 494-504 feet during their existence, which is quite close to our expectation, and is probably virtually identical, because we have made some assumptions, and Home Run Tracker has made some estimates. They estimate where a ball would have landed at field level by using the known parameters and sometimes those observable parameters are not always detailed enough to get the distance precisely right. At any rate, only one homer in the past ten years traveled, or rather would have traveled if allowed to land at field level, 500 feet or more. In late September of 2008, Adam Dunn blasted a 504-footer off Glendon Rusch at Chase Field.

That one is a completely legitimate 500-footer, in that it received only a minimal amount of assistance from meteorological conditions. HRT estimated that it would have traveled 502 feet in our defined standardized conditions, and that is an exact match for our guess for the theoretical realistic maximum. It's important to realize, however, that today's players are bigger and stronger than their predecessors, yet those brobdingnagians produced only one 500-foot homer in more than ten years. The conclusion to be drawn is this: any time you read of a homer traveling more than 515 feet, it can only be attributable to Mother Nature or Mother Goose. Even 500-foot homers are exceedingly rare. Giancarlo Stanton, for example, at 6'6" and 240 pounds of solid muscle, and almost certainly the strongest hitter in baseball today, if not in all of history, has never hit a ball 500 feet, with or without the wind, as of the end of the 2015 season. At that point he had hit 181 official major league home runs, and the longest one recorded by HRT was a 494-footer he hit in August of 2012 - and that was in Coors, aided by the altitude! (The video is below.) In the 2016 Home Run Derby, he hit 61 blasts, including the eight longest of the competition, but still failed to reach 500 feet with his longest (497).

What about the legendary homers in history?

Mythology or meteorology. As Sherlock Holmes might advise, rule out the impossible and find the solution among the other options.

Based on the same theoretical model, the only legitimate 500-foot homer in history I could find that was not affected by the weather conditions was Mickey Mantle's blast off the facade in Yankee Stadium in 1963. Mickey said this was the hardest he ever hit a ball, so let's assume he produced a ball velocity of 120 mph off the bat. He would not be able to go to go much beyond that, because Mickey, at 5' 11 1/2", 195 lbs, was much smaller than Stanton or Dunn, and his shorter arms would be at a major disadvantage in creating the kind of torque produced by those giants. (Adam Dunn played at 6'6", 285.) Furthermore, the pitchers of Mickey's day were not consistently throwing with the velocity of today's pitchers, so Mickey wasn't getting as much help from them. (Disregarding the spin, the general rule is: the faster the pitch, the faster it comes back off the bat). We know precisely where Mickey's homer struck the facade, and it was at a spot 363 feet from home plate and 102 feet in the air. If we assume a lift angle of 25.5 degrees at 120 mph, we can get the ball to that exact point, and we therefore can determine that the ball would have traveled 502 feet in the air if allowed to land at ground level. The temperature was 70 degrees and there was a 13 mph breeze blowing that day, but it was blowing out to left field and Mantle hit his ball to straightaway right, so the wind was no factor and it was a certifiable 500-footer.

Note: the original image above shows that the facade was 370 feet away and 118 feet in the air. If that is correct, then the ball would have required a lift angle of 30 degrees to get there, and would therefore have come down sooner, at 496 feet. That is a possible alternate assumption, but we believe the revised distances (363, 102) to be correct.

One analyst asserted that Cecil Fielder hit a 502-foot homer in 1991. The distance on that one is certifiable, so Fielder may join Mantle and Dunn in the 500 Club, but the wind information is missing, so we cannot be sure.

One other ball that we have good data on came close to 500.

Roberto Clemente timed a hanging breaking ball from the great Sandy Koufax in 1964 and blasted a low liner into a light tower at Forbes Field. It was already 457 feet from home plate when it hit the tower, and that spot was 32 feet above the ground. If the ball left the bat at 119 miles an hour, just slightly sub-Mantle, with a low lift angle of 21 degrees, typical for Clemente, it would get to that exact point, and we can therefore extrapolate that the ball would have traveled 492 feet if unobstructed, as shown in the baseball card above. There was no appreciable wind that day. Surprisingly, neither Clemente nor the Pittsburgh sportswriters seemed suitably impressed at the time. The article in the next day's Pittsburgh Press (click on the thumbnail to the right to see it at full size) said that Clemente felt he hit one better in an earlier game - and that one was caught for an out.

Of the other alleged 500-foot homers in the past, they fall into two categories: mythology or meteorology. Either they did not travel 500 feet at all, or they were greatly assisted by the wind and/or other weather factors. Home Run Tracker debunked the ones that simply did not go that far. Here are five that did travel that far, in descending order of the distance they would have traveled if unimpeded:

1. A young Mickey Mantle hit a legendary blast off Chuck Stobbs at Griffith Stadium in Stobbs's first start of 1953. Baseball lore has recorded this as having traveled either 562 or 565 feet. It didn't go that far, but it went a long way, and it still seems to be the longest one we can validate. We know two things about its path: (1) it nicked a sign 460 feet from home plate and about 55-60 feet in the air; (2) it had to strike or clear a 22-foot roof about 512 feet from home plate in order to get into the backyard area of another set of row houses; (3) it did not clear because the ball was ruptured from where it struck the roof. We also know what the weather report was that day. Mantle himself has said that the tailwind was "about 50 mph," but Sam Diaz, a local meteorologist, reported more precisely that the wind was 20 mph, gusting to 41. If we assume the ball left the bat at 115 mph (remember Mantle said he didn't hit it as hard as the other one), took off at a 29 degree angle, and had an average wind velocity of 20 mph (a ball is typically not affected by the wind for about the first 15% of its flight), the model produces the exact values we need for all points on the parabola, and tells us that the ball would have carried about 542 feet unobstructed. A researcher and a physicist studied this homer in depth and came to the same conclusion, albeit with slightly different assumptions.

2. Reggie Jackson really cranked one in the 1971 All-Star Game. Although it was only July, baseball's Mr. October hit a transformer about 380 feet from home plate and 100 feet above the level of the field. The wind gusts in his favor ranged from 17 to 31 mph, averaging 24. Assuming an exit velocity of 114 mph, a lift angle of 31 degrees and an average impact of 21 mph (85% of 24) from the wind, we can get the ball to that spot we are sure of, and thence determine that the ball would have traveled 541 feet. (Home Run Tracker estimated 539 feet with slightly different assumptions. There are multiple scenarios which would produce the required point on the curve, but the final results don't vary much.)

3. Ted Williams launched his famous "red seat" homer at Fenway in 1946. It landed 502 feet from home plate, into a fan seated 30 feet above field level. The wind was 19-24 mph that day, averaging 21.5, so we'll take 85% of that and assume that the average assistance from the wind was about 18 mph. A ball velocity of 115 mph off the bat and a lift angle of 30 degrees will get the ball right to that seat, and project that the ball would have traveled 537 feet if it had landed at field level. (Home Run Tracker estimated 530 with slightly different assumptions.)

4. Dave Kingman blasted a mammoth drive out of Wrigley Field in a 1976 game, assisted by a 16 mph tailwind. We don't need much theory to determine where that would have landed, because we know exactly where it did land - on the porch of the third house from the corner on Kenmore, 530 feet from home plate. To my knowledge, Kingman's homer landed the farthest from home plate of any blast in history, because the ones we consider longer are based on theoretical landing places, while Kingman's actually came to earth.

5. On May 11, 2000, a Cubbie named Glenallen Hill hit a moon shot out of Wrigley Field and onto the roof of a building across the street from the stadium - about 30 feet above the field and 460 feet from home plate. There was an 18 mph wind behind him, so placing 85% of that into the model and assuming 111 mph exit velocity and a lift angle of 28 degrees will get the ball to that exact spot and produce the final unobstructed distance of 500 feet. This homer is partially tainted since Glenallen later admitted to having used PEDs, but he has earned his way back into the game's good graces through tireless efforts as a long time coach and minor league manager.

Note that none of these five homers were hit with enough force to travel 500 feet without the wind. Each of them would have been in the 450-485 range, which is still a rare achievement. With these five eliminated, Mantle and Dunn are the only two guys who can be said to have driven a ball 500 feet on their own power, and even those two come with some caveats. Dunn's 504 was powered by steroids, and Mantle's 502 may actually have been 496 if those originally published stadium dimensions were correct. I have not covered every tape measure shot in baseball history, but you can be quite confident that any hit from a wooden bat carrying beyond 515 feet must be created by extenuating circumstances because the laws of physics determine that they cannot be entirely self-propelled. Slightly shorter historical homers, those purportedly in the 503-515 range, could have been entirely self-propelled, but almost certainly were not.

What about Mantle's 634 or 643 foot homer off Paul Foytack that went out of Briggs Stadium in 1960? (It was renamed Tiger Stadium the following year.) That landed in the lumber yard across the street.

Well ...

It is possible to hit a ball 634 feet if it is lifted at 30 degrees with a speed off the bat of 120 mph in a 40 mph wind. Given that nobody has reported such a wind that day, it would be wise to maintain a healthy skepticism. It was very possible for a 500-foot homer from that park to cross Trumbull Avenue and hit the roof of Brooks Lumber on a nearly windless day. These are not places shrouded in myth. Brooks Lumber is still where it always has been, as is the home plate of old Briggs/Tiger Stadium, and we can get a scaled map from Google Maps. Shown below is a very plausible 500-foot path from home plate.

The men who saw it "land" do not know whether it landed there on the fly or the bounce. How could they? Here is a physically possible scenario: Mantle launches the ball at 116 mph, less than his facade shot, at a 31 degree angle. With just a gentle 10 mph breeze behind him, he easily clears the back of the 94-foot grandstand at a point some 385 feet away at that angle, and gets the ball to the lumber yard roof, about 499 feet from home plate and about 18 feet in the air. He then gets an enormous bounce off the hard surface of that roof, and the story is born. My guess is that it landed at point X in the picture below and caromed left-rear into the company's open courtyard area, where the employee may well have seen the ball land some 600 feet or more from its launching pad - on the first or second hard bounce.

That happened on September 10, 1960. It's worth noting that Mantle's homer that day, unlike the monster blast he unleashed at Griffith Stadium, gathered no special attention from observers. The Associated Press report which appeared across the country the following day (click on the thumbnail to the right) was casual about the achievement, simply noting that it was the third time Mantle had cleared the roof, and the only other player to do so was Ted Williams. At the time, nobody felt it might be the longest homer in history. It later grew from a homer to a legend.

Afterthought: some weeks after I wrote this article, I ran into the annotated picture below. The author (whom I have failed to identify) drew almost the exact same conclusions as I did about the Briggs blast, although he feels the homer's first bounce was probably on the road rather than on the roof of the lumber yard. That is actually more likely than my hypothesis, since it would require about 490 feet of carry rather than the 510 or so necessary to go a few more feet forward and hit the roof that high. I like his similar theory better, but when I created mine, I thought the road had been ruled out as a possibility.

One more case study ...

Like Mantle's blast in Detroit, Josh Gibson's legendary blast out of Yankee Stadium started as a homer and grew into myth. In this case we don't need any physics to debunk it because it never left Yankee Stadium. It landed in the bullpen. Here are two articles (1, 2) which explore this matter in depth, using contemporary accounts and interviews with other players who were there that day.

What about other 600-foot blasts from Gibson, Mantle and others? Once again, it is possible to hit a ball 600 feet with a massive tailwind, so don't assume every account is false, but remember that Mantle's blast out of Griffith Stadium, even if you believe the hype, did not go 600 feet, and that was Mickey Effin' Mantle with a tailwind which may have been as strong as 41 mph, so approach such accounts with caution and skepticism. And if you read about such a thing happening on a calm day or in an indoor stadium, well ... it never happened. Simple as that.

A note written after the 2021 Home Run Derby: This article reported that the new record for a homer at sea level, without wind assistance, is 513 feet. That distance was reached by an Aaron Judge blast in Miami in 2017. That is very close to the maximum achievable under our tightly defined neutral conditions.


  1. Wow, thanks for assembling this. Fascinating. I'm a little surprised Bonds didn't hit any 500+ footers. I would have thought some of his monsters would be right up there.

  2. I couldn't deal with every homer that was claimed to be 500+. Bonds may have had some in there somewhere. I did think there was enough evidence to conclude that anything greater than 515 is impossible without Mother Nature or Mother Goose.

  3. The longest home run I have ever seen was hit by Sammy Sosa in the early to mid 2000's at PNC park in Pittsburgh. It cleared both bullpens and then bounced on the rounded top of a storage shed behind them and the kept going. The way I saw it, it cleared the shed, but that was apparently not the case. I would love to know how far that would have gone.

  4. I have seen accounts by some physics people who believe Mantle could and did indeed hit home runs over 500 feet because of the mechanics of his swing and of course his power and strength. Interesting article you have written for sure.

    1. At sea level indoors, there are only two basic elements to calculating the distance of a launched object - launch speed and trajectory. We know the human parameters of the former and we know the physics of the latter. The mechanics of Mantle's swing are irrelevant other than as components of the launch speed. Could he have produced a super-human launch speed with his average height and relatively short arms? Highly, highly, highly unlikely. Imagine the size of Stanton and McGwire, then compare that to Mantle. As I've noted in the article, the physics are well supported by reality. All of the homers longer than 515 feet are attributable to weather or mythology.


      It is possible to hit a ball more than 500 feet outdoors, at high altitudes, with a strong tailwind. Mantle's famous homer at Griffith Stadium did travel more than 500 feet - but with a 41 MPH tailwind, as Mickey himself often noted.