RADAR LOVE

Fascination with the fastball (a.k.a. smoke, cheese, cheddar, heat, gas) is as old as baseball itself. But now everyone—scouts, fans, Little League dads—is obsessed with differentiating between fast and faster. It's the golden age of speed freaks: one nation, under the gun
April 03, 2011

Three thousand, seven hundred forty-three pitches into last season, Tigers righthander Justin Verlander peered in at Shin-Soo Choo of the Indians and decided on the most basic, brutal means of getting him out. It was the bottom of the seventh on Sept. 29, and Verlander, finishing his sixth year in the majors, intended his next three deliveries to be his last of 2010. So he became the nine-year-old kid at the pitch-speed booth in a Class A ballpark, or the teenager at the county fair with only a pyramid of milk bottles standing between him and the stuffed animal that would light up his girlfriend's face.

All of which is to say Verlander went all Charlie Sheen on Choo: He channeled Rick Vaughn, the fictional flamethrower played by the actor in the first two Major League movies. "I tried to throw it as hard as I could," said Verlander, whose average fastball velocity of 95.4 mph last year was the highest among American League starting pitchers. "I had two outs, and I knew it was my last inning of the year."

With Detroit and Cleveland out of contention, Verlander put on a light show—the lights belonging to the digital pitch speed readout on the scoreboard at Progressive Field. Verlander struck out Choo on three straight fastballs that lit up the Tigers' radar gun at 102, 102 and, on pitch number 3,746, 101. "A lot of adrenaline," Verlander says, "always helps."

Something is up in major league baseball: velocity. By any name—cheddar, cheese, heater, hummer, dead red, express, number one—the almighty fastball fascinates us like never before, thanks not only to the ubiquity of those throwing it but also to the ubiquity of those clocking it and displaying it. Welcome to Radar Nation, where the ideal velocities resemble temperatures in Phoenix in July.

Among the crop of young arms that helped turn 2010 into the Year of the Pitcher are some delivering so much heat that they are pushing world records and the very fibers of their bodies. Last season marked the debuts of the hardest-throwing starting pitcher and the hardest thrower—ever. The Nationals' 21-year-old rookie Stephen Strasburg (average fastball, according to the website Fangraphs: 97.3 mph) packed ballparks and boosted television ratings until he blew out his right elbow in just his 12th big league start. And Reds rookie reliever Aroldis Chapman, now 23, hit triple digits on the radar gun with regularity, including a lightning bolt to Tony Gwynn Jr., then of the Padres, on Sept. 24 that was clocked at a world-record 105.1 miles per hour.

Three months ago Chapman walked into a tattoo parlor in Miami to make sure the historic radar gun reading acquired more permanence. On the underside of his left wrist is a baseball with a trail of orange flames behind it and an inscription that reads 105.1 mph. What kind of editing might be required if Chapman throws even harder? "I'm going to leave it there," Chapman said this spring through his interpreter and friend, trainer Tomas Vera, "and I'll put 106 on my car."

Chapman is an aficionado of cars that—surprise!—go fast, and he has tagged his Lamborghini, Mercedes and Porsche with a series of vanity plates that began with 102 mph and are up to 105 mph. Asked what travels faster, his fastball or his Lamborghini, Chapman chuckled and replied, "No se," then decided, "Lambo."

The fastball is the Lamborghini of pitching: Sexy and sleek, it turns heads as it passes by with a dangerous if darkly pleasing whoosh. From Walter Johnson to Bob Feller to Steve Dalkowski to Nolan Ryan to Sidd Finch to Nuke LaLoosh to Rick Vaughn to Colt Griffin to Joel Zumaya to Chapman, the fastball has blazed across baseball history, leaving a vapor trail of stories true and imagined.

In sorting out fact from fiction, here's some advice: Don't blink.

You can't hit what you can't see.

—A scout's report on Walter (Big Train) Johnson, 1907

Every millisecond counts. A respectable heater, at 92 mph, takes 400 milliseconds to reach home plate, assuming it leaves the pitcher's hand about 5½ feet in front of the rubber. Last year 24 pitchers (minimum: 60 innings) averaged 95 mph or better with their fastballs—those took 398 milliseconds to arrive home. Chapman's 105.1-mph heater traveled the same distance in 360. The blink of an eye takes between 300 and 400 milliseconds.

"There's not much difference between 98 and 100," Gwynn says, "but after that it's kind of a blur. You've got to go up there looking for a fastball, so if Chapman throws his slider for a strike, there's not much you can do. Being lefthanded, that's not a good time against him. Righthanders probably see it a little longer—a little."

Velocity is the eye candy of pitching, especially with radar gun readings flashed in ballparks, on television and in online game accounts. General managers, managers and coaches all love velocity too, because speed allows for a greater margin of error. The 17 hardest-throwing starting pitchers last year, whose fastballs averaged at least 93 mph, combined for a 3.43 ERA and a .601 winning percentage (244--162). The 17 softest-throwing starting pitchers, who averaged 89 mph or less, had a 4.13 ERA and a .476 winning percentage (185--204).

Heat creates energy at the ballpark, going all the way back to 19th-century fireballer Amos Rusie, who threw so hard that he helped persuade the game's architects to move the distance of the mound from 50 feet to 60'6". But now the quantifying of velocity has added to the buzz. In fact, the radar gun readings at the ballpark often get a bigger reaction from fans than the pitches themselves.

Chapman can cause a stir simply by warming up, as happened during his major league debut last Aug. 31. "You could see fans started moving to the bullpen to watch him," says Cincinnati G.M. Walt Jocketty, "and then when he came into the game, they started moving behind the plate."

Listed at 6'4" and 185 pounds, Chapman is a skinny bundle of fast-twitch fibers with an arm as flexible as a garden hose. Part of the wonder of Chapman is that he doesn't look all that powerful, at least until he uncoils toward the plate with an especially long stride. "I look at how his delivery works, how much the trunk and back and big muscle groups are involved, and there's a lot behind the ball," says Reds pitching coach Bryan Price. "But look at [6'10"] Randy Johnson. He was a short-strider with a very limited lower half. You can't say, Let's take all the hard throwers and look at the delivery and find a common thread."

Ask Chapman where the velocity comes from, and it might as well be his diet ("In the beginning, I liked Cuban food. Now I like everything"), viewing habits ("Five to seven soap operas a day") or superstition on the mound ("I wear underwear that is old and kind of ripped up. I can never take that away").

Says Chapman, "Those mechanics things are for science people. When I'm pitching I do things the same way. Sometimes I put more power into ones than the others. I think you're born with speed, and then I think the work I did since I was little helped me a lot. I don't know. It's something my Lord gave me."

Velocity may be heaven sent, but measuring it is a man-made convention that has helped to change the game.

Every hitter likes fastballs just like everybody likes ice cream. But you don't like it when someone's stuffing it into you by the gallon. That's how you feel when Ryan's pitching.

—REGGIE JACKSON, 1975

For baseball's first century there was no express way to clock pitches, though scientific devices sometimes were rigged to gauge speeds for promotional purposes. In Cleveland in 1917 a wire-and-steel contraption called a "gravity drop interval recorder" timed Johnson, Christy Mathewson and Smokey Joe Wood, some of the era's hardest throwers. They produced respective readings of 134, 127 and 124 feet per second. (A 95-mph fastball travels 139 feet per second.) In 1946 a photo-electric cell device built by the Army at Washington's Griffith Stadium clocked Feller at 98.6 mph in a promotional event that drew 31,000 fans, well above the hometown Senators' average. The cell measured Feller's fastball as it crossed the plate and entered the unit—not as it left his hand, the way today's radar gun does, which would have resulted in a higher reading.

Such machine testing was rare and inconsistent until 1973, when Michigan State coach Danny Litwhiler, a former major league outfielder, borrowed the radar gun used by campus cops and clocked his pitchers from inside a car parked behind the backstop. Police had been using the guns since at least the 1950s. Aimed at a moving object, they send a beam of electromagnetic waves that bounce off an object and back to the gun, which measures the frequency shift in the waves that return to calculate the speed of the object.

Litwhiler found the gun did not always give a reading on pitched balls, so he called CMI Inc., the Colorado company that manufactured it, and learned that it could be recalibrated to read smaller objects. Litwhiler made the adjustment, and that prototype is now in the Hall of Fame. Litwhiler made one more change. Radar guns at the time were powered through the cigarette lighters in cars. He asked the JUGS company, which produced pitching machines, to develop a battery-powered radar gun. Within a decade JUGS would become synonymous with pitch tracking, the guns standard issue for big league scouts.

Meanwhile, in 1974, Ryan was creating such excitement with his fastball for the California Angels that the team summoned technicians from Rockwell International to rig up radar timing devices and asked fans to guess the speed of his fastest pitch against the White Sox. Ryan reached 100.8 mph—in the ninth inning of a game in which he threw 159 pitches. Two weeks later he hit 100.9 mph. Ryan's pitches were clocked when they were about 10 feet from home plate, which subtracted as much as 6 mph to 8 mph from their peak velocity.

Are today's top throwers as fast as he was? "It's hard for me to say," says Ryan, 64, now president of the Rangers. "I don't doubt that every generation that comes along has guys who throw as hard as guys in my generation and before. We know more about mechanics and sports medicine, so I just think [hard throwers are] more available."

One year after the Rockwell test, in the spring of 1975, Michigan State played a tournament in Florida, and Litwhiler brought his gun. He called up Earl Weaver, the manager of the Orioles, who trained in Miami, and said, "I've got something to show you." Weaver loved the device. He used it on his pitchers, his outfielders and even a plane as it descended. "All of our scouts," Weaver recalls, "no matter who it was, they would always say, 'This guy throws as hard as [Jim] Palmer.' I once put the radar gun on one of them, and he threw about eight or nine miles an hour slower than Palmer."

Weaver used the gun as a managing tool. He liked knowing if one of his starters was losing velocity late in a game and might need to be pulled. He especially liked using the radar gun to ensure that Baltimore's pitchers kept a wide gap in speed between their fastball and their breaking pitches. "When [Mike] Cuellar threw his screwball a little too hard and it didn't break," Weaver says, "you could tell right away on the radar gun."

The Orioles and the Dodgers were two of the early radar gunslingers. In 1975, in a unique intersection of two of the most important developments in pitching, Tommy John operated a radar gun behind home plate at Dodger Stadium while recuperating from the first elbow-reconstruction surgery, the procedure that would come to bear his name. He would predict rallies when he saw a pitcher's velocity drop late in a game. By '78 nine teams were using radar guns, and by the early '80s the tool had become essential, especially for scouts. (John was replaced by Mike Brito, a scout who sported a Panama hat and smoked a cigar in his field-level box behind home plate in L.A., lending panache to the job.)

"I started traveling with a gun in the early '80s," says Joe McIlvaine, a special assistant to the general manager for the Twins who was scouting director for the Mets then. "Before that it was really hard to gauge velocity, especially if you were out at night on a dimly lit field. It could trick you. A guy could look so much faster under those conditions. I once recommended a kid I saw at night. When the scouting director came out to see him and brought his gun, the kid was throwing only about 79 miles an hour. I felt awful. But those were the challenges back then."

The Red Sox have pregun scouting reports on file that defined velocity with words such as rapid or firm and rated prospects overall with a simple scale of 0, 1 or 2. The human eye made for a much less accurate gauge of speed, but it helped launch legends. None was bigger or more cinematic than Steve Dalkowski, a pitcher Cal Ripken Sr. once estimated threw 115 miles an hour.

Joe Reardon (manager): "He walked 18?!"

Larry Hockett (coach): "It's a league record."

Reardon: "Struck out 18."

Hockett: "League record. And he hit the radio announcer, a sportswriter, and the bull mascot twice—also league records. Joe, the guy's got some serious s---.

—From Bull Durham

Pitchers who throw hard are drafted higher, sign for more money and get more chances to fail than those who don't. That's because the baseline of velocity, like the baseline of foot speed, can increase only so much. "With young guys," Price says, "we feel like if he has arm strength, we can teach him how to pitch, how to clean up his delivery, how to take velocity off the ball and make it spin a certain way. But you can't teach arm strength. You can't guarantee that a kid who has a good body and good delivery and is throwing 84, in three or four years he'll be throwing 94."

Not without steroids, at least. Pitchers learned they could add speed with illegal drugs. Righthander Dan Naulty, for instance, a 14th-round pick of the Twins in 1992, told the New York Daily News in 2007 that his fastball jumped from 86 to 95 mph in three years with a regimen of steroids, human growth hormone and amphetamines. "Steroids definitely made pitchers throw harder," says one AL general manager. "And that is why the crackdowns on age falsification and performance enhancers have been big issues in Latin America. If a kid in Latin America shows enough arm strength, he's going to get signed. But for a long time, when you had trouble verifying age and with drugs available, it was buyer beware."

Says Rockies ace Ubaldo Jimenez, a Dominican native whose average fastball velocity of 96.1 topped all starters who qualified for the ERA title last year, "Ninety is a very big number in the Dominican. So is 16. You know if you can throw 90 in a workout for scouts when you are 16 that you can get signed. Everybody knows how important 90 is."

That same awareness is creating what some scouts call "velo whores" in this country. Showcase tournaments, in which high school prospects pay hundreds of dollars to be seen by college and pro scouts, often allow pitchers to face as few as four batters in a game setting. As a result, many young hurlers learn to throw as hard as they can in the hope of getting noticed and don't bother to cultivate well-rounded pitching skills.

"What we're doing now is taking hard throwers and pushing them quickly into the big leagues as relievers because they have velocity," Brewers G.M. Doug Melvin says. "We're probably missing out on some very good starting pitchers because we don't have the patience to develop a good arm."

Still, the landscape is littered with pitchers who failed even with premium velocity. In 2001, with the ninth pick, the Royals drafted righty Jonathan Colt Griffin from Marshall (Texas) High and gave him a $2.4 million bonus. He was purported to be the first high school pitcher clocked at 100 mph, though Allard Baird, the Royals' G.M. at the time, says, "We never had him at 100. He touched 97, 98, but we never had 100."

Griffin was out of professional ball five years later. He advanced no further than Double A, with a career record of 19--25, a 4.79 ERA and more walks than strikeouts. "After we signed him, we never saw the same velocity," Baird says. "It went down immediately."

Griffin was among the 13 hardest throwers listed in Baseball America's 2002 Prospect Handbook. Of those 13, five failed to make the majors or had little more than a cup of coffee in the Show. Only two are big league starters today: Carlos Zambrano of the Cubs and Aaron Cook of the Rockies, who now average 90 and 89 mph, respectively.

Radar gun technology has made finding fireballers something close to an exact science. It wasn't always so, and while the human eye made for a much less accurate gauge of speed, it also helped launch legends—like the one surrounding Dalkowski. "Steve Dalkowski," says Weaver, who is 80, "threw harder than anybody I have ever seen. He threw harder than Ryan. He was a lefthander, throwing directly overhand, and he had that rotation on the ball that would make it hop six to eight inches. The ball looked like a golf ball driven off a tee."

The 5'11" Dalkowski, who signed with the Orioles at age 18 in 1957 after graduating from New Britain (Conn.) High, pitched nine seasons without ever reaching the majors. Ted Williams reportedly once stepped in to hit against him during spring training, let one pitch go by and walked out, swearing he never saw the ball and vowing never to return.

The stories about Dalkowski are Bunyanesque. He threw a ball through a wooden fence—in four different ballparks. He broke the mask of umpire Doug Harvey in three places, sending him to the hospital. He tore off part of a batter's ear with high heat. He fired a ball through a backstop, causing the fearful crowd in Elmira, N.Y., not to sit behind the plate. While pitching for Class D Kingsport, Tenn., in 1957, Dalkowski had 24 strikeouts, 18 walks, six wild pitches and four hit batters—in one game.

"Right out of high school he had trouble getting it into the [batting] cage," Weaver says. "He had a great second half of a season for me in Elmira [in 1962]. I had him throwing at 90 percent to get the ball over, and he was still throwing 95 to 100 miles an hour. Sometimes coaches would have him throw 80 to 90 pitches in the bullpen, just to be a little tired. It wasn't easy for him to learn about pitching."

Dalkowski hurt his arm in 1963 and was out of baseball after the next two seasons. In '66 the Orioles signed an infielder who would hear stories about Dalkowski as he traveled through minor league outposts such as Bluefield, Stockton, and Rochester. That infielder, Ron Shelton, would use those Dalkowski stories to help shape the character of Nuke LaLoosh in his film Bull Durham.

I threw so hard I thought my arm would fall right off my body.

—SMOKEY JOE WOOD, on the last two outs of Game 1 of the 1912 World Series

The arm can withstand about 80 Newton-meters of torque on the elbow before the joint snaps. Pitchers who can reach 100 mph press against this limit every time they throw, which is why you are unlikely to see someone who is freakishly faster than everyone else. The giveaway was in the biomechanics when George Plimpton created Sidd Finch and his 168 mph fastball for Sports Illustrated in his April Fool's Day classic of 1985. Unlike sprinters, swimmers and jumpers, pitchers are not becoming much faster. But better training has produced more arms with elite velocity.

"I think we're at the limit," said Glenn Fleisig, research director for the American Sports Medicine Institute in Birmingham. "For these hard throwers to stay healthy, a big thing is to listen to their bodies."

A study published last year by Brandon D. Bushnell, an orthopedic surgeon in Rome, Ga., and colleagues followed 23 pitchers over three seasons to determine if there was a link between velocity and elbow injury. Nine of the pitchers hurt their elbows during those three years. The study concluded that "pitchers capable of throwing at a higher maximum ball velocity had a higher risk of elbow injury and that the players throwing at the highest velocity had injuries requiring surgical reconstruction."

It's a simple enough link: The harder you throw, the more torque you put on your elbow and shoulder. And the younger you are when you develop high velocity, the more at risk you are to the effects of stress and overuse. Until Chapman came along, the Tigers' Zumaya owned the fastest recorded pitch: a 104.8-mph hummer in the 2006 American League Championship Series. He has since suffered repeated injuries to his right arm and elbow.

Said Fleisig about high velocity, "It's a blessing and a curse."

Though new technologies, such as Pitch f/x, can track the speed and break of a delivery on its path to the plate, radar readings used on television and in ballparks can be manipulated for entertainment and competitive reasons. Home teams, for instance, have been known to show lower readings for the visitors, trying to cause their pitcher to doubt his stuff or to try harder. The radar readings have become as much a staple on scoreboards as runs, hits and errors. Many teams clock pitches in spring training. When Jacob Turner, a 19-year-old prospect for Detroit, threw in a 10 a.m. simulated game last month in Lakeland, Fla., a dedicated scoreboard lit up with his readings.

"Yeah, I look at it," says Red Sox reliever Daniel Bard, who led all pitchers with at least 60 innings last year in average fastball velocity (97.9 mph). "I'll get a ball back and start rubbing it up, and then I'll take a peek at the board. Usually it's when one felt really good coming out of my hand and I think, I wonder how fast that one was?"

I threw him an 87-mph fastball, and he crushed it. Last year I averaged 96. Now when I reached back, it's just not there. I can't believe that I forgotten how to throw heat.

—RICK VAUGHN in Major League

The love affair between a pitcher and velocity is cruel. Velocity prefers younger men, and it can desert them quickly when they age. Of the 17 hardest-throwing starters last year, all were between 23 and 28 years old with the exception of the Yankees' CC Sabathia, 30, and A.J. Burnett, then 33.

When you expand the sample size to include relief pitchers—the 24 pitchers with at least 50 innings who averaged 95 miles an hour or more—only six still could bring the heat past their 30th birthday: Santiago Casilla, 30; Matt Lindstrom, 31; Jose Valverde, then 32; Matt Thornton, 34; Fernando Rodney, then 33; and Billy Wagner, 38, who took his 95.7-mph fastball into retirement. (Curiously, Wagner and Thornton were the only lefthanders among the fastest 24.)

Ryan was 27 when the Rockwell folks showed up in Anaheim to measure the famed Ryan Express. He would lead the league that season with 332 2/3 innings and 367 strikeouts, not to mention 202 walks. He ran up epic pitch counts and threw every fourth day. Ryan told SI then, "I don't look for longevity. I look for productivity. If I can escape injury, I should be a fastball pitcher for maybe another five years."

Nineteen years later, at age 46, Ryan still was throwing fastballs past big league hitters until his elbow finally gave out. When he recorded his 5,000th strikeout, in 1989, the pitch that blew by Rickey Henderson was clocked at 96 mph. Ryan was 42 years old. "We had nothing to base it off of," he says of going 14 years past his expected expiration date. "In those days it was about at 32 when power pitchers faded to the wayside, either due to injury or a lack of velocity.

"It's a God-given ability. It's genetics and staying away from injury. I didn't show velocity until I went out sophomore year for the high school baseball team. That's when I hit my final growth spurt, and I think that's when it came together. Prior to that I didn't throw it any harder than other kids, but I could throw it farther."

Today radar guns are in constant search of the next Nolan Ryan. Look behind the backstop at a spring training game when a new pitcher enters: As many as a dozen $700 devices are raised in unison by the sun-screened scouts, forming a veritable firing squad. Look at the biggest summer amateur showcases: A hundred guns or more are snapped into ready position by scouts and college coaches. And look behind the plate at a youth game in a well-to-do suburb: Starry-eyed dads are hoisting the Pocket Radar, the latest advancement in the velocity wars, a $200 tool the size of an iPod that turns anyone into a technician at the Aberdeen Proving Grounds.

We've come a long way since Danny Litwhiler pulled a car behind the backstop and plugged a campus police radar gun into the cigarette lighter—but not as far as you might think. Velocity is a bit like the moon, mapped and measured so well that much of its romantic mystery is gone. We know to one tenth of one mile per hour how fast Chapman's fastball travels over every inch of its 55½-foot path. It is not 168 miles an hour. It is not green cheese.

"All of baseball has used the radar gun as a tool," Ryan says, "but sometimes you can call it a crutch. The first thing people will ask is, How hard does he throw? I don't think they evaluate [pitchers] much on what their natural stuff is. How much trouble does a hitter have picking up a pitch? What kind of movement does he have?"

Velocity alone can't determine which pitchers succeed and fail. Jamie Moyer threw a shutout at age 47 last year with his fastest delivery at 83 mph; Matt Anderson, the No. 1 pick of the 1997 draft, who once hit 103 mph, washed out with a 5.19 career ERA. There are devices better than the radar gun at deciphering those deeper mysteries, which are more art than science, more Norman Rockwell than Rockwell International. They are called, just as they were in the days of Rusie and Smokey Joe and the Big Train, major league hitters.

GOING BACK TO THE GAME'S EARLIEST DAYS, HEAT HAS ALWAYS CREATED ENERGY AT THE BALLPARK. BUT NOW RADAR GUN READINGS OFTEN GET A BIGGER REACTION FROM FANS THAN THE PITCHES THEMSELVES.

"YOU CAN'T TEACH ARM STRENGTH," SAYS PRICE. "YOU CAN'T GUARANTEE A KID WHO HAS A GOOD BODY AND A GOOD DELIVERY AND THROWS 84 WILL BE THROWING 94."

PITCHERS ARE NOW FOLLOWED BY AN ARMY OF GUN WIELDERS—FROM THE MAJORS DOWN TO YOUTH LEAGUE GAMES, WHERE A DEVICE CALLED THE POCKET RADAR TURNS ANYONE INTO A SCOUT.

PHOTOPhotograph by MICHAEL J. LEBRECHT II/1DEUCE3 PHOTOGRAPHYGUNSLINGER Verlander was the hardest-throwing AL starter in 2010: His average heater whistled in at 95.4 mph, but he could easily pump up his radar readings to triple digits. PHOTOROBERT BECK; BACKGROUND BY SI IMAGING (CHAPMAN)CUBAN MISSILE Chapman's radar postings dazzle fans and then disappear from scoreboards, but over the winter he had his record 105.1 mph delivery preserved forever with a tattoo on his left wrist. PHOTOAL BEHRMAN/AP[See caption above] PHOTOESPN TV (MIDDLE)[See caption above] PHOTOBETTMANN/CORBIS (FELLER)MEASURES OF RESPECT The Army clocked Feller at 98.6 mph in '46; Dalkowski (inset) was gauged only by naked eyes, but those who saw the wild lefty swore he could crank up his fastball to 110. PHOTOFORREST JACKSON/TIME MAGAZINE (DALKOWSKI)[See caption above] PHOTOBRAD MANGINMAGIC NUMBER The game's hardest-throwing starter, Jimenez learned to bring the heat in his native Dominican Republic, where hitting 90 on the gun is the key to catching scouts' eyes—and landing a contract.
PHOTOJOHN BIEVER[See caption above] PHOTOTOM DAHLIN; BACKGROUND BY SI IMAGING[See caption above]

HOLE YARDS PAR R1 R2 R3 R4
OUT
HOLE YARDS PAR R1 R2 R3 R4
IN
Eagle (-2)
Birdie (-1)
Bogey (+1)
Double Bogey (+2)