Manchester United may have suffered a nightmare Premier League campaign last season, but according to the latest edition of ESPN's Luck Index, Ole Gunnar Solskjaer's side were actually fortunate on several occasions and should have finished even lower than sixth.

United would have been four points worse off without their good fortune and ended the season in seventh place behind Everton, who were found to be the unluckiest side in the league last term.

- Marcotti: Findings from the 2019 ESPN Luck Index

Had Solskjaer's men finished seventh, they would have had to pull out of their International Champions Cup preseason tour, as the club would have had to play Europa League qualifiers instead.

United sacked Jose Mourinho in December and appointed club legend Solskjaer as his replacement, but both enjoyed good fortune, with the index showing no difference in luck between the two.

Last year's edition of the Luck Index showed that United were fortunate, too, and should have finished with six points fewer, as they were named the luckiest team of the 2017-18 Premier League campaign.

Champions Manchester City were found to be unlucky, with misfortune found to have cost them a record point total of 101 -- one better than the previous year.

This year's Luck Index also found that if you removed all of the fortunate goals from the player's scoring totals, City striker Sergio Aguero should have finished as the Golden Boot winner with 20 goals -- just one goal worse off.

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Arsenal striker Pierre-Emerick Aubameyang, who shared the Golden Boot with Liverpool's Mohamed Salah and Sadio Mane, was found to be by far the luckiest of the top scorers. He scored 22 times, but eight of them were found to be lucky, meaning that his adjusted total amounted to a less impressive 14.

Salah and Mane both scored four lucky goals, and they would have finished joint second in the top-scorers list.

Liverpool's title chances were not affected by fortune with their post-Luck Index point total unwavering at 97.

The luckiest team were Brighton, who survived relegation by two points, sacking manager Chris Hughton at the end of the season.

Instead, newly promoted Fullham should have stayed up. Their misfortune cost them five points and Premier League survival.

Brighton were actually one of the unluckiest teams in the 2017-18 campaign, finishing six places lower than they should have.

The unluckiest team this time around were Everton, who finished ninth but should have actually made sixth, meaning they would have qualified for the Europa League.

The ESPN Luck Index uses adjustments for red cards, penalty decisions and disallowed and deflected goals, among a host of other factors, to calculate the luck involved in each Premier League campaign.

We've all watched and wondered. We've all felt hard done by. We've all cursed the sliver of fortune and happenstance that turns victory into defeat. That's what prompted ESPN and the team led by Dr. Thomas Curran, at the London School of Economics, to compile the Luck Index, which returns for a second season.

The 2018 version found that luck had a profound effect on the top of the table. It gave Liverpool, the unluckiest side, an additional 12 points, which would have catapulted them from fourth to second. It also found that the gods were harsh on Arsene Wenger's final Arsenal side, who lost eight points due to misfortune, while being very kind to Jose Mourinho's Manchester United, gifting them six points: take them away and rather than finishing second, they would have been fourth.

- It's official: Man United were lucky all season long

We know that luck does not necessarily even out; not over a season, not over several seasons, probably not even over a lifetime. (Just ask Forrest Gump.) But as a predictor of trends for the following campaign, the Luck Index didn't do too badly.

Liverpool ended up as runner-up to Manchester City, pushing them hard all season and winning the Champions League and, according to the Luck Index, it was fully deserved. United crumbled, changed managers mid-stream and finished sixth despite being one of the luckier teams in the league once again. Arsenal, under Unai Emery, were one point off the top four -- actually, right where they should have been -- and reached the Europa League final.

This season's results are similarly intriguing:

It feels weird to say, but champions Man City were unlucky

Manchester City were unlucky this year and lucky the year before, suggesting that the 2018-19 version should have gained 101 points (misfortune cost them three points) and finished four points clear of Liverpool, while the centurions from 2017-18 were actually fortunate and gained an extra three points.

Man United were even worse than it looked

Ole Gunnar Solskjaer got a lot of credit -- and a full-time job -- for rescuing United from the disaster that was the first four months of Jose Mourinho's third season but when you break down the numbers, they were fortunate to finish sixth. Both managers at Old Trafford had good fortune in 2018-19 but when you break down the myriad injustices suffered by Everton, who were the unluckiest team in the Premier League last year according to the Luck Index, United should have finished seventh and out of the European places, with Everton finishing sixth on 62 points, ahead of United on goal difference. It's no wonder both teams have been busy making signings this summer.

Look away if you're a Fulham fan...

If Fulham feel hard done by their 19th-place finish and relegation last season, the Luck Index would tend to agree. It says they should have had an additional five points last season, which would have been enough to leapfrog Cardiff and Brighton in the adjusted table. (Both of those sides were extraordinarily fortunate to get an extra seven and eight points respectively through good fortune.) Viewed through that lens, Brighton's decision to part ways with manager Chris Hughton despite staying up makes a bit more sense.

Sergio Aguero was robbed

Luck also played a massive part in the race of the Golden Boot, which was shared by Mohamed Salah, Sadio Mane and Pierre-Emerick Aubameyang, each scoring 22 goals. Apply the Luck Index adjustments and the two Liverpool strikers lose four goals each, while Aubameyang loses a whopping eight. (The Arsenal striker paid a price for deflected goals, incorrectly awarded goals and converting incorrectly awarded penalties).

Check out the table:

All of this means we would have had a different top scorer last season: Sergio Aguero, whom the Luck Index stripped of only one goal, leaving him on 20 (rather than the 21 he had in reality).

Incidentally, there might be something to the old cliché whereby strikers make their own luck: each of the top eight goal scorers in the Premier League had goals taken away by the Luck Index.

This may be the point at which you wonder how on earth Dr. Curran and his team determine whether an incident was lucky/unlucky and what impact it might have had on a result. In this year's Luck Index, four types of incidents were considered: red-card incidents (both for players that should not have been sent off and players that should have been), penalty incidents (again, both those incorrectly given as well as those incorrectly not given), goals that were incorrectly disallowed (either by an errant offside or a nonexistent foul in the build-up) and deflected goals.

For the three categories of incident related to officiating errors, a panel that included qualified referees made the determination. There had to be consensus for the incident to be considered an error. The panel made a judgement call with regard to the deflected goal: only shots where the deflection played a key role, either in redirecting the ball on target or in misdirecting the keeper were considered.

On the first morning of the Test they were primed.

This was Fortress Edgbaston after all, a fortress that has long felt like a football ground; Tim Paine had dismissed, dismissed this as the 16th-most hostile venue in the world.

The first hour was a prelude; only a few lagers had been consumed in the morning. With each appearance of The Three during the pre-match warm-ups and fomalities, the boos grew in stridency and, by the time David Warner and Cameron Bancroft walked out to open the batting, they were occasionally punctuated with thumping cries of 'Cheat! Cheat! Cheat!'

The Barmy Army's Central Command was roughly in the middle of the Hollies Stand. Billy the Trumpet steered the chanting toward songs that supported the bowlers but it was several bays across where the vocal knives were unsheathed at the appearance of Steve Smith.

Eric Hollies denied Bradman a hundred average and - by Jove! - the stand bearing his name was going to deny Smith a happy return to Test cricket. Not by a googly, but by verbal laceration.

'We saw you crying on the telly', they sang, some of them wearing crying-on-the-telly-Smith face masks. Ho ho ho. Take that!

Each day it rose and fell, this wave of mockery and hostility. Some of it was pantomime, some vindictive. When Smith reached his masterful first-innings century, most of the crowd stood and applauded. But boos are louder than claps and so the minority jeerers held sway. Some were clapping and booing simultaneously and so on it went.

Warner tried to win them over by joining in the pantomime when he was sent to field in front of the most vociferous section of the Hollies Stand. When they sang "he's got sandpaper in his hands", to the tune of "He's Got The Whole World In His Hands", he obligingly held up his palms and turned out his pockets and clapped and waved.

Bancroft, perhaps viewed as the fall guy, was spared the worst of the abuse.

And Smith? Well he remained in his impenetrable bubble that, ultimately, was the true fortress of this Test. He just batted and batted. And batted.

By the time he lifted his bat to celebrate his second century of the match the booing had diminished and the applause dominated for the first time. Although, of course, it was renewed with vigour when he was dismissed, having taken the game far out of England's reach. He turned and acknowledged the Hollies Stand as he walked off, the only time he seemed to notice it was even there.

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His wife, Dani, had sat in the relative quiet of the enclosed press box the previous day, anticipating that the excesses of Saturday drinking would bring out the worst; Smith's personal armour does not extend to those who care for him and it's hard to imagine how it would have felt to listen to thousands of people eviscerating a loved one.

As Australia gained the upper hand in the match, their fans - sitting in a large block between the Hollies Stand and the dressing rooms took their cues from what had gone before. "Same old Aussies, always cheating" became "same old Aussies, always winning". The ugliest chant was saved for Ben Stokes: "He punched to the left. He punched to the right. That Ben Stokes he should be inside." It was hardly edifying stuff and brought to mind the thought that some sports end up segregating fans: we don't want to end up there.

It did, however, illustrate the whataboutery that was bandied about through the Test. Whatabout the way Stuart Broad was treated in the 2013-14 Ashes? Whatabout the time cheating Broad (didn't) smash the ball to first slip in the 2013 Ashes and declined to walk? Whatabout Warner doing the same thing now? Whatabout Athers and the dirt? Faf and the zipper? Faf and the mints? Hang on, now you mention mints, whatabout the Murray variety and Tresco and 2005?

They've done their time; they should've been banned for life. Opinion about The Three will probably forever remain polarised along these lines.

It will be far quieter at Lord's, but a certain level of cacophony will surely follow them throughout the rest of the series, although it will just as surely lose its bite if Australia keep winning. The noise may have become drearily repetitive for some who were there each day but many people can only afford the time or money for one day at a Test this summer and will see it as their single opportunity to take a shot. We've paid a lot to be here, they will say, and we have every right to sing and chant and fling whatever insults we please. It also stands that others have the right to consider their behaviour boorish and excessive.

At the conclusion of the match, Smith stood near the boundary in front of the dressing rooms and his post-match interview was broadcast on the PA. The remaining fans in the Hollies Stand struck up the crying on the telly chant. It sounded distant and feeble as Smith smiled and chatted on the telly, holding his player of the match trophy and a bottle of champagne.

When he finished, the fans in front of him - both English and Australian - warmly applauded.

There wasn't a single boo to be heard.

GREEN BAY, Wis. -- Before the Texans and Packers held a joint practice on Monday, J.J. Watt finally got to participate in the Green Bay tradition of players riding a kid's bike to practice, something he said was "a dream he had as a kid."

And then he broke the bike.

"The bike that I was using was not equipped for a 290-pound man, and the seat broke off," the Houston defensive end said. "We have purchased a new bike for the boy. So, I apologize for that."

Watt said he chose the first kid in line, even though he was wearing a Packers jersey.

"I mean, I can't walk past a kid," Watt said. "That's hard. He had a [Aaron] Rodgers jersey on, which is fine. I respect it. I support loyalty. The welcome and reception I've gotten since I got back here. To see people wearing my jersey, it's pretty crazy."

Watt later upgraded his bike to a larger model to finish off the ride.

"It's one of the coolest traditions," said Watt, a Wisconsin native. "Growing up here, I know how special it is to get to interact with a player from the Green Bay Packers. For them to have that tradition, where kids get to be up close and personal with their favorite players and they get to hold their helmet.

"I mean, that's what it's all about. Those are the memories that those kids are going to have for a lifetime. For me to be able to participate in it as a player was cool."

GREEN BAY, Wis. -- Houston Texans rookie Lonnie Johnson Jr. didn't make any friends on the first day of joint practices with the Green Bay Packers, and he didn't even get to finish the workout because his coach kicked him off the field after the cornerback leveled two players in what was supposed to be a non-tackling session.

"It was a play that developed over there, and it was time for Lonnie to head to the showers," Texans coach Bill O'Brien said.

O'Brien added that it was "not a big deal."

That's not how the Packers felt after Johnson, a second-round pick, drilled Packers rookie tight end Jace Sternberger, whose helmet went flying off. When Johnson stood over Sternberger and flexed, several Packers players came running over to confront Johnson.

"That was unnecessary," Packers receiver Davante Adams said. "You've got plenty of time for that. You can do it in the games and you get fined. Be a coward when you do stuff like that in practice, it's not a good look. We take care of each other up here. I don't know how they practice, I don't know what they do over there, but there's consequences for stuff like that. ... It's a brotherhood across the league, period. I had plenty of times where I could take somebody out but I decided not to because I felt like that's not the appropriate thing to do when we're trying to get better and look out for one another."

Packers tight end Jimmy Graham called it "kind of ridiculous."

"I respect a lot of those guys over there on the Texans; I've played against them quite a bit over my career," Graham said. "Obviously he's a rookie and he needs to know you can't be hitting guys live in practice. That's absolutely ridiculous. And we're not going to stand for that here, obviously. I know his older guys over there are going to be on him about it because my young guy's just running through a zone, obviously. Just run by him. We know you're going to blow him up in a game. This isn't a game. We're going to play on Thursday. You can do that then. It's one of those things, rookie on rookie, but [No.] 32 has to chill out."

Sternberger returned to practice after he was evaluated for a concussion, but Johnson actually delivered another hit -- to Packers receiver Trevor Davis on a kickoff return -- before O'Brien removed him. Davis did not return.

"I thought there was no place for that," Packers coach Matt LaFleur said. "We addressed it. It's an unfortunate deal, because I was pretty clear with our guys we're not doing that stuff."

Packers right guard Billy Turner relayed what LaFleur told his players.

"He was clear with us, and we were clear with him: If they started taking shots on our players, then we're not just going to stand there," Turner said. "We're not punks by any means, and that's what happened. So we were men of our word, just like he was a man of his word."

When asked if the Texans got the same message before practice, LaFleur said: "I can't speak for them, I have no idea. I just know what I saw out there, and that particular play, that's not what we want to be about."

Sternberger said he did not have a problem with the hit, but also did not realize at the time that Johnson celebrated the hit.

"I didn't know the whole second part, the whole flexing thing," Sternberger said. "I guess that's why my teammates were so upset. Yeah, I mean, I don't know what to say about that. I still think it's football. It could've been the exact other way. Everybody's playing aggressive and intense, so it's a good thing."

Turner said he would not be surprised if there's a fight Tuesday on the second day of joint practices.

"I'm not going to say I expect it, but, again, I'm going to protect my teammates at any cost," Turner said.

Johnson did not speak to reporters after practice but posted a response on Twitter, writing: "Not trying to hurt nobody just wanna be great!"

Texans reporter Sarah Barshop contributed to this report.

FLORHAM PARK, N.J. -- Continuing to address their offensive-line deficiencies, the New York Jets acquired guard Alex Lewis from the Baltimore Ravens for a 2020 conditional seventh-round pick Monday.

The teams announced the deal, which is pending a physical.

Lewis had announced Monday morning that he was being released by the Ravens, but they found a taker before placing him on waivers.

The Jets, who have the No. 3 waiver priority (based on last season's record), evidently felt there was a chance he'd be claimed by the Arizona Cardinals or San Francisco 49ers. Lewis, who has one year remaining on his contract, is due to make $2 million in 2019. He projects as a backup for the Jets.

This was the second offensive-line move in four days by the Jets, who lured former Pro Bowl center Ryan Kalil out of retirement.

Lewis, a 2016 fourth-round pick by the Ravens who started 10 games last season, was expected to compete at left guard. He has struggled to stay healthy throughout his career (missing a total of 28 games over three seasons) and began training camp on the physically unable to perform list while recovering from shoulder surgery.

Two days after passing his physical, Lewis posted on Instagram that he was no longer in the Ravens' plans.

View this post on Instagram

Thank you to the Baltimore Ravens for drafting me back in 2016 and giving me an opportunity to play in the NFL. It has been a memorable three years. Appreciate all my teammates and coaches I have met along the way. Loved the atmosphere of Baltimore and the amazing fans that supported us! Unfortunately, I was released today. Thank you Baltimore! "As one door closes another opens. "

A post shared by Alexander Lewis (@alexlewis72) on Aug 5, 2019 at 5:02am PDT

Lewis didn't endear himself to the Ravens this offseason when he chose to rehab his shoulder away from the team.

Asked 10 days ago about Lewis, coach John Harbaugh said he looked strong and was moving well. Harbaugh anticipated Lewis returning in early August but added, "We were given a date by his doctor."

That leaves the Ravens' left guard spot even more up in the air. Options include: Jermaine Eluemunor, who failed his conditioning test to start camp after working with the starters in the spring; Ben Powers, a rookie fourth-round pick; and James Hurst, who finished last season as the starting left guard but has primarily worked at tackle this year.

Lewis becomes the Ravens' second one-time draft pick the team has moved on from in a week. On Wednesday, Baltimore released former fifth-round pick Jordan Lasley two days after he was involved in a fight and then threw a ball into a drainage pond.

LAS VEGAS -- Gregg Popovich on Sunday night gathered his newly-formed Team USA for its first in the six-week journey toward the World Cup in China.

He'd been preparing for this gathering in one way or another for almost four years, since he was named as Mike Krzyzewski's successor in late 2015. The message he delivered to the patchwork roster was aimed at responsibility and unity, two things he thinks are going to be vital. Not just because Team USA has had numerous players drop out of this summer's event but also because of the weight of playing with "USA" on their chests at this point in time.

"It's our responsibility to not only be the best team we can be but also conduct ourselves with the USA on our shirt, we're representing a lot of people," Popovich said after he conducted his first training camp practice Monday at UNLV. "We have a huge responsibility not only for the country to do this in a classy manner but to continue the success that USA basketball has had over the last 12 years."

Both Popovich and Team USA assistant coach Steve Kerr, who are known for making political statements, refrained from doing so Monday as they attempted to set a tone of unity.

"We can't fix the divisiveness in our country, but what we can do is be a great example of how people come together for a common goal and achieve it," Popovich said.

"I watched the women's World Cup team win the World Cup and it was inspiring," Kerr said. "To me that's what sports are about, the competition and the unity. Bringing out this great spirit and energy with the fans. We have a chance to do something that is very positive and unifying."

Popovich's roster was in flux up until this past weekend, with players still dropping out and being added. On Monday he made more roster changes as he promoted De'Aaron Fox and Joe Harris from the Select Team to play with the national team in practice. Fox ran point guard for the second unit backing up Kemba Walker as Kyle Lowry remained in a cast recovering from thumb surgery. Donovan Mitchell also played some point guard in the team's scrimmage.

More than a dozen players who were on the national team roster elected to remove their names, leaving the team thinner than is preferred at some spots.

"All I care about is who's here," Popovich said. "I've got a fine group of guys and we're going to get the best possible team we can...this is the most satisfying form of putting a bunch of guys together and them have empathy and love for each other to form the kind of team they're going to have to have to beat some really good European teams."

Popovich has poured himself into preparation for this job, studying everything from Team USA's history against certain opponents to opposing personnel with challengers from Europe to where in Shanghai he can get good wine.

"We're all used to pressure and those things but I can say a day hasn't gone by in the last year when I haven't thought about USA Basketball, what I would want to do with players, who are the coaches, it's been on my mind," Popovich said. "It's like thinking about two teams at the same time for that period. Coach K did that for 12 years so I can try to do the same."

LAS VEGAS -- Kawhi Leonard reached out to Kyle Lowry to personally break the news that he was leaving Toronto to join the LA Clippers.

And despite losing an All-Star partner for the second straight offseason, Lowry was thrilled for Leonard and his decision to return home to Los Angeles. While Leonard's departure was a massive blow for Toronto, it didn't change the way Lowry felt about what the Raptors accomplished by bringing Canada its first NBA title.

"No, not at all," Lowry said emphatically. "Not at all. We are champions. No matter what. [It will] never be taken away from us. Ever. Ever, ever. Ever, ever."

Following USA Basketball's first training practice leading up to next month's World Cup, Lowry talked about Leonard's decision to leave the newly crowned NBA champions to join forces with Paul George. And despite the Raptors having to try to defend their crown without their NBA Finals MVP, Lowry said he would love to remain with the Raptors long term.

Lowry will be a free agent after this upcoming season and he recently hired Mark Bartelstein as his agent.

"I want to be there, I would love to do a long [term] extension, but we'll see what happens," Lowry said when asked about wanting to remain a Raptor past his current contract. "I'm here for USA Basketball and support the guys and be around the group."

"[But] I would love to be there long term, but we'll have that discussion when the time is right."

The Raptors will also have to consider an extension to Pascal Siakam's rookie contract. The NBA's most improved player is eligible for an extension before the start of the regular season or the forward becomes a restricted free agent.

"He going to get paid," Lowry said when asked what it will be like to see younger players like Siakam take on a bigger role with Leonard gone. "What else do you want to hear from me? He going to get paid ... For a guy like that, you just got to keep improving and keep it going."

Toronto hopes Siakam is ready to take another big leap forward after averaging 16.9 points and 6.9 rebounds, since the Raptors will have to defend the title without Leonard.

"I don't know," Lowry said of what it will be like for a champion to return without the reigning Finals MVP. "First time you ever seen it. Who knows?"

Lowry did not participate in USA's first practice as he recovers from a procedure to repair a torn tendon in his left thumb a little over two weeks ago. Lowry played throughout the Raptors' title run with the thumb injury to his non-shooting hand, and the point guard hopes to be able to play for the national team in the FIBA World Cup in China in September.

USA Basketball coach Gregg Popovich said the team will have to consider the possibility of carrying an extra point guard on the roster while Lowry recovers.

"It depends on the doctor," Popovich said of Lowry's availability. "He's still in a hard cast. Some time here soon he goes to the doctor and that will have a lot to do with the decision."

As for the biggest decision in free agency last month, Lowry lost an All-Star and Finals MVP teammate, but said he could not have been happier for his friend.

"I'm happy for you," Lowry said of his reaction to Leonard's news. "... I am happy for the guys that ... especially a guy that helped do something fantastic and something great. He's an unbelievable friend of mine and is a good guy. He made a decision to go home and he is happy with that and I am happy for him. Truly. I am genuinely happy for him. It gives him a chance to be around his family and friends. You got to respect the guy and be happy for him."

At 42 years old, eight-time All-Star Vince Carter has agreed to a one-year contract to return to the Atlanta Hawks for his final NBA season, league sources told ESPN.

Carter will play an NBA-record 22nd season, where he will spend a second straight year mentoring one of the NBA's youngest rosters, which includes seven players under 23 years old.

Carter will pass Dirk Nowitzki, Kevin Garnett, Kevin Willis and Robert Parish, all of whom played 21 NBA seasons.

If he plays in a game in 2020, Carter will be the first player in NBA history to appear in a game in four different decades, according to Elias Sports Bureau research.

Carter is one of the most popular players of his generation, once a dynamic above-the-rim performer who electrified the league in his prime with Toronto and New Jersey. He has averaged 17 points in 1,481 regular-season games, and he won an Olympic gold medal and NBA dunk contest in 2000. Carter also won the NBA's Rookie of the Year award in 1999.

Carter averaged 7.4 points in 17 minutes a game for the Hawks in 2018-19, which included him playing 76 regular-season games.

Gleyber Torres is in the New York Yankees' lineup Monday against the Baltimore Orioles, a day after leaving Sunday night's game with a "core issue."

Torres was taken to New York Presbyterian Hospital, where he underwent tests and was later released.

Torres is batting cleanup against the Orioles and serving as the designated hitter.

Gio Urshela, who also left Sunday night's 7-4 victory over the Boston Red Sox with an injury, is not in Monday's lineup.

X-rays taken on both of Urshela's legs Sunday were negative after he fouled two balls off his legs during an at-bat against Red Sox reliever Ryan Weber.

Heading into Monday's game, Torres was hitting .286 with 23 home runs and 62 RBIs.