It has been a tough return to the top flight for Luton, who have lost their first four Premier League matches, while Sheffield United have picked up just one point from five games.
Everton have also banked one point from their first five fixtures, which leads us to take a look at the teams who have recorded the lowest points tallies in a Premier League season.
Staying in the top division is the main objective for Luton, Sheffield United and their fellow strugglers but they will also be keen to get past Derby's record-low mark of 11 points, set in 2007/08, as quickly as possible.
Managed by Peter Reid, Howard Wilkinson and Mick McCarthy throughout the 2002/03 campaign, Sunderland were not spectacularly bad in the first half of the season, winning 1-0 away to Leeds and beating Aston Villa, Tottenham and Liverpool at the Stadium of Light.
After Christmas, though, they picked up just one point from 19 matches and finished the campaign with a 15-game losing streak.
Just three seasons earlier, Kevin Phillips had won the Premier League Golden Boot with 30 goals, but in 2002/03 the entire Sunderland team mustered just 21 league goals with Phillips leading the way with six.
Villa's final season under American owner Randy Lerner was one to forget as Tim Sherwood, Remi Garde and interim managers Kevin MacDonald and Eric Black combined to claim just 17 points from 38 matches.
Having reached the FA Cup final the previous season, Villa started 2015/16 with a 1-0 win at Bournemouth and a home defeat by the same scoreline to Manchester United.
Exciting homegrown youngster Jack Grealish scored his first senior goal in September's 3-2 loss at Leicester but, by the turn of the year, Villa had taken just five points from 18 games since their opening-day win.
After Sherwood was sacked at the end of October, Frenchman Garde steered Villa to a 0-0 draw with Manchester City in his first game in charge.
The new year brought home wins over Crystal Palace and Norwich, but Villa lost 12 of their final 13 league games, finishing 22 points adrift of safety, and the final act of a grim campaign was a 92nd-minute own goal from keeper Mark Bunn, sealing a 4-0 defeat at Arsenal.
Huddersfield defied the odds to stay up in the 2017/18 Premier League, and they warmed up for the 2018/19 campaign with friendly victories over Lyon, Bologna and RB Leipzig.
That was about as good as it got for the Terriers, however, as they lost 3-0 to Chelsea and 6-1 to Manchester City in their first two fixtures.
David Wagner's men struck a rich seam of form in November, beating Fulham 1-0, drawing 1-1 with West Ham and winning 2-0 away to Wolves, but they lost 13 of their next 14 matches, drawing the other one 0-0 at Cardiff.
Wagner's replacement, compatriot Jan Siewert, helped Huddersfield complete a league double over Wolves and they took a point off Manchester United in their penultimate game but, like Derby in 2007/08, their relegation was confirmed before the start of April.
In 2005/06, Sunderland established a new Premier League record after being relegated on just 15 points.
The Black Cats started the campaign with five straight defeats, but September's 2-0 win at north-east rivals Middlesbrough briefly lifted the mood.
However, they took just one point from 13 games between mid-October and mid-January, and Mick McCarthy was sacked in February with Kevin Ball taking caretaker charge.
Sunderland won just three matches all season, finishing 15 points adrift of second-bottom West Brom, although they managed to hold Manchester United to a goalless draw at Old Trafford in April.
Derby's 2007/08 campaign has gone down in Premier League history for all the wrong reasons as the Rams claimed just one victory.
They scored 20 goals and conceded 89, and their relegation was confirmed before the end of March.
Manager Billy Davies had been sacked in late November 2007, but his successor Paul Jewell was unable to turn things around and Derby finished the season with just 11 points from 38 games.
Remarkably, four of those points – 36% of the overall tally – came against Newcastle.
Kenny Miller scored the only goal of the game when they beat the Magpies 1-0 at Pride Park in September, and the former Scotland striker also notched in December's 2-2 draw at St James' Park.
The Rams' last three matches in front of their long-suffering supporters ended in a 6-0 rout against Aston Villa, a 6-2 loss to Arsenal and a 4-0 defeat to relegated Reading on the final day of a wretched, record-breaking season.