We're not talking about which teams currently have the best players - more of a look at who would bring most to the table, including tradition, trophies, wealth and, of course, fans.
Will your club make the cut? Let's take a look…
Champions of England
Arsenal, Everton and Aston Villa round out the top five - all three being clubs with a large following and rich tradition.
Manchester City and Chelsea follow and as multiple champions in the Premier League era, they are impossible to leave out.
You're in: Manchester United, Liverpool, Arsenal, Everton, Aston Villa, Manchester City, Chelsea
Tradition takes many forms but one of them is regular attendance at the top table.
Arsenal, Chelsea, Everton, Liverpool, Man Utd and Spurs are the six ever-presents in the Premier League era - although you youngsters should know football did exist before 1992.
The Gunners boast the longest unbroken run in England's top flight, having played at that level since 1919, while Everton have had more seasons than anyone in the top division. The Toffees, founder members of the Football League in 1888, have had just four seasons at a lower rung of the pyramid - one in the 1930s and three in the 1950s.
Of those who haven't already been selected for their title success, Newcastle score highly on this metric - they have the seventh-most top-flight seasons in history.
Tottenham are one place further back and while their 1960/61 Double season is just one of only two times which they've been crowned champions of England, they are a genuine modern-day behemoth with real financial muscle and a regularly-packed spaceship-like stadium rising up out of a gritty part of north London.
Sunderland also make the top 10 with West Brom, Bolton and Blackburn all just outside.
One team's position will surprise some.
Leeds sit only 25th in this list - they are currently competing in just their 52nd top-flight campaign. Formed in 1919, they've played 45% of their seasons at a lower level, putting them behind the likes of Leicester and Burnley.
You're in: Newcastle, Tottenham
No one's ever really been able to write a widely-accepted definition of 'big club' down and I'm not going to try here.
But it's fair to say that a large supporter base has something to do with it, particularly given the other things that can lead to, including greater financial power.
The usual suspects score well again here.
For all the taunts Manchester United get about their fans coming from all corners of England, their popularity is undeniable, while match attendance hardly paints a different story - barring some temporary moves to Wembley, Old Trafford has been the most-attended ground for many years.
Leeds is one club yet to get a mention but it smashes it up on this front.
The West Yorkshire city is one of England's largest and, crucially in football terms, it is a one-club city.
The stable ownership of Andrea Radrizzani - has recently awoken this Kraken but even in the troubled times which involved time in League One, Leeds were drawing in big crowds.
It's worth delving into the lower divisions to find the current sleeping giants - attendance here is a huge indicator for that 'big club' factor.
The most notable right now is surely Sunderland, stuck in League One after years of mis-management, but still able to generate an average crowd of more than 30,000. Yes, they've won more than they've lost this term, which always helps, but it's far from a golden campaign (they currently sit outside the automatic promotion slots in fourth) and so this is an impressive figure.
It's higher than anything in the Championship, whose attendance table is topped by Sheffield United, averaging 27,000-plus.
The Blades have a rich history, although the club's best moments came pre-war - they were champions and four-time FA Cup winners.
It would be easy to reject their claims on lack of recent success but Sheffield is a proper football city, as those fan figures show.
It's therefore hard to leave them out and the same can be said of Steel City rivals Sheffield Wednesday.
They are averaging 22,000 crowds in League One - there aren't many cities where 50,000 people are attending a league match every fortnight.
In terms of highest ground capacity, Wednesday sit 12th, between Everton and Leeds.
While the list means little in terms of our search, it does reflect, to some degree, the level of potential - big stadia are rarely built as a vanity project.
Interestingly, if the Premier League was made up of the clubs with the biggest grounds, Middlesbrough, Derby, Cardiff and Coventry would be among the EFL sides making the cut, with the likes of Southampton, Crystal Palace and Wolves missing out.
You're in: Leeds, Sunderland, Sheffield United, Sheffield Wednesday
If you've managed to conquer Europe, even if you've done little else, you've got good claims to call yourself a big club.
England has provided five winners of the Champions League/European Cup over the years.
Six-time winners Liverpool, Manchester United, Chelsea and Villa are already in our 'strongest' league but what about Nottingham Forest?
Incredibly, they've won the European Cup twice - double their number of domestic titles - and that fairytale era of Brian Clough is a story easily used to sell the club and any competition it plays in.
Forest's glory years may seem a long time ago but there's real potential in the East Midlands; you only have to have witnessed this season's FA Cup run and crowds to see that.
Premier League football back at the City Ground? We'd love to see it.
But what about other European trophy winners?
West Ham could easily have made it in several of our other categories - they're filling one of the largest grounds in England these days - but previous European success cements their place in our top 20.
Bobby Moore led the Hammers to Cup Winners' Cup glory in 1965 in a team also featuring Geoff Hurst and Martin Peters.
The trio would lift the World Cup 14 months later. 'West Ham won the World Cup', they said. Another score on tradition.
West Ham were always going to make it. We'll ink them in here.
You're in: Nottingham Forest, West Ham
Money often proves divisive in that 'big club' argument but it's impossible to deny that wealth plays a huge part in modern-day football, especially the Premier League.
The recent Saudi takeover at Newcastle has seen Manchester City replaced as England's richest club in terms of the ownership's wealth - it is said the country's Public Investment Fund is worth more than £300billion!
While it's difficult to have completely accurate figures about every club owner in a constantly-changing financial environment, it's interesting to see Villa in the top five on this list.
The Chinese money at Wolverhampton Wanderers is also noteworthy - they round out the top six here.
Wolves are a club who have made great strides under their current ownership and have undoubted spending power in the current era. Remember they splashed close to £40million on teenager Fabio Silva last year.
The Old Gold score highly on other factors too - 67 top-flight seasons, an era of dominance (including three titles) in the 1950s.
You're in: Wolverhampton
The best of the rest
Four spaces are left up for grabs and we are down to clubs who don't have an outstanding case to be made in the above categories.
Given our selections so far are essentially based in the heartlands of English football, there's an argument to be made that widening things out geographically would make the league a stronger product.
In East Anglia both Norwich and Ipswich are well-supported clubs who drag in fans from a wide area, while in the west, Bristol City has some pulling power, albeit there seems to be a greater affinity for rugby union.
But it is Southampton who hold the strongest case on this front with a club south of London also clearly a benefit in this category.
Along with Brighton, they are currently the best-supported club in the south, possess owners with plenty in their pocket but also have a richer top-flight history than their south-coast rivals.
We're being kind here but Southampton sneak in.
If recent success means anything, Leicester are must-haves - few will ever forget their 5,000/1 triumph of 2015/16 and in a 'strongest' league which has little room for the true underdog, that famous triumph sprinkles some much-needed fairy dust.
Down the road, it's fair to say Derby aren't exactly scoring strong financial points right now but one of the reasons their current plight is so sad is that there's huge untapped potential at the club.
The Rams averaged over 30,000 the last time they were in the Premier League and attendances haven't been too far below that mark since. Not bad for a city of just over 250,000 people.
Derby's two league titles have both been won more recently than the likes of Spurs and Wolves.
In a similar way to Leeds, you have to think 'if only there was some financial stability'…
The final spot in our line-up goes to another club from one of football's traditional hotspots.
Middlesbrough may have only ever won one trophy, the League Cup in 2004, but they are another club with a fanbase many would crave.
A recent study found the town has produced more England internationals per capita than any other - legends Brian Clough and Wilf Mannion were both from Teesside, while more recently Jonathan Woodgate and Stewart Downing have pulled on the Three Lions' shirt.
This is proper football territory and while fans of Bolton, Blackburn and West Brom won't be happy, Boro scrape into our strongest Premier League line-up.
You're in: Southampton, Leicester, Derby, Middlesbrough
'Strongest' Premier League line-up in full (in alphabetical order):