These are historic times. Just look at the top of the Premier League table, where the two Manchester teams are divided only by the most dizzying of goal differences. It is not unprecedented for a team to have a goal difference of plus 20 or more after seven games but it is extraordinarily rare. It happened four times in the 19th century and three times in 117 years since, Manchester City this season becoming the latest side to achieve the feat.

People think of the early days of the Football League as wild times, with disorganised defences coping miserably with the fact that nobody had invented Tony Pulis yet and allowing forwards called Ted or Horace or Dixie to plunder goals with affable ease before polishing their boots, combing their moustache and posing for a daguerreotype with their favourite pipe. In fact, the era we are living through is threatening to make those days look positively orderly.

In 1907-08, Manchester United lost one of their first 14 games, winning the rest. In addition to that solitary defeat, their first seven fixtures featured two 4-0 home victories and two 4-1 away wins, which took their goal difference to plus 20. It was plus 29 after nine games, at which point they calmed down a little, going on to win the league by nine points and with a goal difference of plus 33.

It would be more than a century before another team started a season so free-scoringly, a century in which it was unusual for a team to have a goal difference even in double figures after seven matches. Suddenly, such achievements have become bewilderingly common: Chelsea were at plus 21 in 2010, while in 2011 United were on plus 19 and City on plus 18. In the last century six teams have built up a goal difference in excess of plus 17 by the end of their seventh game; all but one of them did so in this still incomplete decade (the other was Liverpool in 1978).

This seems to be more than just coincidence, and a blow to the English top flight’s boast of being the world’s most competitive league. But we are living in an age of remarkably honed forward lines and shredded defences: the current leaders of the top divisions in Spain (Barcelona), France (PSG), Germany (Borussia Dortmund) and Italy (Napoli) also have goal differences of plus 19 or more.

The timing of City’s goals is also interesting. The leaders have scored seven first-half goals, the same as United, Liverpool and Tottenham, and one more than Arsenal, Burnley and Chelsea. In the first half of matches they are merely quite good. Last season, their goals were split fairly evenly between the first and second halves, and in the final 45 minutes they outscored opponents by a ratio of precisely two goals to one. This term, they have an aggregate post-interval scoreline of 15-0.

United’s is 14-1, and in the final 15 minutes the two clubs are 8-0 and 10-0 up respectively. This almost certainly reveals something very interesting about their opponents, possibly a lack of fitness or concentration but just as likely a growing desperation, with the end of the game screeching ever closer, to be somewhere else.

Statistics offer Palace a glimmer of hope

This season we have witnessed not only wild overachievement at the top of the league but spectacular failure at the bottom. There is hope for Crystal Palace in the fact that of three teams since the start of the 20th century to have had a goal difference as bad as theirs after seven games, only one went down.

That was the Manchester United team of 1930-31, whose record for consecutive season-starting defeats Palace are chasing, but Everton in 1948 and Woolwich Arsenal in 1909 had a goal difference of minus 20 after seven matches and recovered (both had at least savoured the encouragement of winning a game by this point).

Poor Palace. How galling it must feel to be stuck in their unenviable position when a flick through the key statistics reveals that one team stand feet and ankles below every other at most things that might cause encouragement – shots on target, touches in the opponents’ penalty area, corners – and that this side are not even them. It is Swansea, for whom 18th place looks decidedly like overachievement at this point.

Palace have had 16 shots on target, two fewer than Brighton and Burnley, one behind Everton and five ahead of Swansea, but not one has gone in. This is not so much anomalous as downright freakish: the next least clinical side is Newcastle, who have scored with 19.4% of their shots on target (at the other end of the scale, Watford are rolling at a surely unsustainable 50%).

Meanwhile on expected goals, a metric that takes into account the quality of chances, there are 11 sides below Palace. In other words, given the chances they have created in actual matches, chance-evaluating professionals would expect them to have outscored most of the division – including Chelsea, who have converted 12 of their opportunities and sit fourth. Instead Palace stand 101 minutes away from overtaking the 1990 Halifax Town side to claim the Football League’s worst season-commencing goalless run.

Of all the significant statistics other than the ones that genuinely matter – actual goals scored and conceded, points won – only on expected goals conceded are Palace statistically the division’s weakest team. In mitigation, they are one of only two sides to have already been shoved mercilessly in front of both the speeding Mancunian juggernauts (Everton, uniquely, have played each of the current top four, a distinction for which many believe Ronald Koeman should be rewarded with the sack).

After seven games, there can be no doubt which team are most wildly exceeding expectations. Burnley are sixth and have already won more points away from home than they managed in the whole of last season. They are also the division’s second-worst side (above Swansea) on shots taken and touches in the opponents’ box, the third worst on total passes, passing accuracy, corners won and shots on target, and the worst of all for allowing their opponents to shoot.

Just like last season, when they were the ninth-best side at home and the 19th away, Burnley have split their games in two and are performing in only half of them. In first halves they lead 6-1 on aggregate and have the division’s third-best record; in second halves they are 4-1 down and are 18th.

Unsurprisingly, teams making bad starts very often turn out to just be bad. In the last 10 completed seasons, half of the 30 teams to have occupied the bottom three spots at this stage were still among them at the end of the campaign. The unusual thing about great starts is that the greatest teams rarely make them. In the past decade, only once have the side in the lead after seven games still been there as the curtain fell. In the same period the team sitting eighth have won the league twice, though all things considered Watford probably should not get overexcited.