First, the usual way of looking at this (see also: the 2011-12, 2010-11, and 2009-10 versions):
• City (1st --> 2nd) = +1
• United (2nd --> 1st) = -2
• Arsenal (3rd --> 4th) = -2
• Tottenham (4th --> 5th) = +2
• Newcastle (5th --> 16th) = +1
• Chelsea (6th --> 3rd) = -4
• Everton (7th --> 6th) = -4
• Fulham (9th --> 12th) = +6
• West Brom (10th --> 8th) = -3
• Swansea (11th --> 9th) = +3
• Norwich (12th --> 11th) = +2
• Sunderland (13th --> 17th) = +3
• Stoke (14th --> 13th) = 0
• Wigan (15th --> 18th) = +5
• Villa (16th --> 15th) = -1
• QPR (17th --> 20th) = +3
• Relegated/Promoted 1 (Bolton 18th --> Reading 19th) = +1
• Relegated/Promoted 2 (Blackburn 19th --> Southampton 14th) = -2
• Relegated/Promoted 3 (Wolves 20th --> West Ham 10th) = -2
Notably better against Fulham, Wigan, Swansea, Sunderland, and QPR. Marginally better against Spurs, Norwich, and City. Liverpool's improvement mostly came against middle-of-the-pack or bottom-of-the-table teams, as well as two sides that Liverpool hope to challenge next season (Spurs and City).
However, Liverpool were notably worse against Chelsea, Everton, West Brom, United, and Arsenal. Four teams who finished above Liverpool and one who finished directly below. Oh, and despite Liverpool's good record against sides below them, Liverpool took three fewer points from this season's promoted sides than last season's relegated sides. That's less good.
versus league place:
• vs 1st = 1 to 0 = -1
• vs 2nd = 1 to 2 = +1
• vs 3rd = 3 to 2 = -1
• vs 4th = 1 to 1 = 0
• vs 5th = 3 to 3 = 0
• vs 6th = 6 to 2 = -4
• vs 7th = 6 to n/a = -6 (combined with 8th)
• vs 8th = n/a to 0 = -6 (combined with 7th)
• vs 9th = 0 to 4 = +4
• vs 10th = 3 to 4 = +1
• vs 11th = 1 to 6 = +5
• vs 12th = 4 to 6 = +2
• vs 13th = 1 to 1 = 0
• vs 14th = 1 to 3 = +2
• vs 15th = 1 to 3 = +2
• vs 16th = 4 to 4 = 0
• vs 17th = 3 to 4 = +1
• vs 18th = 3 to 6 = +3
• vs 19th = 4 to 4 = 0
• vs 20th = 6 to 6 = 0
Again, remarkably worse against the sides directly above and below them in the table. But Liverpool either bettered or equalled their points total against 9th through 20th place. More confirmation that Brendan Rodgers' side really were flat-track bullies.
For a different look, here's the chronological version comparing the last two campaigns:
Those first five games. Ugh. That led to a five-point gap on last season's total, a gap this season's Liverpool didn't close until the start of the new year, not passing the 2011-12 points mark until early March.
In Liverpool's defense, only QPR had a harder first five games. The average final place of Liverpool's first five opponents was 6.4, facing the 8th, 2nd, 4th, 17th, and 1st-placed sides. It was 6.0 for QPR, who played the 9th, 11th, 2nd, 3rd, and 5th-placed sides. Every other club faced an average of 8th place or worse.
Last season, Liverpool played the 13th, 3rd, 18th, 14th, and 4th placed sides in the first five games, an average of 10.4. Which is almost exactly this season's mean. And took seven points compared to this season's two. Not that it helped much in last season's final points tally.
Incidentally, the teams with the easiest starts? Chelsea, who played the 18th, 19th, 16th, 20th, and 13th-placed sides, and Tottenham, who played the 16th, 8th, 11th, 19th, and 20th-placed sides. Here's the full order, from toughest to easiest, if you're curious.
Liverpool's tough start was made worse by being the first five matches for Liverpool's new manager, implementing a new system. That doesn't excuse the disappointments that followed, nor explain why Liverpool finished 12 points behind the Champions League places. Yes, Liverpool probably would have struggled in those matches regardless of opponent. And yes, the schedule obviously evens out over the course of the season. But had Liverpool had an easier start, or had Liverpool managed to win its two draws in the first five matches, it could have built momentum that Liverpool weren't able to build until later in the season. Who knows what earlier momentum could have done for the side's progress. Confidence begets confidence, good results beget more good results.
At least, unlike last year's side, Liverpool ended the season in excellent form. Only Arsenal and Chelsea took more points than Liverpool over the last 10 matches of the season. And that's why we're optimistic – probably too optimistic, knowing precedent – about Liverpool's chances for next season.