Since 1995-96, when the Premiership shifted from a 42- to 38-match season, just four teams in Premier League history have improved by 20 points or more on their previous seasons' total: 2001-02 Newcastle, going from 51 to 71 points; 2004-05 Everton, going from 39 to 51 points, 2005-06 Liverpool, going from 58 to 82 points; and this season's Liverpool, going from 61 to 84 points.
The average difference for the highest-rising team in the league each season was 16 points, a range of a seven-point increase by Bolton in 2009-10 to a 24-point increase by Liverpool in 2005-06.
I've also included the season before the season before in the above graphic as well, in a lighter color, as a useful barometer. In some cases, in shows just how much a team's improved over the three campaigns, such as this season's Liverpool. Conversely, there were a few instances of a team "bouncing back" after a bad season: '97-98 Blackburn, '99-00 Liverpool, '03-04 Arsenal, '04-05 Everton, '12-13 Chelsea. Which takes a bit of the gloss off the achievement. Not included were 1994-95 Sheffield Wednesday, who played 42 games, or 2009-10 Newcastle, as they were in the Championship rather than the Premiership.
Liverpool's three-season increase from 2011-12 to 2013-14 was 32 points, from 52 in Dalglish's last season to 84 in Rodgers' second. That is, by far, the biggest jump over a three-season span; the only team even close to that was Tottenham's 24-point rise from 2007-08 to 2009-10, and they've hovered around the 70-point mark in three of the four subsequent seasons, aside from falling to 62 in 2010-11.
Only one team in the above graphic finished with more points than this season's Liverpool, only one finished in a higher position: 2003-04 Arsenal in both cases, winning the title with 90 points after a something of a collapse (all the way down to 2nd) the season before.
As I'm obviously Liverpool biased, what jumps out at me are the similarities between those two highest increases, in Brendan Rodgers' and Rafa Benitez's second seasons.
Benitez's Liverpool went on a 12-match unbeaten run in 2005-06, including a 10-match winning streak. Rodgers' Liverpool went on a 16-match unbeaten run in 2013-14, including an 11-match winning streak.
Benitez did it with defense, Rodgers with attack; the differences in Goals Scored and Goals Conceded by the two managers' sides are significant. Benitez's two most important second season signings were Reina and Agger. Rodgers' most important signings arguably took place in January of his first season: Sturridge and Coutinho. Let's not talk about the attacking signings from last summer.
Yes, Liverpool's squad was stronger (and the league arguably weaker as a whole) when Benitez became manager, but it also had to cope with extended FA Cup and Champions League campaigns in 2005-06.
If this the precedent for what's to come for Rodgers' Liverpool over the next couple of seasons, I'm okay with that. But the goal is obviously to surpass it.
Coincidentally, the outstanding Match Story independently did a slightly different version of this today, which you should absolutely check out.