Liverpool sit a reasonably contented sixth in the table. They have conceded fewer goals than anybody else in the Premier League and, although a gap of 11 points to the leaders is probably too much to make up, there is no reason why they shouldn't mount a strong challenge to qualify for the Champions League. The one niggling doubt, and the one reason that they're not in with a chance of winning the title, is their repeated failure to kill sides off at home.

Although they ended up winning relatively comfortably against Newcastle on Friday, that was only their fourth win in 10 home games this season. A record of 14 goals from 10 matches at Anfield tells the same story as the memory of countless headers flashing just wide and opposing goalkeepers making save after save. Andy Carroll, mocked as he is, seems to have been particularly unfortunate in that regard, being denied late winners by barely credible saves from Manchester City's Joe Hart and Blackburn's Mark Bunn.

Luck, the unspoken deity that haunts football more than anyone likes to admit, has played its part, and it may be that the second half of the season will follow the model of the Newcastle game rather than the 1-1 draw with Blackburn as success breeds confidence. Much of success in sport, though, is about manipulating percentages, and it's perhaps there that Liverpool bear a level of responsibility for their failing.

The statistics are remarkable. Opta figures show that in nine home matches after Kenny Dalglish took charge last season, Liverpool scored 20 goals, compared with 14 in 10 home games this season: 2.22 goals per game compared to 1.4. Yet last season in games under Dalglish, Liverpool averaged 12.89 shots per game, compared with 15.4 this (in 2009-10 Liverpool had 14.89 shots per game at home, and the season before that 17.79).

Now, while it's clear that not all shots are equal – an open goal from two yards yields a far higher likelihood of a goal being scored than an overhead kick from 30 yards – there is obviously a high correlation between shots and goals. In an interview in The Blizzard the Norway manager Egil Olsen notes that three-quarters of games are won by the side who had more shots and explains that he abandoned his attempts to quantify how good a chance was because it yielded almost identical results.

Liverpool this season score a goal with every 11 shots they have at home. Last season they scored every 5.81 shots. In 2009-10 they scored every 6.59 shots and in 2008-09 every 8.24 (at least since statistics began to be recorded, a basic rule of thumb has remained that every nine shots will yield one goal). Away from home this season, the figure is even worse, a goal coming every 11.51 shots. It would be easy to blame that on Carroll's profligacy, but he's not the only one at fault. In terms of shooting accuracy, there's not a great deal to chose between Liverpool's four strikers. Craig Bellamy has got five of 11 shots on target, Carroll 14 of 34, Dirk Kuyt seven of 17 and Luis Suárez 28 of 69. The big difference is in chance conversion – how many of those shots go in. Bellamy has scored 36.4% of his chances (from an admittedly small sample size), Suárez 7.2%, Carroll 5.9% and Kuyt none.

Is there a reason for the comparative lack of effectiveness beyond simple profligacy or lack of confidence? Are, in other words, Liverpool creating chances that are difficult to take? The signings of Stewart Downing, Jordan Henderson and Charlie Adam were apparently motivated by the fact that all three were among the top eight chance-creators in the Premier League last season (Blackpool, Aston Villa and Sunderland were eighth, 13th and 17th in the scoring charts last season; it may be that the sort of chance Adam, Downing and Henderson create is not the most efficient sort of chance, precise as Henderson's ball to Steven Gerrard for the third goal on Friday was).

At home this season, Liverpool have played 481.8 passes per game, completing 80.34% of them. It's been suggested that they've become more direct, which would logically be reflected in fewer passes and a lower pass completion rate, but in 2009-10 at home they were averaging 492 passes per game at 80.05% completion, and in 2008-09 514.2 at 81.65%. In so far as passing stats reveal style, little seems to have changed since Rafael Benítez's time. There is a danger that pass-completion stats can give a misleading impression if a side passes the ball among its back four before launching long balls, but pass completion in the opponent's half has barely changed either: 73.10% this season, 72.61% in 2009-10 and 73.82% in 2008-09.

Last season under Dalglish at home, though, Liverpool played only 445 passes per game, with a success rate of 78.55%, and 70.81% in the opponent's half. Those figures, taken with the stats on crossing, do seem to reveal a trend. In 2008-09 Liverpool averaged 33.16 crosses per home game. In 2009-10, 30.58. This season, the figure is 33.7. Last season under Dalglish, though, Liverpool hit just 23.33 crosses per game. Cross completion this season has been markedly better this season: 24.03% at home as opposed to 15.38 under Dalglish last season and 20.27% and 19.63% in the last two seasons under Benítez.

So Liverpool were almost twice as efficient in front of goal last season when they played fewer crosses and were more direct. That may change if Carroll's efforts stopped hitting the woodwork or the outstretched fingertips of assorted goalkeepers, but Liverpool seem to have run into the theory postulated by Herbert Chapman in the 1920s. Rapid forward passes, he said, were "more deadly, if less spectacular" than the "senseless policy of running along the lines and centring just in front of the goalmouth, where the odds are nine to one on the defenders".

It's a fine balance, of course: create as many chances as possible, or create fewer chances that are easier to take? After 10 games, simple misfortune could still be playing its part, but it may be that Liverpool need to recalibrate a touch from the former to the latter.