IN what has been something of an education of a season for Liverpool, maths must be proving the most popular subject around Anfield lately. For many reasons. Primarily though, to tot up what exactly it's going to take to topple Tottenham and Manchester City for fourth. Here however, despite a desperate season, despite 10 league defeats, despite all sorts of talk of a core of players now avidly "despising" Rafa Benitez, the numbers start to add up.

Because whatever advantage both sides have – in terms of points and the extra game to play after today – could well be wiped out by the start of May. Tottenham of course have Arsenal and Chelsea at home as well as two trips to Manchester. And, even if the match at Eastlands isn't the draw that would do Liverpool the biggest favour, City themselves have United there as well as Arsenal away. That's over half of both sides' remaining fixtures that are going to cause some high tension. Amidst a fairly elementary run-in for Liverpool that takes in Fulham and West Ham at home and Burnley and Hull away, by contrast, only Chelsea at home stands out as a challenge.

Well, that and Birmingham away today: a fixture with a few discouraging figures of its own. Alex McLeish's team have taken points off each of the top five at St Andrew's and proven stubbornly difficult to break down. Benitez, meanwhile, has never beaten Birmingham. Add in the eight days' rest Birmingham have enjoyed and two and a half Liverpool have endured and it's all set up for another difficult day.

Also discouraging was the number of kicks Fernando Torres received against Benfica on Thursday and the impact that appeared to have on his energy. The waste of a one-on-one with 20 minutes to go was extremely rare for a striker in such form and clearly born of fatigue. Given Liverpool's greater dependence on his goals, that's going to be an added worry today. The hopes is Torres didn't come out of it too bruised.

In such circumstances, and out of the recent trend of approaching football from an economics angle, one German academic, Dr Henning Vopel – who has received a lot of attention from Bundesliga clubs – has come up with a theory that may well be of interest to Liverpool fans. Looking at club economics and performance over the past decade, and using the original Real Madrid galacticos as his base, he arrived upon the 'Zidane clustering theorem'. Through it, he argues that it's infinitely more effective to sign a greater number of very good players, rather than a team made up of some average players, some good players and a small cluster of superstars. Sound familiar?

While that theory gets into the age-old debate about Benitez's spending, given the dependence on Torres it remains disconcerting that the manager, still, effectively has no Plan B. Not enough "very good players" – look at the little money Benfica signed the likes of Pablo Aimar (€6.5m), Javier Saviola (€5m albeit with added clauses), Oscar Cardozo (€11m) and Angel Di Maria (€8m) – to fill in when the Spaniard isn't firing. There is hope, however, in the fact that Benitez has always done some maths of his own. Whatever the doubts about his decisions throughout the season, his teams going back to Extremadura have always proven relentless in run-ins. Thanks to scientifically-based condition, taking the last six games of the season over the past four years, Liverpool have the best record in the run-in out of all the big four with an average of 14 points from 18. The peak, of course, was 2006 when they won all of their remaining nine games while last year they only dropped two points from the final 18. Contrast that with Chelsea, 13.5 and greatly boosted by Jose Mourinho's 2005-06 season; Arsenal, 12.5; and Manchester United, 12.5. And what of Tottenham and Manchester City, neither of whom have any experience of a high-pressure run-in other than Spurs' ill-fated Champions League charge in 2006 when they, literally made a mess of things?

Benitez will be hoping his side's greater experience and energy tells. Because, even if today's game is a little too close to Thursday's to truly illustrate the latter, there has been a noticeably greater zip to Liverpool's play recently, starting with that victory over Portsmouth at Anfield and coinciding with the exact moment they suddenly picked up last year.

Indeed, that supreme victory over Sunderland last week was familiar to the ferocious fashion they despatched the likes of Aston Villa last year. If Torres does suffer from all those kicks today, then the key for Liverpool will be to similarly press Birmingham very high up the pitch, forcing the sort of errors that will allow the efficient Dirk Kuyt and resurgent Steven Gerrard to capitalise on.

It all depends on how fit Liverpool are after Thursday and whether Birmingham are as bolshie as ever. Break them and Liverpool will get to enjoy the only sort of maths that matter: adding on three points.

FA Premier league: Birmingham v Liverpool, Today, 3.00, St Andrew's