The Central Limit Theorem
By Matt Rowson
The Central Limit Theorem consists of three statements:
[1] The mean of the sampling distribution of means is equal to the mean of the population from which the samples were drawn.
[2] The variance of the sampling distribution of means is equal to the variance of the population from which the samples were drawn divided by the size of the samples.
[3] If the original population is distributed normally (i.e. it is bell shaped), the sampling distribution of means will also be normal. If the original population is not normally distributed, the sampling distribution of means will increasingly approximate a normal distribution as sample size increases. (i.e. when increasingly large samples are drawn)
...which in itself proves nothing. Nothing concerning the Division Two table, at any rate.
However, if you postulate that any one game in Division Two is a completely random event unrelated to any previous or subsequent such events, and further that each game has a roughly one-in-three probability of being either a draw, a win to the home side or a win to the away side (this corresponding roughly to the approximate 2:1 ratio of "undrawn" to drawn games in Division Two thus far) and you repeatedly simulate a league table after thirteen or fourteen games, you obtain something painfully similar to this.
(Except for Rotherham, but it's 8pm on a Sunday, I've been failing to write this preview since getting back from Derby yesterday and it's still a good argument, so run with it...)
If you're already falling asleep then pity me, this is my life. But the gist is this: whilst not proving conclusively that every match in this division (not including those featuring Rotherham) is completely random in its outcome, the league table is largely consistent with that premise. Which is how we find QPR in third (for pity's sake), ourselves still eddying around in ninth despite two points from four games, and Ipswich, West Ham and, yes, Sunderland in play-off positions despite starts to the season that can only generously be described as steady.
The Black Cats' recent form has mirrored our own, with four good wins at the start of September giving way to defeat at Bramall Lane and a disappointing draw at home to Derby before steadying themselves with a one-goal victory over Millwall this weekend.
There's a subtext for Sunderland of course (and for West Ham too), the knowledge that come the end of this season they might as well forget about their bedsit and start looking around for more permanent lodgings as without parachute payments they can expect to be around in Div Two for a while... and with debts still rumoured to run into several tens of millions, it's perhaps not surprising that Mick McCarthy's squad rebuilding has focused largely on cherry picking players from the lower divisions. As ever, McCarthy epitomises the word "dour", and his sides follow in the same mould with the most frequent criticism on messageboards being an inability to turn the screw and create chances with possession. One suspects that the grumbling would increase in volume should the side hit a poor run of results.
Mart Poom remains a very big plus for McCarthy's side, probably the best goalkeeper outside the Premiership which has left Thomas Myhre, signed less than six months before Poom, in varying levels of audible disquiet on the bench.
The centre of defence has been largely rebuilt with Phil Babb and Joachim Bjorklund out of the door over the summer and Ben Clark, to a few quizzical looks from the stands, reputedly on the verge of joining Hartlepool. Gary Breen is still around, but will miss Tuesday night's game with the last of a three-game suspension meaning that Stephen Caldwell and Neill Collins should again turn out. Caldwell made the brave move from Newcastle over the summer and hasn't convinced everyone... "he's always got a mistake in him" is one reflection, although McCarthy bigs him up on Sunderland's official site. Collins was recruited from Dumbarton in August and has impressed - Tuesday will be his first appearance away from the Stadium of Light. Collins' namesake Danny, a recent recruit from Chester City, will add competition in this position.
Stephen Wright's one match ban saw former Man United trainee Mark Lynch come into the side against Millwall but Wright should reclaim his place on Tuesday whilst Northern Ireland international George "Ringo" McCartney has no obvious competition at left back and should captain the side having recovered sufficiently from a hamstring problem to play at the weekend. Darren Williams is on loan at Cardiff.
In midfield, Carl Robinson and Jeff Whitley appear to be the favoured central pairing. Whitley, a largely destructive player, is the current boo-boy; Robinson impressed during loan spells with a variety of clubs over the last couple of years before signing a permanent deal from Pompey this summer. It has been suggested that, playing next to Whitley, he could do with sitting less deep and supporting the attack more. In wide positions, Julio Arca on the left continues to be idolised although Celtic-orientated rumours persist; Dean Whitehead, more conventionally a central midfielder, is wide on the right having arrived from Oxford in the close season. Another tribunal signing, ex-Mansfield man Liam Lawrence, has been effective coming off the bench whilst Darren Carter, on-loan from Birmingham, is another option. Colin Healy's recent second leg fracture rules him out for the timebeing whilst Matt Piper is still a few weeks away from a return after his tenth operation. John Oster and Sean Thornton appear to be persona non grata at the moment, with Thornton's sulky tantrums and pronouncements taking up several pagesworth of largely unsympathetic messageboard space.
McCarthy has been rotating through combinations of strikers in search of a winning pairing in the absence of Kevin Kyle, out until December with a hip injury. Stephen Elliott, recruited from Manchester City over the summer, has perhaps been the most convincing; he missed out against Millwall with a groin problem but is expected to be back in contention for Tuesday. Marcus Stewart's thigh problem may explain whilst he was restricted to the bench whilst youngsters Chris Brown and Simon Johnson, the latter on loan from Leeds, have also played. Michael Bridges would be a popular selection, however when even Sam Allardyce is prepared to write off a talented player as a lost cause you have to worry a bit. Bridges scored in his last game against us, for Leeds at Elland Road in May 2000. He also scored against Everton five days later, his twenty-first goal of that season, but has not found the net since in a four-and-a-half year spell ruined by injury.
Back to the Vic for the first time in three weeks, then, for whatever dice-roll fate has in store for us. Frankly I'm not too fussed about the randomness theory, it gives us an even shout for one thing which is more than we've had for a couple of seasons. And there are worse things to do with Saturday afternoons (or Tuesday evenings) than Snakes and Ladders with added beer and shouting. Bring it on.
