It may not seem a good time to be predicting relegation for Reading (just after they’ve beaten us), QPR (buoyed by big new signings with an escapologist in charge) and Aston Villa (didn’t we somehow contrive to make even them seem half-decent?). But John McCormick has been pottering around with his blinding statistictal science again, attempting to calculate the impact fluctuating goal differences can have on survival prospects. As things stand, he sees safety for Sunderland but not by a comfortable margin and a possible lifeline for Reading, at Wigan’s expense …
A few weeks ago (December 30: https://safc.blog/2012/12/mccormicks-craic-spot-the-difference-in-the-relegation-dog-fight) I posted something about goal differences in which I wrote:
“I think it’s safe to say the teams from the bottom which will avoid relegation are those whose goal differences show the greatest improvement”
This is the chart I used at the time to show how our goal difference was doing:
Since then we’ve played at most six games, so it’s early days, but this is the current position:
The downward trend is continuing as we are losing as many games as we are winning but, as before, it isn’t falling off a cliff. We got walloped by Liverpool but recovered with a 3-0 win over West Ham, since when we’ve picked up a few points and moved away from the relegation zone, despite some surprising results from those whom I said were doomed at Christmas.
But you’ll remember what I said at the top of the article, it’s the teams which have the greatest improvement which will avoid relegation. So how do we compare with the other clubs in the mire?
“Not badly” is the answer.
The New Year posting compared us with Wigan, Villa, Reading, QPR, the Mags and Southampton, the bottom clubs at the time, and I included Fulham as they had had a run of iffy results. Here are their goal differences since the start of the season:
QPR and Reading were the bottom two and looking likely candidates for the drop, so I made this prediction about the six others:
“I’m going to stick my neck out and say that the five whose goal differences show the greatest improvement in the second half of the season will avoid relegation, irrespective of their points on Boxing Day, and a consistent decline will point to the doomed team.”
You can see where Villa had two horrendous weeks but other than that it’s difficult to see from the chart who has shown the least or the most improvement since the New Year. To get a clearer picture I did a little playing around with a spreadsheet to reset goal difference to zero at the halfway stage, ie at game 19 for all of the teams, and then recalculated goal differences until the end of January.
You can see the results in the next chart, which shows changes in goal difference since game 19. As I had already consigned QPR and Reading to relegation I have taken them out to simplify the picture; maybe events will prove I acted too hastily. As I’m looking for a third candidate I hope Reading and QPR fans will forgive me and read on:
This chart shows NUFC and Villa were both in decline but NUFC’s goal difference now appears to be heading upwards. Sunderland’s 3-0 defeat and 3-0 win show up as a dip but after that their line doesn’t move up and down much, which is not surprising as we haven’t won or lost by more than one goal since West Ham. Fulham’s goal difference stays within a narrow band, as does Southampton’s. Wigan’s goal difference appears to show as much variation as Sunderland’s, their graph has a mirror-image look to ours, but they are actually not doing as well as we are.
The chart wasn’t particularly helpful so I generated a trendline for each of the lines. You can see the results below. It transpired the trendlines could be put into two groups. Villa’s and Wigan’s goal differences are heading downwards. So too are NUFC’s, slightly less steeply. Sunderland’s, Southampton’s and Fulham’s lines are more or less level (ours is heading slightly uphill but our goal difference has actually declined by 1 since game 19. I’ll come back to this later).
If my original premise about a consistent decline in goal difference in the second half of the season is correct then one of the clubs showing this trend, ie Villa, NUFC or Wigan, are destined to become the third team to go down.
There are two caveats, however, and they are both important. Firstly, this is a very small number of games, especially as changes in January need to be accommodated – new players and even a new manager need to bed in – and small samples do not make for good predictions.
Secondly, I looked at something called the coefficient of determination (R2) for each of these trendlines.
R2 gives an idea of how close a trendline is to all of the actual points on the graph. An R2 value can be anywhere between 0 and 1 and the nearer it is to 1 the better is the fit. (If the R2 was 1 then the trendline would go through all of the points on the graph).
The Sunderland trendline had an R2 value of 0.02, which might explain why a decline in goal difference could be represented by an uphill line. The R2 value for NUFC was about 0.35 and for Wigan it was 0.5. Only Villa’s R2, at just over 0.8, supports the notion that their trendline is reliably indicating where their goal difference is heading, and I’m sure there will be mathematicians who want to disagree with me about even that.
Nevertheless, at the time of writing what we see at the bottom of the league table is reflected in the goal difference and trendline charts. If I did have to use them to make a prediction I’d say it is Villa who will go down and Wigan who will join them if Reading manage to stay out of trouble.
Am I confident about this?
Let me put it this way: I’m reasonably confident we’ll be safe but I won’t breathe easily until we get 42 points (and I don’t expect more than 43 for the season) or three other clubs are certain to finish below us – after all, this is Sunderland we’re talking about. I’ll revisit goal difference in another month or so and we’ll see if my prediction is still holding true and, if necessary, I’ll put the lines for Reading and QPR back in, with an apology.
** And if all those charts and statistics leave you in need of light relief, try Monsieur Salut (and lately Pete Sixsmith’s) Sunderland pages at ESPN. Latest posting: The Loneliness of the Long-Distance Supporter, at this link: http://soccernet.espn.go.com/blog/_/name/sunderland/id/1046?cc=5739#
I know pilots sometimes announce important sports results but somehow sensed it was not going to happen (with Saturday’s game at Reading). The airline toilets may not be fitted with the equivalent of smoke detectors to trap clandestine use of mobiles – “the checking of football scores is strictly against international aviation regulations” – but you do get the impression it would be frowned upon.