So who is going down? For virtually the first time this season neutrals are mentioning Sunderland as serious contenders. Given our awful run, and the tough bunch of games to come, that is hardly surprising. John McCormick has been studying trends again and comes up with potentially good news for Aston Villa, though he still sees QPR and Reading going. At whose expense would Villa survive? Ours? Not according to whatever can be gleaned from the stats John has been reviewing. Read on but expect to be blinded by this branch of science …
It’s now ten games since the Christmas period, when I started looking at goal differences. Since then there have been enough unexpected results to make me wonder why I stuck my neck out by predicting that QPR and Reading would be joined in the championship by the team whose goal difference showed the most consistent decline in the second half of the season, while the others at the bottom would show a greater improvement. (If you want to look at the original posts click on my name at the top and find them in the archive on the page which appears).
My idea was always speculative, not to say fanciful, but after 5 games it did appear that it might have substance. Trendlines pointed firmly at Villa as the third team, with Wigan also looking a possibility for the drop should Reading maintain a magnificent run of form which netted them thirteen points when the best of the other teams were achieving four or five. Since then things have tightened up, so much so that I’ve had to include QPR and Reading in the charts. My apologies to their fans for the original omissions and my forecast of doom but, as you’ll see, celebrations on their part could yet be premature.
I began by showing Sunderland’s goal difference over the season. There was a downward trend, unspectacular but consistent. This trend has continued, with only a rare draw to slow the decline:
This has to be a cause for concern but my question was, and is, “how does this compare to other teams?”
So here are the goal differences for the teams which were propping up the premier league at the time, plus Fulham, who weren’t doing too well after a promising start:
As before, we aren’t doing too badly in comparison with some of the others. There are teams around us who are conceding at least as many goals. However, starting at August doesn’t let us examine the idea that it’s the way goal difference goes in the second half of the season which will be the indicator.
So, once again, here is a graph to show changes since Christmas, when I reset the goal differences to zero:
And, once again, I’m sure you’ll agree the chart is too messy to make interpretation easy and it’s time to call up trendlines.
Ignore the difference in the positions of the starting points on the left. It’s the slopes (the gradients) of the trendlines which matter. NUFC and Fulham’s are almost horizontal and I’d say those two will be safe. The other six have gradients which are not too different. Putting that together with the jumble on the actual goal difference chart I’d say my original prediction has no substance. There’s nothing in goal difference to say who is going down. Did anyone really expect anything different?
Having said that, I want to continue what I’ve started so I’m going to update my prediction anyway, using the trendlines as my starting point and using their R² values to get an idea of how reliable they are. An R² value actually gives a measure of how well a trendline fits the points on a graph. If it’s 1 the trendline will go through all of the points. If it’s 0 the trendline will be miles away from them. I’m working on the principle that trendlines which are close to many points (i.e. with high R² values) will be reliable indicators. This sounds reasonable but it’s not a mathematically valid principle. However, having introduced R² values in the previous post I have decided to operate on the mathematically valid principle of “in for a penny, in for a pound” and carry on with them. Here are the R² values:
When I look at the slopes of the six remaining trendlines I can see two groups:
Reading and Wigan have the two steepest slopes. Their R² values are above 0.6, which foolhardy souls might interpret as meaning there is an element of reliability and GD will continue to go down over the next 9 games.
That leaves Southampton, QPR, Villa and ourselves. Their downward trends aren’t quite as steep and their R² values show a lot of difference (Villa’s R² is one of the highest of the eight, Sunderland’s the lowest of the six teams showing a decline). I’m interpreting the differences in R² as meaning Villa’s GD will continue downwards, QPR’s probably will, Southampton’s might and Sunderland’s could go anywhere.
So, for what it’s worth, and I do hold a well-deserved place at the bottom of Goldy’s predictions league, here is my updated prediction:
QPR and Reading are still doomed. They have points to make up but are still trending downwards so won’t close the gap.
The team which will join them is most probably Wigan but it’s a very tough decision. They have a steeper downward gradient than Villa. However, they do have a game in hand, which I think is against Man City, and a win could change things around, and then there’s a certain game on the last day of the season.
Villa, Southampton and Sunderland are the next three in line for relegation, in that order. Their trendlines have similar gradients – perhaps Villa’s is slightly steeper – so will keep their relative position.
You’ll notice that this prediction actually mirrors the current league positions. It was the same when I did the graphs after five games. This is intriguing, given that I’ve decided goal difference is a useless predictor. It’s interesting enough for me to want to follow it through, especially as the dog-eat-dog games waiting in the wings will surely have an effect on the trendlines. I’ll try to revisit in about five games to get a last prediction before the table gives us the final and irrevocable truth.