The Stat Man: How many points might it take for Sunderland to achieve League One promotion?

It’s a question a lot of people have started asking since what seemed preposterous at Christmas became a genuine possibility: how many points might achieve automatic promotion this season?

There are several ways to try to answer this question, some of which are subjective. But subjective is not my style so, as usual, I will attempt to be entirely objective. To do this, we need to dig into the archives of seasons past, but first a little background information.

There are broadly two types of league table at the end of a season – linear and non-linear. An example of each follows.

The season shown is 2015/16 in League One. Points per game achieved by each team are plotted against their league positions.

The identity of the teams is unimportant, what matters in this example is that the datapoints more or less form a straight line. You get an indication of how straight the points are from the number at the top-right of the plot. I will spare you the technical definition of the number (this isn’t a maths lesson) and just mention that it tells us 98.34% of the variability in the data is ‘explained’ by the straight line you see superimposed. Or to put it another way, the data is over 98% straight.

When a season such as this occurs, there are no exceptionally good sides running away with the league at the top end. Nor are there exceptionally bad sides trailing behind the rest at the bottom.

In a non-linear season, such as 2005/06 in the Championship (presented above), the data forms a different pattern.

Here we see the datapoints in less of a straight line. This is reflected in the number at the top-right being 87.23% (significantly less than the 98.34% in the previous case).

The main feature I want to draw your attention to, though, is the locations of the datapoints for league positions one and two. This is an example of a non-linear season in which there was a clear winner who performed much better than the rest of the league.

Now we have established what I mean by a linear and non-linear season, I can move on with my explanation.

Oxford United v Sunderland - Sky Bet League One

In order to identify how a league tends to behave with and without runaway teams, I grabbed data from the most recent fifteen seasons in the Championship, League One and League Two. For each of those 45 seasons, I individually calculated the mean number of points per game. This gave me a set of 45 means.

Side observation: the results are remarkably consistent with an average of 1.358 points and a standard deviation of 0.016 across all the seasons.

Next, for each of the 45 league seasons, I obtained the difference between points per game for the team in first place at the end of the season and the average for that division in that season. This provided an intentionally simplistic numerical value for how significant a team’s lead at the top of the division was.

If I haven’t lost you already, then hold onto those thoughts for now.

How linear, or non-linear does the current League One season appear to be? Is any one team running away with the league? Let’s take a look.

It will come as no surprise to you to learn that this is a ‘linear season’. Even without this chart we know that things are tight at the top of the league table but it is still helpful for this discussion to illustrate that the line formed by the datapoints is pretty straight. This is supported by the ‘straightness’ value at the top-right of 96.38%.

Using linear regression – a process in which an equation is generated that describes the relationship between the ‘non-linearity’ of a season and points per game – it is possible to calculate a set of probabilities for automatic promotion. As you would expect, the probability of promotion increases with the number of points gained.

I present the results here with total points on the left and the probability of automatic promotion with that number of points on the right (given as a percentage).

Note: Because the background work has been done using ‘points per game’, the Bury-factor does not come into play. The fact League One has only 23 teams this season is already factored into the calculations.

So it seems that, if we want to be almost completely certain of automatic promotion, we need another 33 points. That’s 2.54 points per game between in our remaining 13 games. Probably too much to ask.

On the other hand, however, if we were to average two points per game for the remainder of the season (certainly reasonable), we would end on 80 points and have a 57% chance of automatic promotion.

Then again, one team might go on a crazy run that skews the league from linear to non-linear and if that happens, all bets are off!

Some additional observations which those of you who are still awake might appreciate:

Of 90 teams promoted in the first two places from their divisions, only 32 (about a third) achieved the supposedly magic number of two or more points per game.
Of the 45 teams promoted in second place from their divisions, only seven got two or more points per game.
Of the 90 teams finishing in the top two, zero needed two or more points per game to finish in that position.
Every side that has achieved two or more points per game finished in the top two of their division and were automatically promoted.
The highest points per game average that did not result in that team finishing in the top two was 1.957.
The lowest points per game average to achieve a top two finish is 1.717 (which results in 79 points in a 24 team league).