Arsenal are not playing this derby. They stand to gain or lose nine points of probability.

Manchester United host Manchester City this afternoon, matchday four of the Premier League. The derby involves neither side in a direct title fight: United are thirteenth, and the model gives them virtually no chance of finishing champions.

And yet, of all this matchday's fixtures, it is the one that will move Arsenal's title probability the most — and Arsenal are not playing.

Six days ago it was a coin flip

At the calculation published on 7 September, after three matchdays, the two contenders were indistinguishable:

A tenth of a point between them on end-of-season expected points. At that distance, the model says nothing except: toss a coin.

Then Arsenal went and won at Sunderland

Friday night, 0-2 at the Stadium of Light. A fourth win in four, eight goals scored, one conceded. The same evening Liverpool — the only other contender rated above 1% — were held to a goalless draw at home by Fulham.

At this morning's calculation, it is no longer a coin flip:

Seventeen points of separation in six days, for a win against the side lying seventeenth.

Except that half of that gap has not been earned

This is where the table lies, and where a model earns its keep.

City have not played their fourth fixture. The three-point gap in the table is therefore not a three-point lead: it is a game in hand, and it kicks off this afternoon.

By imposing each possible outcome on the derby and replaying the season, we can separate what has been won from what has not:

Nine of the seventeen points rest on nothing more than City not having played. Seven come from genuine superiority — Arsenal's four-matchday dominance, and Liverpool's stumble.

What the derby is worth, outcome by outcome

Nine point three points of range for Arsenal, ten point nine for City. A matchday-four fixture, in September, worth that much.

And United, beating the reigning double champions in a derby, would go only from 0.6% to 1.1%. Thirteenth after four matchdays, the club carries a deficit that ninety minutes cannot repair.

The draw is not neutral

It is the least intuitive line in the table. Sharing the points raises Arsenal by two points, while changing nothing in the relative standing of the two sides.

Arsenal gain more from a City defeat than City gain from a win

Look at the movements against the reference:

Arsenal gain 5.2 points if City fall; City gain only 4.8 by winning. The asymmetry comes from position: when you are already the favourite, your rival's stumble is worth more than their expected performance. City are supposed to do well at Old Trafford — doing so earns them only what was already priced in.

Where the strengths stand

Arsenal		1.42
Manchester City		1.54
Manchester United		1.37
Liverpool		1.34

For their part, Arsenal sit top of the table, with a defence of 0.62 — one goal conceded in four matches. It is that solidity, more than the attack, that carries their title probability.

What this does not say

A probability that swings ten points is not a prediction. It says the fixture carries weight, not that it will decide anything — thirty-four matchdays remain.

The model does not know the line-ups. It has no idea who will take the field at Old Trafford, who is injured, who is coming off a week of three matches. It sees results, seven seasons of results, and what they say about each side's ability to score and to concede.

And the calendar imbalance settles itself: by half past six, City will have played their fourth match, the comparison will be clean again, and nine of today's seventeen points will have been decided on the pitch rather than by a date.