As Mikel Arteta returned from Dubai, after a trip that was supposed to be rejuvenating for his squad, the Arsenal manager was poring over various ideas to navigate a proper injury crisis. Arteta’s staff are big on the maths of the pitch, and often run tactics through algorithms. Right now, only a few simple sums matter.

Arsenal did not sign a forward in January. That left an already shallow range of attacking options at risk from injury. Now, the worst has happened. Kai Havertz’s hamstring injury, which is expected to sideline the German for the rest of the season, means three first-choice attackers are all out.

They only have three forwards available for the next few games, and one is budding 17-year-old Ethan Nwaneri, with little experience. Moments like these are where you get that experience, and, although there are vintage examples of youngsters seizing the opportunity in the past, it's an unreasonable amount of responsibility.

From that history, it’s occasionally been said that title races ultimately turn on individual moments, those that carry the weight of a season’s accumulation of events.

Such statements are usually intended to mean decisive goals on the pitch. As regards Arsenal’s challenge to Liverpool, however, this might be it. That the Havertz news leaked on the day of the leaders’ crucial derby trip to Everton only added depth to it. Given these attacking options, Arsenal may need to be more concerned with those underneath them and the Champions League places.

It also poses a huge depth of questions for Arteta and his club. The manager himself spoke of the need to keep everyone fit before the Carabao Cup match at Newcastle United. This will now feel worse than that elimination.

In the short-term, the maths ensure it is almost impossible to see Arsenal keeping pace with Liverpool, let alone overhauling them.

They might get by with one or two games but the real issue with situations like this is asking players to do more than can be fairly expected over an extended run. That’s when drop-offs become apparent. And this is at a point where Arsenal really needed to be at their maximum, without making a single mistake, while hoping Liverpool abruptly falter.

In the medium term, there’s also the question of the Champions League challenge, which had been looked as potentially saving the season. Arsenal had seemed well set up, right down to players coming back fresh... until now.

There’s then the long-term discussions to be had about how recruitment combines with preparation.

Arteta now has to face up to one highly uncomfortable fact. It is not just that his entire front three are out, given the absences of Bukayo Saka and Gabriel Martinelli. It’s that they’re all out with different types of hamstring injuries. Within football, these and quad injuries are usually taken as signs of players being overworked.

That is perhaps a natural consequence when your attack is already so thin. The issue will nevertheless invite inevitable questions over the intensity of Arteta’s training, in the same way that has happened to Ange Postecoglou, Erik ten Hag and countless other managers that have faced injury crises.

The sheer number of them shows the new calendar obviously hasn’t helped, and clubs had already flagged this as the most intensive January ever. That's on top of four years of congestion. It should be acknowledged Arsenal didn’t face these issues last season, and Martin Odegaard’s ankle injury wasn’t from fatigue. It was just a challenge, and bad luck.

Some of it still comes down to how you manage it all, mind. A player like Havertz, no matter his physical capabilities, has just played too much over too short a period. There’s now an obvious feeling, in the words of one source, that some of this “avoidable”. Was there really such a need for the main attackers to play so many minutes in such a period? And what of the decision to sell Eddie Nketiah, who would be so valuable now?

It’s why Arsenal could have done with even a loan deal in January. Arteta was against bringing in “a body” but they now need that more than anything. It’s all the worse that it seems so obvious now.

For all the emotional angst this is going to cause around the club, there was still some logic to those decisions. They attempted to look at the bigger picture, and five-year plans rather than just this one difficult season.

It was a calculation, even if now looks like a gamble that has backfired, that itself based on hope of no further issues. That now seems even worse, as Arteta makes other calculations.

How Arsenal set up against Leicester City on Saturday is going to be instructive. Rather than just playing the same 4-3-3, it is possible that Arteta leans more on his disproportionate number of midfielders and goes to a 4-5-1 with more attacking focus on Odegaard. That at least spares some of the burden on Leandro Trossard, Nwaneri and Raheem Sterling, too. The latter will be ineligible to face Chelsea on 16 March due to the terms of his loan deal, though Saka may have returned by that point. Trossard and Mikel Merino look poised for spells in the side as forwards too.

Some might say it is just as well they "only" face a relegation-threatened Leicester. That can work the other way if a straining attack fails to score.

By the same token, Arteta will now fully lean into his usual response to these situations, which is to be as positive as possible. He is aware that constant talk of injuries can negatively affect a squad, so will instead point forward. That can often seem delusional, but that’s part of the point: to shut out doubt.

Similarly, it is some small consolation for Arteta that February is a much less intense month, where Arsenal have no European matches and finish it with another FA Cup break. If they can just get through these games against Leicester away, West Ham United at home and Nottingham Forest away, they can then take stock.

There might be hope that Saka and Martinelli will be back from their own injuries by then, but that will invite another calculation, and potential dilemma. You don’t want to be rushing anyone back after a situation like this. That can just compound the problems.

Getting through and taking stock in that way has also felt the story of the season, that started with such hope. For now, the title isn’t quite settled. The prospect of a race, to use the language around these situations, is nevertheless down to the bare bones.