It was another big weekend for VAR this weekend, though the interventions don't just speak to luck and obscure rule analysis - they also show how Manchester City make the rules work for them, while Liverpool and Arsenal do not.

Before we unpack this difference, though, it's important to understand why the pivotal calls were decided as they were.

As many have noticed, Arsenal were once again incensed this weekend after one of their players picked up a red card - and as they dropped points. The challenge that cost William Saliba was deemed a denial of a clear goalscoring opportunity, and thus VAR recommended a sending off.

When calculating the factors in a DOGCO challenge versus a more standard professional foul, the officiating bodies will look at:

The distance between the offense and the goal - often the aspect with the most weight; The general direction of play; The likelihood of the player who was fouled being able to keep or gain control of the ball had the offense not taken place; and The location and number of defenders (to determine whether a teammate could offer cover). It's a call that once again uses the "obvious" terminology: officials must be quite certain that, had the foul not taken place, the player would have been able to get a clear shot on goal uncontested. Fouls that take place near the half line, for instance, are often not deemed DOGSO fouls as there's a lot of ground to cover, allowing teammates to provide cover.

In Arsenal's case, Saliba was deemed to have committed a DOGSO offense given that the following is true about the situation:

Evanilson was a long distance from goal, BUT The ball was played centrally and toward the goal AND Played at a pace likely to come under Evanilson's control while not falling to goalkeeper David Raya, who was retreating AND The closest nearby defender was far away. These factors, taken together, saw VAR deem the offense a DOGSO foul, leading to the sending off.

In Liverpool's game, Diogo Jota was cynically pulled down (and landed upon - likely the cause of his injury), but in this case it was determined that:

Jota was a long distance from goal, AND The ball was played into the channel, away from goal AND Played at a pace that it would be more challenging to take control and move into a dangerous position AND The closest defender could likely have provided cover given the position of the ball. Looking at it this way, you can see how the differences cause one to be deemed a DOGSO offense and the other simply a yellow card for professional fouling, even if both are cynical challenges designed to stop an attack. The logic is sound even if it feels frustrating - though arguably less so than in previous seasons where the same categories led to decisions of no DOGSO (often due to defender proximity and the ball not being in the attacker's control) much closer to the goal. These situations all feel like DOGSOs even if the rules as written deem them not so.

In this particular type of scenario, ESPN's Dale Johnson has suggested analyzing the situation by mentally deleting the player committing the foul from the picture, and eying the situation to determine if the attacking player is likely to get a shot off without a different opponent impacting their shot with proximate pressure.

Though Liverpool won their match, further VAR interventions and non-interventions saw a penalty overturned and another two not given (Mohamed Salah had a real shout; the early handball always unlikely under current rules). Of course, VAR also failed to intervene to suggest an on-field review on a coming together between Trent Alexander-Arnold and Jadon Sancho, though this is perhaps less discussed.

Regardless, this weekend saw Liverpool and Arsenal working alongside or against VAR and the other officials, even if the calls themselves were correct. This is very different from what happened to Manchester City.

Thus far this season, two of the three teams seem either at odds with the rule language (when it comes to Arsenal's unforced errors for kicking the ball away, certainly) or at least in a neutral relationship with the rules, if often unlucky.

Meanwhile, Manchester City have attacked the small margins to gain advantage by looking for loopholes in the rule language that will allow them to go against the spirit of the laws of the game while staying on the right side of the rule application.

Because the experts all agree that Bernardo Silva was not impacting play when standing offside and impeding the goalkeeper...despite the play itself designed to impede the goalkeeper until the final possible second.

The attention to the small margins in a cynical sense, Manchester City have (ironically, given, you know) wrangled the rule language in their favor.

Bernardo Silva was deemed to not be affecting play in an offside position when the header was taken, despite having been actively impeding Jose Sa a moment earlier. A moment earlier, however, Silva was onside since no player can be offside on a corner. Silva stops this action right before John Stones' header, and ducks. Due to this action, he's off the hook; while the impact of his previous actions affect the play, but he's smart in that he - surely according to plan - stops committing the potential offense right as it would become one.

This sort of action is clearly against the spirit of the game, but Silva never actually fouls Sa, just distracts him and impedes his movement. Silva's awareness of the rule as written allows him to effectively remove Sa from the play without committing an offense.

While it's certainly possible that Sa might have conceded without Silva's antics, this instance nonetheless illustrates something that Liverpool and definitely Arsenal lack: a cynicism aimed at harnessing the rules of the game in favor of the team.

While it's a bit ugly, Liverpool might want to look into ways to gain these small marginal advantages rather than letting officiating happen to them. It's a small distinction, but these small margins can sometimes be the difference between Champions and Runners Up.