If the way to measure a team's progress is their resilience when things go against them, their ability to perform in situations that carry additional weight and their ability to shape-shift into something more effective, then Unai Emery's Arsenal are definitely on an upward arc.
They found themselves 2-1 down at half-time in the North London derby despite arguably playing better than Spurs and conceding on a goalkeeping error and a hugely dubious penalty. (Heung Min Son may have been touched; whether that meant it's a penalty or he needed to scream and roll around is another matter.) We've seen softer versions of the Gunners fade in these situations, but Emery's half-time substitutions -- Alex Iwobi and Henrikh Mkhitaryan off, replaced by Aaron Ramsey in the hole and Alexandre Lacazette joining Pierre-Emerick Aubameyang up front -- gave them another gear and they never looked back.
The back three -- and bear in mind, it includes the much-maligned Rob Holding and Shkodran Mustafi -- dealt with Spurs' attacking firepower for much of the match, Lucas Torreira and Granit Xhaka were dominant while the various forward permutations did what they were supposed to do.
You can chalk some of it up to Mauricio Pochettino's choices and a bad day at the office. Leaving Toby Alderweireld on the bench seemed to mess up both his direct replacement, Juan Foyth, and his defensive partner, Jan Vertonghen. Eric Dier, who clearly isn't 100 percent physically, struggled after half-time with Arsenal's new setup, and Tottenham's tactical reaction came late. But make no mistake about it, a ton of credit has to go to Arsenal and Emery in this match.
The other side of the north London derby
Two off-the-pitch issues also surfaced at the North London derby. One was the banana skin some idiot threw in the direction of Aubameyang. It's an ugly legacy of football-related racism from the 1980s and obviously has no place today. Tottenham have said they will ban the supporter; naming and shaming him wouldn't be a bad idea either. (On Monday, news emerged that the supporter had been arrested.)
The other concerns Emery. I appreciate he's new to the Premier League, but somebody needs to have a word with him about how the media work. Last week, he justified the decision to leave out Mesut Ozil by talking about the "physicality" and "intensity" of the opposition -- when they were playing Bournemouth. This week, he said Ozil had back spasms but then added that he didn't know when they were diagnosed or whether he had even bothered to show up at the Emirates at the derby.
Maybe he's just being honest to a fault, but what he's also doing is giving the impression that something is wrong in his relationship with Arsenal's highest-paid player. And he's leaving plenty of room for speculation.
Here's a tip. Next time, simply say: "Yeah, unfortunately Mesut hurt his back on Friday and it's a real shame because he's such a gifted player." And leave it at that. Unless, of course, you're trying to start something.
UEFA's big idea: another tournament
As expected, UEFA's executive committee approved changes to European competition, reducing the teams in the Europa League to 32 and adding a third club competition (known as UEL2 for now).
The idea is to increase the standard of the Europa League and make UEL2 the sort of competition open to more leagues around the continent. UEFA say it makes matters more "inclusive" as the number of participating countries will go from a minimum of 26 to a minimum of 34. What that exactly means to fans in those countries, and whether it's commercially viable, remains to be seen.
Mourinho makes himself the story again
Last week I wrote about Jose Mourinho's seeming inability to not make everything about himself. The trend continued on Saturday in Southampton, where Manchester United drew 2-2 and Saints manager Mark Hughes was later sacked.
Mourinho reportedly called Paul Pogba "a virus," saying he didn't "respect players and supporters" and killed the mentality "of the good honest people around you." The thing about this story is that it comes from Duncan Castles, a reporter who is very close to Mourinho's camp. And that suggests that Mourinho is happy for the contents of this dressing down to be out there.
Maybe he thinks (a bit like the vice captaincy nonsense) that it's the best way to motivate Pogba. Heck, it's his choice. But players aren't stupid. It's one thing to be metaphorically crucified in a dressing room in front of your teammates; it's quite another when it gets leaked to the press and you're pretty sure who is responsible.
One more thing. Helpfully, the Pogba story was accompanied by stats showing that Pogba had handed over possession more than any other midfielder in the Premier League this season. That's an average of 19.4 per game. But before we destroy Pogba (or drown him in antiviral drugs), we may want to consider this "lost possessions" stat because it came up last year too.
At the time of that tweet, Kevin De Bruyne had lost possession 22.1 times per match and Cristian Eriksen 20.8 times per match. And, of course, we all know De Bruyne and Eriksen are notoriously selfish, unproductive "viruses" who infect everything around them.
Real Madrid win but still lack identity
Santi Solari is going to do things his way at the Bernabeu. Valencia may be underperforming this season, but when they visit Real Madrid, it's by definition a "trap game." Yet there he was with Dani Ceballos and Marcos Llorente in midfield (later joined by Federico Valverde) and Sergio Reguilon at the back. And, most notably, Isco and Marco Asensio on the bench while Toni Kroos and Marcelo watched on in the stands.
Valencia gifted them an early lead via Daniel Waas' own goal and Lucas Vazquez made it 2-0 late. In between, we saw a number of chances and sloppy play from both sides with Madrid, arguably, having the upper hand. The good news is given the way La Liga is going, it's another step forward up the table. The not-so-good news is that it's still tough to figure out what this team wants to be, and the big guns -- from Gareth Bale to Karim Benzema to Luka Modric -- aren't quite stepping up.
Roma and Inter put on a show
Roma and Inter served up a 2-2 draw that was not unlike the heavyweight clash between Tyson Fury and Deontay Wilder out in Los Angeles a few hours earlier. These are two teams with flaws and issues who nevertheless went for it, landing plenty of body blows and serving up a ton of entertainment.
Roma will feel aggrieved that neither the referee nor VAR spotted Danilo D'Ambrosio's trip on Nicolo Zaniolo, which could have been punished with a penalty. (Oh, and at 19 years old, Zaniolo was starting just his second game and was arguably man of the match.) But the fact that they created, and finished, chances on a day when they didn't have Edin Dzeko up front is significant: Cengiz Under took responsibility, and Patrick Schick played like the guy they thought they had bought. The draw should remind his critics that the players, at least, remain loyal to Eusebio Di Francesco.
As for Inter, despite the psychological baggage of the defeat at Tottenham in midweek, they came to play and imposed themselves on the match for long periods. Performances are starting to match their results, and they continue to grow. All positives for Luciano Spalletti.
Bayern win but remain a mess
After the club's recent Bundesliga outings and the acrimonious annual general assembly of club members, it was critical for Bayern to bounce back with a win at Werder Bremen. Mission accomplished, then, as two goals from Serge Gnabry helped them to a 2-1 victory. It was their first victory since October.
The bad blood hasn't gone away, however, nor has the fallout from Uli Hoeness' decision to ban club legend -- and his former teammate -- Paul Breitner from the team's VIP areas. Breitner had been critical of Hoeness and Karl-Heinz Rummenigge.
How clubs handle former legends is always tricky (just ask Manchester United), but Hoeness is only adding fuel to the fire when he accuses a guy like Breitner of damaging Bayern "in an unspeakable manner." All it does is draw more attention to the criticism and the negativity.
Liverpool win ugly -- again
If Liverpool are still just two points behind Manchester City, you need to credit Jurgen Klopp, the players and smoke and mirrors. Because that outrageous last-ditch injury-time winner from, of all people, Divock Origi, came entirely out of the blue and was a gift from on high. Before that, Everton had more than held their own, and few would have had a problem if it had ended in a draw.
Credit Liverpool's "stick-to-it-ness" but realize also that they haven't really fired on all cylinders since October. Klopp needs Roberto Firmino to return to the form he showed last year, and he needs someone -- Naby Keita? Fabinho? -- to step up in the middle of the park. Otherwise, unless City somehow collapse, you can see Liverpool falling behind.
Dembele has his day in Barca's latest win
Without Luis Suarez (and Arthur) and with Philippe Coutinho and Arturo Vidal struggling for form, Barcelona needed somebody else to team up with Lionel Messi and help them past Villarreal. That somebody turned out be Ousmane Dembele, who is finally achieving some level of consistency and quality for Ernesto Valverde's crew.
Dembele set up Gerard Pique's opener in the 2-0 win and was a reliable outlet throughout the match. A late goal from the much-hyped Carles Alena, coolly taken and nicely set up by Messi, secured the victory which took Barcelona top of La Liga.
Barca are taking their time with Alena, who is just seven months younger than Dembele but has yet to start a league match. You only need to look at the Frenchman's up and downs to see what can happen when you get pushed too hard, too fast. But both can play an important role for Valverde in the second half of the season.
Milan overcome the odds to beat Parma
When your three first-choice central defenders are all injured and you need to line up with Ignazio Abate (who started as a flying winger and played as a pacy full-back for most of this career) at centre-back, then you'll almost always get a pass from me. Particularly when you're also missing two of your first-choice central midfielders (Lucas Biglia and Jack Bonaventura) as well as your star centre-forward (Gonzalo Higuain) and are playing Jose Mauri, who had played just 13 minutes of Serie A football in the previous 18 months, in the middle of the park.
Milan got a bit lucky with the VAR-assisted penalty decision in the 2-1 win over Parma, and it was more of a battling performance than a scintillating one But right now, given all the mitigating circumstances, that's all you can ask for.
Don't be too hard on Gabriel Jesus
The visit of Bournemouth was the perfect opportunity to check in on Gabriel Jesus. With Sergio Aguero out, the Brazilian centre-forward led the line against the Cherries but again failed to make much of an impact. It sort of mirrors his season thus far, particularly in terms of goals. He scored in a 6-1 drubbing of Huddersfield, nailed a hat trick in a 6-0 against Shakhtar Donetsk (two of them were penalties) and got a goal against third-tier Oxford United in the League Cup.
That's not quite the return you expect after 17 appearances from Brazil's first-choice central striker. Still, it's worth remembering that despite being around for a while, he's still just 21 years old. At that age, you'll have big swings in form. Should something happen to Aguero, there's still the option of Raheem Sterling -- who has nine goals in 17 appearances, all from open play -- up front.
Finally, PSG have dropped points in France!
It was going to happen sooner or later, so it's really not a big deal that Paris Saint-Germain, after 14 consecutive victories to open the season, failed to win away to Bordeaux, settling instead for a 2-2 draw.
Far more relevant down the line is that after two cameo appearances, Dani Alves made his first start in more than six months and lasted more than an hour. If they are going to have an impact in the Champions League (and, obviously, they're still not through to the knockout stage), they are far better equipped with the veteran wing-back and the leadership and experience he brings.
Alcacer scores again, Dortmund win again
We've said it before but Borussia Dortmund's ability to win both pretty and ugly is what has Lucien Favre's team at the top of the table. Against a Freiburg side intent on clogging space and hitting on the counter, they were patient in picking their spots, taking the lead through a Marco Reus penalty. That was before Paco Alcacer -- who else -- came on to seal the 2-0 win.
Needless to say, his numbers don't even make sense. He has 10 goals, nine of them off the bench, in 286 minutes on the pitch. That's one goal every 28.6 minutes. And that's absurd.
Sevilla still in good shape despite slip-up
Sevilla surrendered top spot in La Liga after being held away to Alaves, who haven't lost at home since April and are themselves surprisingly close to the top of the table. Against an organized and defensively well-drilled opponent, there was only so much Pablo Machin's men could do in the first half, but business did pick up after Quincy Promes came on after the break.
There's a toughness to this Sevilla side under Machin that wasn't there in previous seasons, which is in some ways reminiscent of early Diego Simeone, although Machin's philosophy is obviously very different. Apart from the trip to the Camp Nou, when they were hugely unlucky, there's a reason they haven't lost a league game since mid-September.