According to “Varzesh3,” time can deceive us all. Even supercomputers.

Unless surprising results occur in this week’s return leg matches, only five teams likely remain with a chance to win this season’s Champions League (Arsenal, Barcelona, Paris Saint-Germain, Inter Milan, and Bayern Munich). This is a significant change from the start of the season when Opta’s data-based predictions showed Manchester City (25%) and Real Madrid (18%) as the most probable contenders.

How are these predictions calculated? Opta’s win prediction model estimates the probability of each match’s outcome (win, draw, or loss) using a combination of betting market odds and Opta’s team power rankings. These coefficients and rankings are based on historical and recent team performances, and the entire competition is simulated 10,000 times to derive the final prediction for each team.

But even these models cannot predict things like Rodri’s decisive injury for Manchester City or Declan Rice’s sudden ability to score direct free kicks like Brazilians.

If success in a competition depends on patience, stability, and gradual progress, Arsenal has arrived at the main contender position for the 2024-25 Champions League at just the right time. According to statistical predictions, Arsenal has steadily increased its championship chances with consistent performances throughout the season and is now in the best position. This report explains how the chances of the eight remaining teams in the quarter-finals (including Arsenal) have fluctuated and what factors have caused these changes.

Arsenal

Arsenal started the Champions League with a 6% chance of winning their first title, behind Manchester City, Real Madrid, and Inter. A 0-0 draw against Atalanta in the first week, along with other results, saw Bayer Leverkusen (who beat Feyenoord 4-0) overtake them. The next two weeks included a 2-0 win over PSG and a 1-0 home loss to Inter. At that point, few considered Arsenal a serious title contender.

But they won their last four group-stage matches with a combined goal difference of 13-1, increasing their championship chances to 17%, tying with Inter and standing just behind Liverpool (24%) before the playoff stage.

Liverpool’s elimination by PSG in the round of 16 and Arsenal’s emphatic 3-0 win in Madrid last week have given them a 27% chance, making them the slight favorite to win.

The season for Mikel Arteta’s team has been marked by injuries and setbacks, but after a six-year absence from top European competitions, they can—and should—continue last season’s quarter-final run with their first semi-final appearance since the 2008-09 season.

Barcelona

Barcelona started the season with a 6% chance of winning the title, level with Arsenal. A surprising 2-1 loss to Monaco set them back, but a decisive victory over Bayern Munich in the third week, along with comfortable wins against Young Boys (5-0) and Red Star Belgrade (5-2), increased this chance to 9% at the halfway mark.

They finished the group stage with three wins and a draw, placing second, but their championship chances remained unchanged until after a 4-1 aggregate win over Benfica in the round of 16, when it rose to 20%. At that time, this was the best chance among the remaining teams. Despite a 4-0 win over Borussia Dortmund last week, they now stand at 26%, slightly behind Arsenal as the second favorite. They might face Arsenal in the final, repeating the 2006 final.

Paris Saint-Germain

If Arsenal’s progress in the predictions has been steady, PSG has experienced a massive leap. They started the season with a 4% chance of winning but managed only one win in their first five matches, losing to Arsenal, Atlético Madrid, and Bayern and drawing with AZ Alkmaar. These results raised their group-stage elimination probability to 42% and reduced their championship chances to 2%. It seemed Luis Enrique’s team was finished.

But a 4-2 win over Manchester City breathed new life into PSG’s European campaign. Then, demolishing Brest 10-2 on aggregate in the playoffs increased their championship chances to 9%. Defeating Liverpool, one of the main contenders, on penalties in the round of 16 more than doubled this chance to 19%.

Now, with a 3-1 win over Aston Villa in the first leg of the quarter-finals, they have a 23% chance to win the competition for the first time.

If momentum and motivation determine the champion, this season’s Champions League seems destined for PSG, unless they throw it away themselves.

Inter Milan

Inter started the competition with an 11% chance of winning (behind Real Madrid and Manchester City). Their only weakness in the group stage was a 1-0 loss to Bayer Leverkusen in the sixth week. They conceded only one goal in eight matches and, with impressive wins over Arsenal and Monaco, their championship chances rose to 17% after the group stage.

Feyenoord was no obstacle in the round of 16, and while their quarter-final against Bayern looks like the closest contest on paper (with a 2-1 result), Inter has an 85% chance of advancing to the final four, giving them plenty of reasons to relax. Can the 2023 runners-up go one step further two years later?

Bayern Munich

Bayern began the group stage with just a 4% chance of winning, placing them sixth. This chance increased slightly (by one percent) after a stunning 9-2 win over Dinamo Zagreb in the first week.

But losses to Aston Villa and Barcelona reduced their chances to 3% and raised their group-stage elimination probability to 6%. Four wins in their last five games saw them finish twelfth. They advanced to the playoffs thanks to Alphonso Davies’ late goal against Celtic and crushed Bayer Leverkusen 5-0 in the round of 16.

However, last week’s home loss to Inter has reduced their championship chances under Vincent Kompany to just 2%.

Aston Villa

Aston Villa has enjoyed their Champions League adventure, which, as expected, started with less than a 1% chance of winning. They achieved memorable results against Bayern Munich (1-0), Juventus (0-0), Bologna (2-0), RB Leipzig (3-2), and Celtic (4-2), finishing eighth and exempt from the playoffs.

Their championship chances rose to 1% after the eighth week and peaked at 3% before the quarter-finals began. But a 3-1 loss in Paris has reduced this chance to less than 1%, and they now have only a 9% chance of advancing to the semi-finals.

Real Madrid

Real Madrid, despite starting the season as the defending champions and the second favorite in predictions, slipped unusually in the group stage, having won 15 of their 18 group-stage matches in the previous three seasons.

They narrowly beat Stuttgart with late goals in the first week, then lost 1-0 to Lille in France and were defeated 3-1 at home by AC Milan, sandwiched between a 5-2 comeback against Borussia Dortmund.

A humiliating 2-0 loss to Liverpool in the fifth week reduced Real’s chances to 6%, with a 7% probability of group-stage elimination. But Carlo Ancelotti’s team won their last three matches against Atalanta, Red Bull Salzburg, and Brest to reach the playoffs, where they crushed Manchester City 6-3 on aggregate. This result increased their championship chances to 11%, placing them behind Liverpool, Barcelona, Arsenal, and Inter.

But last week’s poor display in North London has reduced this chance to less than 1%. Miraculous comebacks at the Bernabéu have happened before, but currently, Real has only a 3% chance of advancing to the final four.

Borussia Dortmund

Dortmund scored 10 goals in their first two Champions League matches this season, leading to early optimism and doubling their championship chances from 2% to 4%. But this optimism was false, as losses to Real Madrid (5-2), Barcelona at home (3-2), and Bologna (2-1) in the next five matches knocked them out of the top eight.

They beat Sporting Lisbon 3-0 in the playoffs, but after a 1-1 draw in the first leg of the round of 16 against Lille, they had only a 38% chance of advancing. However, they came from behind to win 2-1 in the return leg. After drawing Barcelona in the quarter-finals (and a potential semi-final against Bayern or Inter), their championship chances rose to just 1%. A 4-0 loss in the first leg showed the prediction model was entirely correct about Dortmund.