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How is Bayer Leverkusen's 51-game unbeaten streak even possible? Crunching the numbers

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Editor's note: On May 18, Bayer Leverkusen defeated Augsburg to complete an unbeaten season in the German Bundesliga, with just the Europa League final (vs. Atalanta on May 22) and German Cup final (vs. Kaiserslautern, May 25, live on ESPN+) remaining on the fixture list for their 2023-24 season. With Saturday's win, Leverkusen extended their unbeaten streak to 51 games. The original article published on May 7 is below.

It wasn't enough for Bayer Leverkusen to win the German Bundesliga. And not just to win the league, but to win the league for the first time in the club's 119-year history, to win the league by ending Bayern Munich's 11-season reign as defending champs, and to win the league by overcoming a team with a wage bill more than four times the size of theirs.

It wasn't enough just to do any of that, and it wasn't enough to reach the final of the DFB-Pokal cup, or the German Cup. And it wasn't enough to beat AS Roma 2-0 in the first leg of the Europa League semifinals, either.

All those accomplishments are great -- congrats to Leverkusen on doing all of those things. But rather, Leverkusen under coach Xabi Alonso have defined themselves by avoiding doing another thing: losing.

We're 48 games into Bayer Leverkusen's season. Provided they avoid a collapse at home against Roma this Thursday, there are five games left in their campaign, and no one has beaten them.

Just how unlikely is Leverkusen's run? Where does it rank in the history of the greatest seasons of all time? And what are the chances that they take this streak all the way?

• Live on ESPN+: Leverkusen vs. Kaiserslautern (German Cup, May 25)

These are the results of all 4,266 Bundesliga matches played since 2010:

• Home wins: 1,926 • Away wins: 1,299 • Draws: 1,041

The home team wins 45% of the time, the away team wins 30% of the time, and the remaining 25% of matches end up in a stalemate. Outside of the COVID period when there were no fans in the stands, this level of home-field advantage has remained relatively steady over the past decade-plus across all of Europe's Big Five leagues.

In the average Bundesliga match, then, the likelihood of the home team avoiding a loss is 70%, while the away team escapes defeat 55% of the time. Based on those probabilities, there is a 0.00002% chance that the average Bundesliga team would go undefeated across a stretch of 16 home and 16 away matches. Or: a 1-in-50,000 shot.

Sure, Leverkusen are not the average Bundesliga team. But just for fun, let's say we had a randomly chosen team of these players: Gianluigi Buffon in goal, Paolo Maldini at left-back, Virgil van Dijk and Franco Baresi in the center of defense, and Philipp Lahm on the right. At the base of midfield, drop in Sergio Busquets, and then throw Patrick Vieira and N'Golo Kanté in front of them. Lionel Messi is out right, Cristiano Ronaldo out left, and the Brazilian Ronaldo is playing up top. All of these players will be in their primes. They'll all be willing defenders, they'll all be perfectly healthy for the entire season, and they'll all be managed by Pep Guardiola.

We'll throw this hypothetical team into the 2023-24 Bundesliga, give them Leverkusen's schedule, and say there was a 90% chance of them winning each game they played and a 5% chance of drawing. Given the low-scoring and relatively random nature of soccer, those numbers would make this the greatest soccer team of all time by a significant margin. (For reference, Manchester City's betting odds in their upcoming game -- a near fait accompli against a Fulham team with nothing to play for -- still only give them a 75% chance of winning and a 15% chance of drawing.) Were this the case, though, their likelihood of making it this far in the season without a loss would still be just 19%.

Take that same all-time great hypothetical team and apply those numbers to the 48-game run Leverkusen are on, and the likelihood of Ronaldo and Messi emerging unscathed would still be just 8.5%. The chances of them taking it all the way to the end of the 53-game season without a loss would be 6.5%. And that's before adjusting for the fact that you can't draw either the DFB-Pokal or Europa League finals -- both of which would tamp down the probability of an undefeated season further.

While Leverkusen's Granit Xhaka and Florian Wirtz and Jeremie Frimpong are great players, they're not quite on the same level as Vieira, Messi and Paolo Maldini. Although that 1-in-50,000 chance only concerns the Bundesliga -- and not the only other 16 games Leverkusen have played in other competitions thus far -- it's probably not far off from the likelihood that they'd go 48 games undefeated when you control for their talent level. The chances that they'd make it this far without losing a game are way closer to that 0.00002% than that 8.5%.

If it's not clear already, this just does not happen. And by that, I mean: it has quite literally never happened before.

In Europe's "Big Five leagues since 1965, the previous record for the number of unbeaten games to start a season was 42, ripped off by Antonio Conte's Juventus in 2011-12. Since they'd finished seventh the season prior, Juve weren't in European competition. They very nearly finished the entire season undefeated -- only to drop the last game of the season, the Coppa Italia final, to Napoli, 2-0.

Leverkusen, of course, are already eight games past Juve's streak. And again, Leverkusen had never won the league before this season.

Despite being relegated to Serie B in 2006 due to the Calciopoli match-fixing scandal, Juventus were the 13th-richest team in the world and the second-richest club in Italy, per Deloitte, for the 2011-12 season. They'd also won the title 27 times before doing it again in Conte's first season with the team. This is Leverkusen's first title, and their most recent revenues didn't even register in the top 30 richest clubs in the world. Leeds United, who were relegated last season, brought in more money than Leverkusen during the most recent accounting period.

Across all of Europe, and not restricted to one season, Leverkusen's win over Eintracht Frankfurt on Sunday equaled Benfica's record of 48 consecutive unbeaten matches from December 1963 to February 1965. Prior to the advent of European competition in 1955, Celtic hold the all-time record for consecutive matches unbeaten, not losing for 62 games in a row between 1915 and 1917. In Belgium, Union Saint-Gilloise made it 60 games unbeaten between 1933 and 1935.

So, only two teams in the recorded history of professional European soccer have strung together longer streaks without losing than the one that Bayer Leverkusen is currently on. And no team -- since we started writing down schedules, keeping track of results, awarding winners, and codifying what body parts are allowed to touch the ball -- has made it this many matches into a season without losing a single game.

Leverkusen likely have five games left:

• Thursday vs. Roma (Europa League semifinal second leg) • Sunday at Bochum (Bundesliga) • May 18 vs. Augsburg (Bundesliga) • May 22 vs. Marseille or Atalanta (Europa League final in Dublin) • May 25 vs. FC Kaiserslautern (DFB-Pokal final in Berlin)

Using betting odds, we can try to estimate the probabilities of each match. Based on ESPN BET's numbers for the Europa League semifinal, they're giving Roma a 16% chance of winning. And against Bochum, ESPN BET sees a 23% chance that Leverkusen lose. Flipped around, Leverkusen have an 84% chance of making it past Roma unscathed and a 77% chance of getting beyond Bochum with at least a point. Take those two probabilities together, though, and there's a 64% chance that this time next week Leverkusen will still have a zero in the loss column.

The next game would then be home to FC Augsburg -- they're above Bochum in the table, but Bochum are still in danger of being relegated, while Augsburg both can't be relegated and can't qualify for Europe. When one team has something to play for and the other team has nothing to play for, there's evidence that the former outperforms expectations while the latter underperforms. (Shocking, I know.)

Taking the Roma match as the baseline -- at Leverkusen, but a better team than Augsburg that also has to win -- let's adjust Leverkusen's non-loss probability for that game up to 94%. Throw that into the probability chain, and we're down to a 60% chance that Leverkusen remain undefeated through the following three matches.

Next up: the Europa League final against either Marseille or Atalanta. We'll be generous here and say that the gap between Leverkusen and either of those teams is similar to the gap between Manchester City and Manchester United. ESPN BET's odds give City an 82.5% chance of lifting the FA Cup trophy. (Shootout losses officially get recorded as draws, but c'mon. We want a true undefeated season here.) Throw that 82.5% into the mix, and we're down to a 50% chance that Leverkusen make it to the final game of the season unbeaten.

As for that game, the DFB-Pokal final against the 14th-place team in Germany's second division? Per ESPN BET's odds, Leverkusen have a 93% chance of doing the domestic double. Combine that with the 50% number, and there's a 47% chance that Leverkusen push this season across the finish line without a single loss.

These are estimates, but they're estimates that are likely somewhat kind to Leverkusen, so the major takeaway here is that the most likely outcome for these final five games is that Leverkusen lose at least one. However, it's seems like Xabi Alonso & Co. would be pretty happy with those odds. One-in-about-two looks like a stone-cold guarantee when you compare it to the 1-in-about-50,000 chance that they'd ever even make it this far.