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A law of averages

There are sports, usually of American origin, where number crunching forms part of the appeal, not only for professional analysts but for regular fans. Football (or soccer, if you prefer) is not one of them, though.

I was reminded of this over the course of the past weekend. On Friday, I found myself on the phone to California for a football podcast and, trying to phrase a consideration we'll come back to in a minute, heard myself utter the spectacularly smart sentence: "Stuttgart don't have many points, you know."

One day later, Borussia Dortmund's CEO Hans-Joachim Watzke appeared on television and, trying to explain why the Dortmund party line is "Don't Mention the Title", said: "We now have 46 points. No team has ever won the Bundesliga with 46 points."

Finally, on Sunday, a reporter working for a German wire service asked Gladbach's goalkeeper Christofer Heimeroth about the importance of having won the first game after the winter break. Heimeroth said there was no reason to rejoice. "We still need a hefty amount of points," he added.

Hearing all those statements, including my own, it occurred to me that we've never really figured out this thing about what your points are worth and how many you need for whatever it is you want to achieve. The only semblance of a guideline we have in this regard is an old rule of thumb: you stay up with 40 points.

At the same time, we all know that this isn't quite true, because in the fifteen years since the introduction of the three-points-for-a- win rule, not a single team really needed said 40 points to be safe.

So let's have a look at what you really should bag, on average, at the top and at the bottom of the table. And what that means for the remainder of an admittedly crazy season which seems to laugh in the face of averages, stats and figures.

Because, in the end, the numbers will even out more often than not. To illustrate this, think back to the 2006-07 season. After the first half of that campaign, Mainz were in last place with only 11 points, already six points behind a non-relegation spot. Most people said the team was beyond all hope but Mainz themselves expressed optimism and said all they needed was a good run.

The team then won the first game after the end of the winter break and also won the second. They drew the third, then won the fourth, the fifth and the sixth. Before February was over, the surefire relegation candidate was suddenly in midfield.

The problem with this Cinderella story was that the season wasn't over at this point. Because after that great string of good results, Mainz reverted back to their regular form and won only two of the remaining games. At the end of the season, people admired Mainz for having put up a brave fight - but the team still finished third from bottom and went down.

Which explains my awkward line about Stuttgart (and of course Gladbach) not having many points, as both teams finished the first half of this season near that Mainz mark of yore, which ultimately did the team in even though they played a lot better after the winter break. I was trying to express the gut feeling that 10 points (Gladbach) or even 12 points (Stuttgart) may simply form an insufficient base from which to launch a comeback charge.

But is that really the case? How many points will those teams realistically need to have on May 14th? To reach an answer, let's check the past 15 seasons. (I know that's not much in terms of statistical data and Bill James would probably be having laughing fits about it, but it's all we have.)

In those 15 years, the teams that finished in 15th place had - on average - 36 points. While it's tempting to now conclude that this is what you need to stay up, it's a wrong conclusion for two reasons. The first is that there is a difference between what you have and what you need to have. Because the teams that finished in 16th place amassed - on average - 34 points, which means 35 points rather than 36 are statistically enough to wrap up a campaign above 16th place.

The second reason is, of course, the return of the relegation playoffs. We have had 12 such playoffs in the past (between 1982 and 1991 and now since 2009) and the Bundesliga side prevailed eight times over the second-division team. While that means reaching the playoffs doesn't guarantee the top-flight team it will stay up, the odds are very good.

As mentioned, the teams that finished in 16th place - the play-off spot - had 34 points on average. But again: this figure does not indicate what you need to finish 16th. Because over the past 15 years, the teams that ended up 17th only had 31 points on average. Thus the data we have suggests 32 points should secure 16th place.

This means Gladbach need 19 points from the final 16 games and Stuttgart need 17 before they even have a decent chance of staying up by reaching the play-offs. That is a tough challenge or, as Heimeroth would say, "a hefty amount". Both teams lost 11 games before the winter break, they will have to cut that number almost in half to even stand a chance of survival.

Looking at these figures and also at the two clubs' recent history, I have to conclude that Gladbach are doomed, while Stuttgart - with their track record of doing well in the second half of the season - still have a chance, although it is smaller than many people realise.

Now, what about the other end of the table, the top? The past 15 Bundesliga champions had, on average, 72 points. But the difference between what you have and what you need to have is even bigger at the peak than at the bottom. Because over the past 15 years, the league runners-up collected an average of only 66 points. Which means that - statistically - 67 points win the Bundesliga.

That tells us that Mr. Watzke is right: 46 points are indeed not enough. But it also tells us Dortmund are merely seven wins away from what statistically is the finishing line. You can do the math(s) yourself, I guess.


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