More Heavy-Duty Stat Shots

By: phil | March 11th, 2012

Welcome back, FC Bayern fans. Hopefully, you’re all still basking in the glow of this week’s big win, and the equally big Dortmund draw. Tonight, we dive into the deep end, courtesy of one of our most astute readers – in fact, one of the brightest guys I’ve ever had the pleasure of speaking with.

So, after our post last week demonstrating some reader-submitted stats, we received a few more e-mails addressing statistical differences between FC Bayern and our Bundesliga rivals. One of our readers, known here as “Ollikahn,” wrote in with a detailed examination of not only goals-for and goals-against, but variability and skew ratios of each club’s results each week. In other words, he set out to determine the effect of all of the club’s (but especially Bayern’s) propensity to rack up big goal numbers some weeks, then have long stretches of quiet. Ollikahn has a much better grasp of statistical analysis than I, so I’m just trying to follow along here as best I can. If I screwed something up, let me know.

This chart shows “Goals For” for each of the three clubs at the top of the 1. Bundesliga in each of this season’s 25 match weeks so far:

Week	BMG	Bayern	BVB
1	1	0	3
2	1	1	0
3	4	5	2
4	0	3	0
5	1	7	1
6	1	2	1
7	1	3	2
8	0	0	4
9	2	4	2
10	0	1	5
11	2	4	1
12	2	2	5
13	5	0	1
14	3	2	2
15	1	4	1
16	0	2	1
17	1	3	4
18	3	1	5
19	3	2	3
20	0	1	2
21	3	2	1
22	2	0	1
23	1	2	3
24	0	0	2
25	0	7	0

The first thing you’ll notice is that Bayern, in addition to generally being a high-scoring team, has a large variance in when the goals come. Some hard evidence for that statement:

	BMG	Bayern	BVB
Total goals	37	58	52
MEAN	1.48	2.32	2.08
Standard Dev.	1.39	1.99	1.55
SKEWNESS	0.86	0.96	0.65
KURTOSIS	0.18	0.62	-0.52
MAX	5	7	5
MIN	0	0	0

“Skewness” indicates the extent to which small numbers of games account for larger-than-usual percentages of the total goals-scored figure. “Kurtosis,” if I understand correctly, refers to the degree to which the number of goals scored when graphed over multiple weeks is “peaked” – in other words, how far each club’s goal scoring from week to week hews is closer to the mean (commonly called “average”) vs. further from the mean (and therefore closer to the peak – whether high or low). BVB’s lower numbers for standard deviation, skewness, and kurtosis indicate that they are a machine of regularity. While their mean goals-per-week figure is slightly lower than ours (2.08 vs. 2.32), they’re basically a good bet to score two goals a week. Whereas we have a slightly higher mean, but we might get 5 or 7 one week, then 0 the next two weeks. But that’s just my interpretation of the data – Ollikahn puts it this way:

“The high skewness of 0.96 for FCB indicates that most of our goals have come against fewer sides whereas for BMG & BVB have lower skew of 0.85 and 0.65 respectively.”

Now, “Goals Against” for the same clubs

Week	BMG	FCB	BVB
1	0	1	1
2	1	0	1
3	1	0	0
4	1	0	0
5	0	0	2
6	0	0	2
7	0	0	1
8	1	0	0
9	2	0	0
10	1	2	0
11	1	0	1
12	1	1	1
13	0	1	0
14	0	3	0
15	1	1	1
16	1	1	1
17	0	0	1
18	1	3	1
19	0	0	1
20	0	1	0
21	0	0	0
22	1	0	0
23	1	0	1
24	1	2	1
25	0	1	0

And the analytical compilation for Goals Against:

	BMG	Bayern	BVB
Total goals	15	17	16
MEAN	0.60	0.68	0.64
Standard Dev.	0.58	0.95	0.64
SKEWNESS	0.28	1.36	0.47
KURTOSIS	-0.72	1.08	-0.54
MAX	2	3	2
MIN	0	0	0

The standard deviations are lower here, because none of these 3 clubs are likely to give up 6 or 7 in a game like Freiburg or TSG might. Nonetheless, our “skewness” and kurtosis are still the highest, owing to the fact that we’ve allowed 3 goals on 2 separate occasions. Neither ‘Gladbach nor BVB has done that even once. As Ollikahn says: “for goals against, BMG is better than both BVB and FCB as they have least skewness.” In fact, take away BMG’s week 9 2-2 draw vs. Leverkusen, and they allow 1 or 0 goals every single week.

Same clubs, same sample size, numbers for “Goal Differential” here:

Week	BMG	FCB	BVB
1	1	-1	2
2	0	1	-1
3	3	5	2
4	-1	3	0
5	1	7	-1
6	1	2	-1
7	1	3	1
8	-1	0	4
9	0	4	2
10	-1	-1	5
11	1	4	0
12	1	1	4
13	5	-1	1
14	3	-1	2
15	0	3	0
16	-1	1	0
17	1	3	3
18	2	-2	4
19	3	2	2
20	0	0	2
21	3	2	1
22	1	0	1
23	0	2	2
24	-1	-2	1
25	0	6	0

For this last chart, “goal differential” refers to the +/- for that particular week, not to the ongoing aggregate goal differential. And, given what we saw on the first two charts, no surprise that the analytical compilation for Goal Differential shows more variability for Bayern:

	BMG	Bayern	BVB
MEAN	0.88	1.64	1.44
Standard Dev.	1.56	2.43	1.66
SKEWNESS	0.86	0.40	0.41
KURTOSIS	0.50	-0.41	-0.43
MAX	5	7	5
MIN	-1	-2	-1

“Skewness” doesn’t really matter as much here, because there is no total pot into which all goal differential numbers are drawn from (aside from the general tabulation of goal differential). But the standard deviation for Bayern’s goal differential is huge, and our “Min” and “Max” are both higher and lower than either of the other club’s numbers for either category. In other words, we are more likely to win by 6 or 7 (which, unfortunately, doesn’t count for any more than a win by 1), whereas the other clubs in are more of a level-sledding “2 goals for and ½ of a goal allowed per week” pattern. Take it away, Olli:

“We have the highest standard deviation when it comes to goals for, goals against and goal difference of 1.99, 0.99 and 2.43 respectively (while BMG is at 1.39, 0.58 and 1.36 respectively) [Even Klopp is not as good as Favre as BVB has std dev of 1.55, 0.64 and 1.66 and both are still better than Heynckes]

The histogram reveals that BMG have won most of their games by 1 or 2 goal margins and FCB are the most inconsistent and stick out in my graphs by having the max number of losses and conceding 3 goals in 2 games.”

[This is Phil again] This is somewhat damning evidence for Bayern – take away our 7-1 win, our 7-0 win, and our pair of 5-0 wins, our impressive-looking offensive stats start to disappear. Because a 7-0 win isn’t worth any more than a 2-1 win, you’d rather be able to count on scoring 2 goals for every game, rather than have a random crap-shoot as to whether we’ll explode for 7 or get shut out.

At the same time, the fact that we can explode for 7 shows that we do have the capacity to do it. What we need to do is improve consistency, and especially to force our way of ruts where we just run our heads into the wall for 30 or 40 minutes at a time.

I’ll stop here, because I don’t want to jinx us for Tuesday. Whatever else we’ve done this year, we won’t be coming into this match in a rut. If we can just keep the form from this weekend going, we have a good shot at getting the 2 goals we need.

I’ll be back tomorrow with the Basel preview, and also with some more reader-submitted stats – some of which may point us in yet a new direction. Thanks for reading.