This is just a very short post as a follow up to the two previous posts in this trilogy, which can be found here and here. Basically, those posts looked at how you could get complete equilibrium in the Champions League group stages, based on the teams' UEFA club rankings and then based on their coefficients.
This post is basically just a correction. I hadn't realised that Real Sociedad, although they had not been in European competition in the five years used as the basis for coefficient calculation, nevertheless have their coefficient calculated for the purposes of the draw. Whilst they don't get any points for their own achievements, they do get the 20% of Spain's national coefficient, which isn't too shabby at all and is actually enough to put them in 31st, above Vienna.
This therefore messes up the calculations I made in those posts for balanced groups and you can't even just make a simple swap of Real Sociedad and Vienna because I had Vienna in Barca's group. The word fiddlesticks comes to mind.
Another point is that, as Sociedad also don't have 0 coefficient points, but 17.605, the calculations for balanced groups would also be different. And it means that they wouldn't be 451st in Europe overall, but would be somewhere around 87th, meaning that balanced groups based on the overall UEFA club rankings are much more possible than I made out.
Whilst this is all quite disappointing, as it voids my results, it doesn't, I don't think, void the methodology, which I am convinced will stand the test of time.
Whilst I'm not going to redo all of the calculations, I can tell you that Sociedad's being ranked 31st of the Champions League qualifiers means that Man United aren't actually as lucky (l) as I'd made them out to be, as they get a luck score of just 1.33 and not 1.67. This doesn't however, affect the bigger picture of English luck, as they remain the only English side with positive (i.e. good) luck, based on the UEFA rankings.
Sorry about the error.
Thursday, 19 September 2013
Wednesday, 18 September 2013
People who write alright are all right
Now it's possible I've written a post on this before. I don't think I have though so I'm writing it now, albeit with the small chance of my repeating myself.
I'll be brief. Already doesn't mean all ready. Always doesn't mean all ways. Alone doesn't mean all one. In each case, the first word has developed from a combination of the other two words to ultimately express a new thought or idea. This is a highly useful feature of language development.
Alright doesn't mean all right.
If I say "they're all right", then I am only talking sense if the "they" in this instance have just all said something like "two times two is four". In that case, they are all right. If one of them says "two times two is twenty-two" then they're no longer all right, as one of them is wrong.
If I say "they're alright" then it is possible that they have all said "two times two is four" but this is an irrelevance. Of far more importance is whether the bus that has just threatened to flatten them has done so or not. If it hasn't, then "they're alright" is a sensible comment. If it has, even if it's only flattened some of them, then "they're alright" is ill-judged, regardless of whether or not they've just said that two times two is four or twenty-two.
This is pretty obvious, but nevertheless worth saying. I don't have any dictionaries to hand so I can't tell you if they all agree with me or, in other words, if they're all right or not. In any case, I'm not here to bag on dictionaries. Most are not perfect because they contain many errors resulting from the fact that they are constantly playing catch-up. But they're generally alright.
I'll be brief. Already doesn't mean all ready. Always doesn't mean all ways. Alone doesn't mean all one. In each case, the first word has developed from a combination of the other two words to ultimately express a new thought or idea. This is a highly useful feature of language development.
Alright doesn't mean all right.
If I say "they're all right", then I am only talking sense if the "they" in this instance have just all said something like "two times two is four". In that case, they are all right. If one of them says "two times two is twenty-two" then they're no longer all right, as one of them is wrong.
If I say "they're alright" then it is possible that they have all said "two times two is four" but this is an irrelevance. Of far more importance is whether the bus that has just threatened to flatten them has done so or not. If it hasn't, then "they're alright" is a sensible comment. If it has, even if it's only flattened some of them, then "they're alright" is ill-judged, regardless of whether or not they've just said that two times two is four or twenty-two.
This is pretty obvious, but nevertheless worth saying. I don't have any dictionaries to hand so I can't tell you if they all agree with me or, in other words, if they're all right or not. In any case, I'm not here to bag on dictionaries. Most are not perfect because they contain many errors resulting from the fact that they are constantly playing catch-up. But they're generally alright.
Sunday, 15 September 2013
The best thing
Hello,
This is just a short post, making use of Google's Ngram Viewer which we all know and love. In case anyone doesn't know about Ngram, it lets you search for word or phrase usage in books over time and gives you a nice graph. So you can see when certain words or phrases were most popular and things like that.
Anyway, inspired by this phone-in on Alan Partridge's Mid-Morning Matters, where the presenter invites listeners to suggest the "best thing ever" and someone says "sliced bread", I decided to have a do a little bit of research.
According to Wikipedia, sliced bread was first sold in 1928 and yet, according to Ngram, the phrase "best thing since sliced bread" only really started appearing in literature around 1974. However, some slightly less half-hearted research shows that "greatest thing since sliced bread" emerged in 1950 and really gained pace around 1962. If we just use "thing since sliced bread", then the first record is in 1947, three years after the famous pre-sliced bread ban of '43, with a real increase in usage in the 1960s, after which it goes up fairly steadily up to the present day.
It's hard to make cast-iron deductions from this information, but the following are possible:
Clearly, all "best thing since" happening before 1928 cannot possibly be referring to sliced bread (unless appearing in some obscure and remarkably prescient sci-fi publications) and, if we believe Ngram, most things before the 1960s and all things before 1947 must have referred to other things too. So what might these have been?
Now the scope of the Massive Blog doesn't allow for a very thorough investigation, but a quick and haphazard click through the links underneath the Ngram give us the following candidates for "best thing" from the period 1800-1914:
Also, the second listed example, "best thing since the war broke out" is probably to be treated with caution, as it a) only really works when the war is still going on and b) isn't necessarily putting the outbreak of war as something good to be compared to, but rather suggesting that all has been rotten since this time. Indeed, the third example is also only valid in the context of political novels and so also not really equivalent to the usage of "best thing since sliced bread". So we're left with compound engines as the idiomatic best thing of the 19th Century.
To finish off, because I don't want the post getting too long and you're free to continue the research yourselves, I'll look at the period before "best thing since sliced bread" caught on. Here is one of the more interesting examples:
It is also slightly odd, because canned pudding is a more recent invention than ice-cream, meaning that the best thing since ice cream would automatically be better than canned pudding, unless you were speaking at a time when canned pudding hadn't yet been invented. Depending on what exactly your feelings are, you should be saying something like: "The best thing since canned pudding would also have been the best thing since ice cream if it had come out before canned pudding had been invented" or "The best thing since ice cream is, just to clarify, also better than canned pudding."
Other examples include "best thing since Voltaire" (1923) and "best thing since we went to the Yalu River in Korea" (1975).
Of all examples, my personal favourite is "the best thing since indoor plumbing", as written in 1988 by Peter S. Wenz. I like this example for two reasons. Firstly, its date, at a time when sliced bread was really taking over, makes us realise just how good indoor plumbing is to be able to compete alongside this great thing. And secondly, it reminds us how lucky we are not to have to go outside and face the elements whenever we want to take advantage of some plumbing: One of life's truly great things.
As briefly mentioned earlier, you're welcome to continue or expand on this research, either by using Ngram or other tools. The Massive Blog always welcomes contributions via the comment function or directly to the author on Twitter @herrbench.
This is just a short post, making use of Google's Ngram Viewer which we all know and love. In case anyone doesn't know about Ngram, it lets you search for word or phrase usage in books over time and gives you a nice graph. So you can see when certain words or phrases were most popular and things like that.
Anyway, inspired by this phone-in on Alan Partridge's Mid-Morning Matters, where the presenter invites listeners to suggest the "best thing ever" and someone says "sliced bread", I decided to have a do a little bit of research.
According to Wikipedia, sliced bread was first sold in 1928 and yet, according to Ngram, the phrase "best thing since sliced bread" only really started appearing in literature around 1974. However, some slightly less half-hearted research shows that "greatest thing since sliced bread" emerged in 1950 and really gained pace around 1962. If we just use "thing since sliced bread", then the first record is in 1947, three years after the famous pre-sliced bread ban of '43, with a real increase in usage in the 1960s, after which it goes up fairly steadily up to the present day.
It's hard to make cast-iron deductions from this information, but the following are possible:
- early sliced bread, invented in the 20s, wasn't all that great and only really won over American hearts when it improved dramatically in the 1960s
- sliced bread was immediately excellent in 1928 but it takes time (around 30-40 years) for phrases like this to develop and find their way into written literature
- sliced bread was good ever since 1928 but there was something else which was still considered better, the popularity of which declined in the 1960s, opening the way for sliced bread to take its place in the phrase
Clearly, all "best thing since" happening before 1928 cannot possibly be referring to sliced bread (unless appearing in some obscure and remarkably prescient sci-fi publications) and, if we believe Ngram, most things before the 1960s and all things before 1947 must have referred to other things too. So what might these have been?
Now the scope of the Massive Blog doesn't allow for a very thorough investigation, but a quick and haphazard click through the links underneath the Ngram give us the following candidates for "best thing" from the period 1800-1914:
- John Bourne, writing in 1878, "I put this heavy mineral oil as the best thing since compound engines."
- William Mumford Baker, writing in 1883, "It 's the best thing since the war broke out."
- The World's Work, in 1903, stating that "As a political novel ... "The Henchman," by Mark Lee Luther, is the best thing since "J. Devlin Boss"".
Also, the second listed example, "best thing since the war broke out" is probably to be treated with caution, as it a) only really works when the war is still going on and b) isn't necessarily putting the outbreak of war as something good to be compared to, but rather suggesting that all has been rotten since this time. Indeed, the third example is also only valid in the context of political novels and so also not really equivalent to the usage of "best thing since sliced bread". So we're left with compound engines as the idiomatic best thing of the 19th Century.
To finish off, because I don't want the post getting too long and you're free to continue the research yourselves, I'll look at the period before "best thing since sliced bread" caught on. Here is one of the more interesting examples:
- The best thing since ice cream is also the best thing since canned pudding.(Life Magazine, 1971)
It is also slightly odd, because canned pudding is a more recent invention than ice-cream, meaning that the best thing since ice cream would automatically be better than canned pudding, unless you were speaking at a time when canned pudding hadn't yet been invented. Depending on what exactly your feelings are, you should be saying something like: "The best thing since canned pudding would also have been the best thing since ice cream if it had come out before canned pudding had been invented" or "The best thing since ice cream is, just to clarify, also better than canned pudding."
Other examples include "best thing since Voltaire" (1923) and "best thing since we went to the Yalu River in Korea" (1975).
Of all examples, my personal favourite is "the best thing since indoor plumbing", as written in 1988 by Peter S. Wenz. I like this example for two reasons. Firstly, its date, at a time when sliced bread was really taking over, makes us realise just how good indoor plumbing is to be able to compete alongside this great thing. And secondly, it reminds us how lucky we are not to have to go outside and face the elements whenever we want to take advantage of some plumbing: One of life's truly great things.
As briefly mentioned earlier, you're welcome to continue or expand on this research, either by using Ngram or other tools. The Massive Blog always welcomes contributions via the comment function or directly to the author on Twitter @herrbench.
Friday, 6 September 2013
Equilibrium in the Champions League II
This post is the sequel to the previous post, hence the II
in the title. So you should probably read that first, if you haven’t already
done so
Based on what I’ve said above, this would make suggest that groups A, E, F and G are fairly balanced, whilst B, C, D and H are either too strong (B and H) or too weak (C and D).
Anyway, the previous post ranked the Champions League
qualifiers from 1 to 32 according to their UEFA club coefficients and used
these rankings as a basis for analysing the balance of the groups and measuring
each team’s luck in the draw.
There are two other obvious ways of measuring the strength of the teams:
- Using the UEFA club rankings;
- Using the club coefficient points.
Using the UEFA club
rankings
The UEFA club rankings seem like a good idea, because they
keep the numbers as nice manageable integers and they add some detail as the
gaps between teams aren’t all the same, thereby taking into account that some
teams are significantly lower-ranked than others. For example, the top 6 ranked
teams in the Champions League are also ranked 1 to 6 overall, but Austria Wien,
31st in the Champions League, are ranked 114 overall.
The problem with using this ranking system is that Real
Sociedad, the team ranked 32nd and worst of all the Champions League
qualifiers, don’t have a UEFA ranking at all, because they haven’t been in
Europe in the last five years. As there are 450 teams with a UEFA ranking, this
would make Sociedad joint 451st.
Unfortunately, this massive leap to the 32nd team
(all other 31 teams are in the top 114) skews the entire system. In the same
way as, with a 1-32 ranking system, we had a total 528 points and 66 per
balanced group, this system gives us 1,328 and 166 per balanced group.
However, the group with Sociedad will automatically be far
worse than average and most groups will be far better, with the only way to get
a balanced group being to have Vienna (114) and three other teams with a total
52 between them, such as Bayern (2), PSG (19) and Dortmund (31). Even the third
worst-ranked team, Plzen (74) cannot be put in a balanced group, with the most
balanced scenario having a total 145, with Benfica (9), Juventus (20) and
Leverkusen (42) completing Plzen’s group.
This is clearly unsatisfactory and, as such, I reject the
use of the UEFA club rankings as a workable system for looking to achieve
balance. They may be useful next year, if there is not such an anomaly, but,
for 2013/14, they must be set aside.
What about using the
club coefficient points?
Using the club coefficient points avoids the problem with
Sociedad. Although they have zero points, this is only 16.575 fewer than
Vienna, which does not represent such a dramatic and exaggerated drop as 114th
to 451st in the ranking. In fact, this is not even the largest
difference between two adjacently-ranked sides, as Arsenal have 17 fewer than Man U.
So this system seems to be workable. And it takes into
account larger and smaller gaps between teams than the more simple ranking
system. So it could be worth a look.
Balance using the
coefficients
Following an equivalent methodology to the one for the
rankings, we have a total 2454.519 points, so balanced groups would each have
2454.519/8 = 306.815 points.
It is unlikely that we will be able to get 8 groups with
this exact score but we could consider them fairly balanced if we had no group
with more than 306.815+(306.815/32) and none with less than
306.815-(306.815/32). 306.815/32 is 9.588 so this means groups between 297.227
and 316.403.
The choice of 32 is fairly arbitrary, basically being used
because there are 32 teams. If anyone has a better suggestion for something
more suitable, they are welcome to comment.
Anyway, let’s start out by looking at the 8 groups which
were balanced with the ranking system. These have scores of:
Group
|
Total
coefficient
|
Difference
to balanced group
|
A
|
310.932
|
+4.117
|
B
|
316.865
|
+10.050
|
C
|
292.228
|
-14.587
|
D
|
295.280
|
-11.535
|
E
|
315.223
|
+8.408
|
F
|
301.727
|
-5.088
|
G
|
299.211
|
-7.604
|
H
|
323.053
|
+16.238
|
Based on what I’ve said above, this would make suggest that groups A, E, F and G are fairly balanced, whilst B, C, D and H are either too strong (B and H) or too weak (C and D).
By making two simple swaps:
- CSKA (D, 77.776) with Donetsk (H, 94.951
- PSG (C, 71.800) with Schalke (B, 84.922)
we redress this imbalance and come out with 8 balanced
groups.
Of course, making these two changes brings about imbalance
according to the 1-32 ranking system. However, if we fiddle about with the
spreadsheet for long enough, then we can come up with the following groups:
Group A
|
Group B
|
||||
Man U
|
130.592
|
5
|
Real
|
136.605
|
4
|
Schalke
|
84.922
|
12
|
Juventus
|
70.829
|
16
|
Basel
|
59.785
|
21
|
Zenit
|
70.766
|
17
|
Celtic
|
37.538
|
28
|
Bucharest
|
35.604
|
29
|
Totals
|
312.837
|
66
|
Totals
|
313.804
|
66
|
Group C
|
Group D
|
||||
Benfica
|
102.833
|
8
|
Bayern
|
146.922
|
2
|
CSKA
|
77.766
|
14
|
Donetsk
|
94.951
|
10
|
Man City
|
70.592
|
18
|
Olympiakos
|
57.800
|
22
|
Napoli
|
46.829
|
26
|
Sociedad
|
0.000
|
32
|
Totals
|
298.020
|
66
|
Totals
|
299.673
|
66
|
Group E
|
Group F
|
||||
Chelsea
|
137.592
|
3
|
Arsenal
|
113.592
|
6
|
Marseilles
|
78.800
|
13
|
Atletico
|
99.605
|
9
|
Dortmund
|
61.922
|
20
|
Leverkusen
|
53.922
|
24
|
Plzen
|
28.745
|
30
|
Anderlecht
|
44.880
|
27
|
Totals
|
307.059
|
66
|
Totals
|
311.999
|
66
|
Group G
|
Group H
|
||||
Porto
|
104.833
|
7
|
Barcelona
|
157.605
|
1
|
Milan
|
93.829
|
11
|
PSG
|
71.800
|
15
|
Galatasaray
|
54.400
|
23
|
Ajax
|
64.945
|
19
|
Copenhagen
|
47.140
|
25
|
Vienna
|
16.575
|
31
|
Totals
|
300.202
|
66
|
Totals
|
310.925
|
66
|
Now it took quite a long time for me to get such a
distribution which suggests that there aren’t all that many possible draws
which offer balance according to both ways of measuring. This is not, however,
by any means to say that this is the only way.
Whilst it is nice to see that it
is possible, given the fact that 1/32nd deviation from the average
was chosen rather unjustifiably, I could have chosen something less stringent
and achieved balance with that more easily, if I’d wanted to.
And what about lady
luck?
As we saw in the previous post, you can measure the luck of
a team by comparing its actual draw, that is the strength of its actual
opponents, with the strength its opponents would have in balanced groups. In
the previous post, the luck (l) was calculated as:
l = (g-66)/3
where (g) was the total ranks of the group and 66 the rank
of an average group.
The equivalent formula with the club coefficients, if we say
k is now luck and the group total is h, would then be:
k = (h-306.815)/3
However, as we want good luck to be positive, we need to
switch this around to take into account the fact that a high-numbered
coefficient, unlike a high-numbered ranking, is given to a strong team. So we
can make it:
k = (306.815-h)/3.
Luck (k) of the
English
We saw in the previous post that, contrary to the claims of
the BBC and, in particular, Phil McNulty, Arsenal and Chelsea were equally (and
only slightly) unlucky, Man City had the worst luck and Man Utd were the only
English side to get lucky.
If we measure luck (k) of the English teams, as formulated
above, we get:
Man City with -5.74
Arsenal with +1.89
Chelsea with -3.70
Man Utd with +9.11
Clearly, whilst Man City and Man Utd retain their positions
from the previous post as most unlucky and luckiest respectively, we see a
significant change with Arsenal and Chelsea.
Chelsea stay unlucky but Arsenal emerge as being a little
bit on the lucky side of balanced. This is perhaps not a surprise as Arsenal’s,
though ranked 6, are a long way behind the 5 top-ranked teams in terms of
coefficient points. So measuring by coefficient points, they deserve, as it
were, to get somewhat stronger opponents.
Luck (k) of the
Celtic
In the last post, Celtic were very unlucky. When measuring
according to coefficient points, this doesn’t change much, as they come out with
a luck (k) score of -15.70, making them 2.73 times more unlucky even than Man
City, the unluckiest of the English sides. And, as with luck (l), Celtic (and
the other teams in group H) have the most rotten luck (k) of all teams in the
competition.
Arsenal, however, prove to be much more fortunate than a lot
of pundits would have us believe.
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