Competitive balance in football: a new approach

Conventional measures of competitive balance – the Noll-Scully index based on actual versus idealised standard deviation of team winning percentages – are flawed in many ways with football because of the low number of games per season. A low number of games per season means that the idealised standard deviation of team winning percentages is relatively large since there is more room for random variation, while the Noll-Scully index ignores how the maximum standard deviation is consistent regardless of how few games each team plays. In low-scoring sports like soccer, gridiron, ice hockey and rugby where a lucky score can easily change the result of a match, this is not important, because even large differences in team qualities will not result in absolutely extreme win percentages.

In football, however, the rules of play allow for teams to score easily and, unlike basketball or netball, teams do not take “turns” with the ball to have opportunities to score. This means that propensities of teams to score or concede points can deviate much more than when the rules give each alternate “turns” – in football, each team requires skill to gain a “turn” at scoring. In fact, as Loek Groot shows in ‘Some Determinants of the Natural Level of Competitive Balance in European Football (Soccer) and US Team Sports: The Role of the Referee, the Scoring Context and Overtime’, a team with half the propensity to score of an competition’s average team would expect a winning equivalent no higher than 2 percent (a practically certain winless season in real-world football schedules) as against 20 percent in rugby and 35 percent in soccer. To put it another way, for the same disparity in win percent team qualities would need to deviate twice as much in rugby as in football.

The problem of not considering an upper limit for standard deviation was noted by P. Dorian Owen in ‘Limitations of the relative standard deviation of win percentages for measuring competitive balance in sports leagues’. Football, crucially, differs from baseball, ice hockey or soccer in that plausible differences in team qualities could easily produce probabilities of winning equal to or negligibly different from 0 or 1, as observed when Hawthorn during its early years as a League club faced the “big three” of Carlton, Collingwood and Richmond. However, at the same time one should not ignore the fact that if teams were equal in winning probability they would not all win the same number of games – especially in short-season sports like football.

Thus, as a new measure of competitive balance I propose the following steps:

1. Calculate what Dorian Owen symbolises ‘ASD^ub’ or the standard deviation of a perfectly unbalanced league
• Owen demonstrates for us that ASD^ub = ((n+1)/(12*(n-1)))^½ where n is number of teams
2. Subtract the idealised standard deviation from ASD^ub (ASD^ub-ISD)
• The ISD as based on the simple binomial distribution is give by (4l)^½/4l where l is number of games per season or average number for unequal schedules
3. Divide this value obtained in (2) into the actual standard deviation

Thus we have a formula for a ‘relative index of competitive balance’ of:

(ASD^actual-ISD)/(ASD^ub-ISD)

which can take values from below zero when the actual standard deviation is less than the ideal to positive unity for the perfectly unbalanced league.

(ASD^actual-ISD)/(ASD^ub-ISD) ratios for the three largest (Australian rules) football leagues between 1898 and 2013.
Note: the zeroes for the SANFL are seasons without regular play during the World Wars (1916, 1917, 1918, 1942, 1943, 1944).

What is notable is that the diagrams show football as competitively unbalanced as theories of competitive balance predict a sport with very high scoring and a very restricted talent pool to be.

The fact that the pre-World War I period without equalisation by zoning or revenue sharing was – despite much lower scoring than later eras – quite close to the hypothetical perfectly unbalanced league implies:

1. that without these regulations football would with higher scoring have acquired (ASD^actual-ISD)/(ASD^ub-ISD) ratios consistently negligibly different from positive unity, and/or
2. that reduced variation in team qualities after World War I led stronger teams to play more attacking football and thus increased scoring
• a proposition supported by more defensive tactics since Docklands supplanted Waverley. This change eliminated opportunities for shorter players of value in wet or windy conditions, made very tall people of limited supply more valuable, and almost certainly increased discrepancies in team qualities.

It’s also notable that the NBA, discussed much for its competitive imbalance, has an ASD^ub of:

• ((30+1)/(12*(30-1)))^½ 
• = (31/(12*29))^½ 
• = (31/348)^½

Thus, the Noll-Scully for a perfectly unbalanced NBA equals:

• (((31/348)^½)/((4*82)^½))/(4*82)
• = ((31/348)^½)/((328)^½)/328)
• = ((31/348)^½)*(328/(328)^½))
• = ((31/348)^½*(107584/328)^½)
• = ((31/348)^½*(328)^½)
• = (10168/348)^½
• = (2542/87)^½
• ≈ 5.40540385

This suggests that, in fact, football is at least as competitively unbalanced within-season as basketball, since a Noll-Scully of 1.90 (typical for football over the past 115 years) corresponds to a (ASD^actual-ISD)/(ASD^ub-ISD) ratio of about 0.65 – larger than the 0.351 of the NBA (for details see pages 65 to 67 from David Berri’s of The Wages of Wins). There are several periods when none of the three leagues graphed ever achieved a value as low as 0.35 (1908-1915, 1946-1953, since Docklands), and in the first period there were two values under 0.5 out of 24.

These are the raw Noll-Scully ASD/ISD ratios for the “major” football leagues since 1898 (again, the zeroes in the SANFL data are wartime seasons without regular football)

The next step needed will be a more detailed analysis of what these figures reveal about competitive imbalance in football and what has driven changes over time.

Abbott’s unspoken goal: a global economic and “opportunity” monopoly for Australia

In the mainstream (Age) and even in business papers, as seen here in the Spectator, there is the ingrained belief that if Australia falls behind in climate action it will suffer economically. There tends to be little evidence or reasoning behind this, but rather an unspoken belief that if Australia removes regulations on greenhouse emissions, pollution and land clearing it will lose opportunities to invest in new technology that will grow its economy.

The fact is, however, that there are a number of severe fallacies behind this myth – a myth that I know has existed for a long time but have taken little notice of.

The basic problem is that it ignores the severe social and economic problems faced by nations with technology-based economies. Without one solitary exception, their fertility rates are extremely low – almost always less than 1.5 children per women or a population declining by 25 percent each generation. Even for historically free market-oriented nations, government debt is a major problem and likely to grow in the future as there are fewer taxpayers to pay it off.

More than this, as taxpayers become fewer in technology-oriented economies, they are forced to specialise in higher and higher technology, which tends to make them even more inhuman – there is so little ordinary work being done by people that those without the most advanced education are excluded. This exclusion, of course, serves to severely limit the range of people a technology-oriented economy can include: in most such cases, even basic necessities such as housing, food and transport become very expensive for those without higher education.

An additional problem is that seeking to emulate technology-oriented economies is the norm throughout the Enriched and Tropical Worlds, because it promises more rapid growth and Enriched and Tropical nations are losing to exhaustion most of the mineral and energy resources they ever had. This produces a uniform specialisation that offers little room for diversification – especially with most major companies thoroughly globalised – and much room for economic decline.

What Tony Abbott wants to do to Australia is what the Politically Incorrect Guides and their allies wanted to do to America in the 2000s:

1. remove all the vast books of government restrictions from minimum wages to pollution
2. remove the high taxes faced by working people
3. dismantle most of the public sector and make what is needed (defence) more efficient
4. privatise such government services as education, national parks, hospitals, public transport, public housing etc. etc.
5. allow entrepreneurs to provide essential services like housing and transport without restriction
6. encourage the poor to depend upon their own labour rather than welfare
7. encourage those with limited academic talents to work in basic occupations and form families

For all the PIGs have told me about how a society without government regulation would be better, there is no practical example of the PIGs’ policies actually being tried in a country for one to evaluate. However, the evidence they do give and what I do know about past history does make me feel instinctively that the policies Abbott wants to implement will shift virtually all the opportunity for work and social capital amongst the poor to Australia. If the poor had no taxes to pay they could save their earnings to a much greater extent than I do – especially with essential services provided at lower cost due to greater incentive for cheapness. If the “super rich” had no taxes to pay the PIGs argue that they would create many more jobs than they can now even in Australia, and unemployment would be eliminated without minimum wage laws as expensive education would be unnecessary to maintain a liveable existence.

There is no doubt that requiring more and more expensive education to maintain a liveable existence is a dead-end – it is making the Enriched and Tropical Worlds elitist and unable to cater for the poor, besides their lack of natural resources. Abbott, on the contrary, desires a nation where the market gives the poor opportunities rather than the radical equality which the poor of the Enriched World wish for – but which invariably produces aselfish and shallow culture with no sense of community.

A famous series factored

1. 1709 is prime
2. 175709 is prime
3. 17575709 is prime
4. 1757575709 is prime
5. 175757575709 is prime
6. 17575757575709 is prime
7. 1757575757575709 is prime
8. 175757575757575709 is prime
9. 17575757575757575709 = 232433*75616446785773
10. 1757575757575757575709 = 11*159779614325068870519
11. 175757575757575757575709 = 2111*83257970515194579619
12. 17575757575757575757575709 = 3943859957*4456486226028937
13. 1757575757575757575757575709 = 173*366802913*27697155836476241
14. 175757575757575757575757575709 = 1381*427079*297997182510316599391
15. 17575757575757575757575757575709 = 31*227*141175273*17691630749494130809
16. 1757575757575757575757575757575709 = 4157*18283051*23125192599076866676387
17. 175757575757575757575757575757575709 = 5552280144181*31655026618528309935689
18. 17575757575757575757575757575757575709 = 61*1747*13773420668783*11974282550887212469
19. 1757575757575757575757575757575757575709 = 359*4895754199375369291803832193804338651
20. 175757575757575757575757575757575757575709 = 131*3301*16649*24412321477226626113603794029211
21. 17575757575757575757575757575757575757575709 = 11*22215689*79153844321*908635225024778431197151
22. 1757575757575757575757575757575757575757575709 = 157005143*11194383343071491459089182559935361963
23. 175757575757575757575757575757575757575757575709 = 197*892170435317643439470850638363328718658667897
24. 17575757575757575757575757575757575757575757575709 = 223*63823*1857752125057*664728362446941928248983050253
25. 1757575757575757575757575757575757575757575757575709 = 1063*1249*2281*2383*3933171103853488169*61919320722043350661
26. 175757575757575757575757575757575757575757575757575709 = 3659* 126019*1777758569*33139200473*6469948268613023137745917
27. 17575757575757575757575757575757575757575757575757575709 = 2909*6041855474650249486963134264612435805285581841099201
28. 1757575757575757575757575757575757575757575757575757575709 = 21521*81667940968159359498051937994319853898869743858359629
29. 175757575757575757575757575757575757575757575757575757575709 = 23302843690014955258934603857*7542323078487034222609522369037
30. 17575757575757575757575757575757575757575757575757575757575709 = 31*37957*62706567193*48786343248739*335752101003029*14542211193761569
31. 1757575757575757575757575757575757575757575757575757575757575709 = 1962726262900441*895476 761480 982102 013000 299201 718009 795541 010149
32. 175757575757575757575757575757575757575757575757575757575757575709 = 11*15977961432506887052341597796143250688705234159779614325068870519
33. 17575757575757575757575757575757575757575757575757575757575757575709 = 613*9103*24424958805029*128954112399003341882222810189440132169042678539
34. 1757575757575757575757575757575757575757575757575757575757575757575709 is prime
35. 175757575757575757575757575757575757575757575757575757575757575757575709 = 18541192627*563253307139758553921128481*16829555184169478233728912256897807
36. 17575757575757575757575757575757575757575757575757575757575757575757575709 = 1951*5035583486513*47082479284759*37996855706984840508397069492813348163262277
37. 1757575757575757575757575757575757575757575757575757575757575757575757575709 = 3217*84463*662713*261672884530021933421*37300295994715906042796884562177859933223
38. 175757575757575757575757575757575757575757575757575757575757575757575757575709 = 5867814178896517*29952818954234195618960924328686498255258236366268654065646777
39. 17575757575757575757575757575757575757575757575757575757575757575757575757575709 = 511169073067345123*34383452563535701064449531892319688724585779827252251020003583
40. 1757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 718493*22352123669*109439152382241910025713677777520585913614792858539694345514348477
41. 175757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 797*112325831*1346124115937*62 335686198837598681339897*23396680404361770014500708277109583
42. 17575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 307*397*79941361540433*865738137714777972308487797*2083661086307718043024536553063923450671
43. 1757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 11*3229*3361*4202739912737*626763772013640445188512537207473*5589184049785809462220696581044051
44. 175757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 1315525279*74408376185177*1692750790631921*1060718158139156356909258195018241558478846803288363
45. 17575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 31*593*15808321*455748915120203815399*327316250494363138054999*405432640057521827534555119546585363
46. 1757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 193*55817*3306343*78611671*627704613688030707273350520257045443735709706744562677925335631768943413
47. 175757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 367*376265317*305357431261173291433*4168168888370230510758531716943971599946182171758611133468736607
48. 17575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 61*18047*282398741*31179632203563251*3578167032684799497524218843*506739602224671324479239846077359498179
49. 1757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 22273*852807887515992442351907*57184507886793672798909503937563*1618101424183202239630794213930783277613
50. 175757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 105594421*59689006847*27885518728427693048576408924014248650898365614890555107475528605224758696228346807
51. 17575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 275183*63869343585023696077067833317310937658124802679517178595973434317372714730109627323481376965785523
52. 1757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 48519733*93980827*385439650645734488904135060635906657389678208060689522395925645952672432306124889499793899
53. 175757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575757575709 = 853*2840041*6763665496930552219*10726506289186464505703680959144185487865094315050383188927412078711499281892307

The table above gives the factorisation of a famous sequence of numbers known for, in its first eight members, producing an uniterrupted sequence of primes.

As is always the case, however, the sequence starts producing composite numbers: of the subsequent 44 members of the sequence, only the thirty-fourth is prime and I do not know how much research has been done to find more primes.

Nonetheless, compiling this sequence as far as I can get it factored is something I have wanted to do for a long time since there is nothing on it on the web. The series, which as you should see has the formula 17(57)_w09, is quite different from those kept by Makoto Kamada, being a variation on the smoothly undulating series where each member is two digits larger than the last.

An everyday consequence of lenience towards Australia

When I asked to have an old Panasonic stereo system serviced a few weeks ago, I was given a guarantee that Panasonic would make the part for the machine, and paid sixty dollars to have a quote given. The people at the place – in a remote corner of Sunshine West – were very nice to me and assured that the part would still be available, despite my mother’s scepticism. I took the view that, although the machine was not playing CDs, it was working so perfectly that it was an utter waste that I should replace it just for that failure, especially as the temporary replacement I bought has two speakers that simply do not function.

However, in the near-month since I sent the machine for service, Panasonic have not communicated with me very well and I have become very worried. A week ago, my worst fears – or so I thought – were realised when I found that the laser was severely damaged, but I was told that I expected a quote in my email very soon. I have been careful – or so I think – to make sure I do not delete such an email by accident, but still I have no recollection from a fleeting memory of any email.

Today, however, came the news my mother expected, but which I thought I had had a guarantee against. I was directed to call TechXperts Sydney headquarters, and they seemed to be saying that the part I need – a new laser – is no longer in production and I will have to buy a new machine for at least $120 and probably more.

People may take planned obsolescence of this thought for granted as technology improves. The fact is, though, that one cannot contain global warming unless planned obsolescence is eliminated. Almost all the minerals for high electronic technology come from the ancient, thick crust of the Australian Craton – not depleted in insoluble refractory lithophile elements by the Alpine Orogeny and large-scale ice sheets. Although occupying only one percent of the Earth’s surface and 5 percent of total crustal volume, the Australian Craton may possess as much as 20 percent of the Earth’s “budget” (total nuclear mass) of titanium, zirconium, hafnium and the myriad lanthanide and actinide elements. These elements, along with silicon, are key components of advanced technologies, but their extremely strong affinity for oxygen meant that they cannot be smelted directly from their oxides; instead they must be converted to halides and either reduced in an inert atmosphere or electrolysed. Thus their use without major climatic consequences requires that:

1. smelting be done only in areas with reliable renewable energy sources – which in practice means mountainous regions with reliable runoff for hydropower
2. transportation be done in such a manner as to eliminate – or if impossible minimise absolutely – greenhouse pollution from vehicles used to transport them

These two factors, by their very nature, require that extremely rigid requirements be imposed on Australia to deal with greenhouse gas emissions, because:

1. owing to its large supply of land and fossil fuels, in the absence of regulations there is no incentive for energy efficiency in Australia
2. the much greater political pressure in the Enriched World means much higher standards regarding greenhouse gas emissions
3. reducing Australia’s emissions from transport to zero – or no more than one percent their current levels which would be required for climatic stability – restricts the amount of raw materials that can be exported to Enriched World high-technology industries

It is for this reason that planned obsolescence is not compatible with a sustainable economy. As I have said many times before, severely restricting energy consumption in Australia and in Australia alone is the keystone for reducing global greenhouse emissions. It would necessarily restrict the production of raw materials from remote regions for electronic goods, and therefore require companies to plan for greatly longer lifespans than observed since the large-scale discovery and use of lithophile metallurgy. It would use many fewer resources to simply replace spare parts than to discard them – the volume of materials required can only be much smaller – and if energy costs in Australia reflected the exceptionally low-energy lifestyle of ecosystems all over the continent this is what would happen.

The pity is that people in the Enriched World do not see what always buying the latest trend does for the continent where the genuine ecological changes are occurring!