Sunday, March 24, 2013

AFL Power Rankings 2013 and the (Temporary) Closure of the Depot

Yes, the AFL Power Rankings will be back here this season, but not for a few weeks. I'm thinking I'll change the format a bit this season, though the calculation will probably remain the same. While there are a couple of minor things about the system that bother me, it seems to work reasonably well, and so I'll probably leave it as is. In the meantime, I recommend following the rankings over at AFL Footy Maths (if you don't already) for all your ranking needs.

I'm going to be offline for a few weeks, which means I won't be able to comment on Richmond's 3-0 start to the AFL season and my SuperCoach team will become a shambles. It also means that there will be no posts here during that time. But it'll be back - I've managed to up the level of posting this year, and I'm keen to keep the momentum going. Enjoy Easter folks!

Saturday, March 23, 2013

The 2013 Annual Wage Review and the Higher Award Classifications

I’ve written quite a bit about minimum/award wages on this blog in recent months, but here’s one more post about the topic anyway. Submissions for this year’s national annual wage review in Australia are due next week, and I want to enjoy my freedom this year to say something about it. I was saying to my wife this morning that I could actually put in a submission to the annual wage review if I wanted to, but I don’t think I’ll bother! First, I quite like my former colleagues, and I don’t want to add to their already busy work schedules. And second, if I put in a submission it would have the air of being ‘Troy Wheatley’s Official View’, whereas I really only have some loose thoughts about the topic. Given this blog is pretty much a collection of my loose thoughts I’ll talk about it here instead.

Anyway, for me, the actual increase this year is not so interesting – though obviously it matters a lot to the people it affects! – those people who follow these things from year to year can probably make as good a guess as me about what is likely to happen. For me, the interesting part is whether the Fair Work Commission will continue to award percentage increases. The Australian system is fairly unusual in that we don’t just have a minimum wage, but a series of minimum wages in awards that, in theory, provide for higher minimum wages for higher skilled employees. For the past couple of decades though, all wages in awards have been adjusted by a ‘flat dollar’ amount (e.g. $20 per week), which means that the ratios of minimum wages at the higher award classifications compared with minimum wages at the lower award classifications have been decreasing (Chart 9.1 in FWC’s statistical reporting provides an illustration of this). But this has changed in the past couple of years, with all award wages being adjusted by the same percentage amount, hence maintaining the relativities between those wages.

One possible justification that has been used for compressing the relativities between award wages is that minimum wages are mainly there to protect the incomes of the lowest-skilled employees. Adjusting these higher award wages by a smaller percentage than the lower award wages could be seen as a ‘passive’ way of phasing the higher award wages out. And yet, there are still people that are reliant on these higher award wages: why is this so?

One of the research reports that the Fair Work Commission released this year, by Maltman and Dunn, investigates the various factors that lead to award reliance at higher classifications. What they found was that, amongst employees on the higher award rates, the need to pursue a higher wage than the award rate was influenced by how reliant these people were on their wage to meet their living costs (or improve their lifestyle). Some people appear to be content to maintain employment at the award wage, and in some cases they perceived advantages from doing so. Other factors that influence the willingness of employees to seek an over-award wage include their perceived willingness for employers to engage in discussion on the topic, and their perceived chances of securing alternative employment.
It will be interesting to see how these findings affect the Fair Work Commission’s views on maintaining the relative values of the higher award rates. Do you not worry too much about maintaining their relative values because it might be that typically those people that stay on the higher award rates are not all that concerned about their wage income? Or do you take the view that there are still, at any given time, people that are heavily reliant on those wages to maintain a ‘decent’ lifestyle? Is more evidence needed? I have my own guess about what the Commission will do, but I guess we’ll find out in a couple of months.

(OK, now I’ll move on to other topics …)

Tuesday, March 19, 2013

The Finger Points Outwards - No. 57

ART: You don’t have to be a sci-fi geek to like Joseph Cross’ art, but it probably helps.

SPORTS: A lacrosse general manager acquires himself in a trade.

COMICS: There is a place where you can read Alan Moore’s classic long-out-of-print ‘Miracleman’ series. It’s every bit as revolutionary as the more well-known ‘Watchmen’ … maybe more so. But I’m not going to be responsible for any nightmares you might experience as a result of reading the horrific issue #15.

Saturday, March 16, 2013

Sack The Coach!: The Effects Of Coaching Changes In The AFL

As someone who tires quickly of the seemingly endless media speculation regarding which AFL coaches are under pressure to hold their jobs, I was really looking forward to showing that coaching changes actually make little difference at all. That’s what I thought anyway. To show this, I was going to compare the changes in teams’ winning percentages the season after changing coach with the changes in teams’ winning percentage in all other seasons.  Well, I did that, and you can see the results in the histogram below.

It turns out that, since 1998 over a quarter of the time when a team changes coach it has improved its winning percentage by over 0.20 percentage points (over 4 wins) the next season! Less than 10 per cent of the time has a team’s winning percentage fallen by over 0.20 percentage points. By contrast, when there has been no coaching change, only around 10 per cent of the time has a team’s winning percentage increased by over 0.20 percentage points the next season, and over 15 per cent of the time the team’s winning percentage has fallen by over 20 percentage points.
To put all this into a neater summary statistic, the average increase in a team’s wins the season after it changes coach is 1.5 wins (compared to -0.2 wins if it doesn’t change). That’s a pretty handy pick-up. However, it could be that a coaching change often occurs when the team just happens to have a stretch when it is performing below its long-run capabilities, and the improvement we see on average when a new coach comes in is just a case of mean reversion. As it turns out, when I looked to see if anyone had suggested this before, I found that a study that looked at coaching changes in Italian football had suggested pretty much the same thing! They concluded that, once you do some controlling for other factors that change when the coach changes, changing a coach does not seem to have a significant impact on team performance.

I’d like to think then, that if I could be bothered to do the econometrics, my first theory would still be proved right in the end. In the meantime though, maybe teams looking to boost membership after a brutal coaching change could send out the above histogram to their fanbases.

Wednesday, March 13, 2013

Minimum Wage Indexation

Picture: Carol Simpson
Currently in the US, President Obama and other Democrats are proposing a rise in the (federal) minimum wage, with the minimum wage to be indexed to inflation thereafter. In the US, because the minimum wage is adjusted infrequently - the last increase was in 2009 – the pattern of the real value of the minimum wage (i.e. the minimum wage adjusted for the cost of living) in the US has been for it to increase sharply, and then to decrease for years at a time. The current proposal would make the real value of the minimum wage more stable than it has been in the past.

While this proposal would enable the value of the minimum wage to keep up with the cost of living, it also means that the minimum wage would likely fall, on average, relative to the wages of other workers in the medium to long term. Average wages should grow faster than inflation over the medium to long term because: a) one would normally expect labour productivity to increase over time; and b) one would normally expect average real wages to broadly increase in line with increases in labour productivity (warning: this does not always happen). If the minimum wage is only being indexed to changes in the cost of living (i.e. real minimum wages are constant), then increases in the minimum wage are not capturing any of the increases in the productivity of minimum wage workers.
In Australia, there are a few commonly used measures of changes in average wages. One measure is the Wage Price Index (WPI), which measures ‘wage inflation’; that is, the average changes in wages abstracting from changes in hours worked or the composition of the workforce. Other common measures are average weekly ordinary time earnings for full-time adults (“AWOTE”) and average weekly earnings. These two measures are affected both by changes in hours worked (less so for the full-time AWOTE measure) and changes in workforce composition. If average hours worked are increasing, or the workforce is shifting towards working in higher-paid occupations, then these measures would be expected to increase at a faster rate than the WPI over the medium to long term. So if minimum wages in Australia were indexed to the WPI, we would still expect minimum wages to fall relative to average wages, albeit the drop would probably not be nearly as much as if they were just indexed to inflation. 

All these points are summarised in the table below:

Indexation method
Real minimum wages
Accounts for:
Does not account for:
Consumer price inflation
Remain constant
Increases in prices
Increases in labour productivity
Increases in hours worked

Shift towards higher-paid occupations
Wage Price Index (Australia)
Expected to increase
Increases in prices
Increases in labour productivity
Increases in hours worked
Shift towards higher-paid occupations
Average earnings
Expected to increase
Increases in prices
Increases in labour productivity
Increases in hours worked
Shift towards higher-paid occupations

As the graph below shows, in Australia increases in average weekly earnings and the WPI have, on average, been greater than increases in the Consumer Price Index in recent years. Increases in average earnings have also been greater than increases in the WPI, reflecting the shift towards higher-paid occupations. However, the other point to take away from the graph is that increases in the WPI are less volatile than increases in average earnings, which might make the WPI more palatable as a (hypothetical) indexation method for minimum wages.

Of course, average changes in the cost of living for minimum wage workers will not be exactly equal to changes in the cost of living across the population (though they will be close). And average changes in labour productivity for minimum wage workers will not be exactly equal to average changes in labour productivity for the rest of the workforce, and so on for hours worked, and shifts towards higher-paid occupations*. The main point to take away from all this though is that while indexing the minimum wage to inflation would allow it to keep up with the cost of living, we would expect that in the long run (assuming that labour productivity increases), the gap between the minimum wage and wages in the rest of the market would further increase.
*Indeed, one might argue it is not the best idea if part of the adjustment to the minimum wage for each occupation was a result of workers having shifted into higher-paid occupations (although you could still make the argument for doing so from a ‘relative living standards’ point of view). My main reason for mentioning these shifts though is just to point out that they have an effect on boosting average wages, and therefore on lowering the relativities between minimum and average wages.

Monday, March 11, 2013

Bob Cousy and the Top Assists Men

In ‘The Book Of Basketball’, Bill Simmons claims that Boston Celtics' Hall of Famer Bob Cousy got ‘screwed historically’ in terms of the way his assists were counted:

“Cousy averaged 8.9 assists for a ’59 Celtics team that averaged 116.4 points per game; John Stockton averaged 12.4 assists for a ’94 Jazz team that averaged 101.9 points per game. How am I supposed to make sense of that? How do we know Cousy wasn’t averaging 15-16 assists per game if we applied the current criteria? … [Cousy had] eight straight [assists] titles and four times where he finished with at least 30 percent more dimes than the number two guy.” (p. 493)

Essentially, Simmons’ argument is that Cousy’s assists numbers don’t stack up to those of other top assist men because assists were much harder to get during the era in which he played. Is this true? Er … not really. The table below takes each of the best assists guys during one of their peak seasons, and compares his average assists per game to the average assists of all teams per game during that season. As you can see, Cousy is a long way behind the other guys, even though the average assists per team per game in his era were not particularly low.   

Average Assists Per Game – Player
Average Assists Per Game - All Teams
Chris Paul
Steve Nash
John Stockton
Magic Johnson
Isiah Thomas
Kevin Porter
Oscar Robertson
Bob Cousy
And yet, Cousy won eight assist titles, and was often well ahead of the next man. I guess what this means is that assists were shared around more evenly in Cousy’s era. Either way, it doesn’t look like Bob-boosters should push the ‘Cousy was screwed’ argument too hard.

Saturday, March 9, 2013

Tanking in the AFL

Most AFL followers believe that ‘tanking’ – teams intentionally losing games, or at least not trying to win them - has occurred in the past, but what is the best way to prove that it happened? Here’s a statistical method that might offer some evidence.
From 1999 to 2006, a team received a priority pick if they had less than 20.5 premiership points (i.e. five wins or less) in the previous season.  This was the largest incentive to ‘tank’, as it gave you an extra high draft pick – at best, the team might not only have the first draft pick but also the second draft pick. Hawthorn’s Lance Franklin and Collingwood’s Scott Pendlebury are examples of players that their teams would not have been able to pick up without this rule. In 2007, the AFL changed the rules so that this incentive was removed; a team could still get a priority pick but it was either in the second round of the draft, or they had to be crappy for two years to get an extra first-round pick.
Hence, one way of finding evidence for tanking is as follows. For each season from 1999 to 2006, we ask: for the last team in the season that disqualified themselves from being able to receive a priority pick (that is, earned over 20 premiership points), how many matches had they played? Then we can compare this to when the last team would have disqualified themselves (that is, earned over 20 premiership points) for each season from 2007 onwards, if the old rule had applied. If tanking occurred, you would expect that the last team in the season to get over 20 premiership points would have done it sooner in the season during the era when the priority pick rule applied. Or in other words, when the priority pick rule applied, teams would hold off on earning more than 20 premiership points for much longer.
The results:
Matches played by last team for season to earn over 20 premiership points
From 1999 to 2006, the average number of matches that the last team that disqualified themselves from the priority pick had played when they earned more than 20 premiership points was 17.4. This included two times when no team disqualified themselves from the priority pick after round 15, which suggests some rather prolonged tanking in those seasons. After the rule was changed, the average number of matches that the last team that disqualified themselves from the priority pick had played when they earned more than 20 premiership points was 19.3. But this number is dragged down considerably by the 2007 season, which may have to some extent been affected by Carlton qualifying for a priority pick under the new rules. Remove this season, and the average is 20.4.
Basically then, there seems to be little to no reluctance to earn more than 20 premiership points for the season now there is no significant disincentive for doing so. Along with the further changes to the rules in 2012, perhaps the removal of this incentive means that tanking allegations are now going to be largely consigned to history.

Wednesday, March 6, 2013

The Finger Points Outwards - No. 56

ECONOMICS: Does retail spending suffer in election years?

CRICKET: A relatively even era of Test cricket.

MUSIC: One Direction fans are pretty scary.

MUSIC: YouTube - the new hit factory.

COMIC BOOKS: DC vs Marvel in the graphic novel market.

ADVERTISING: Yes, you really can compare the meerkats.

BASKETBALL: Apparently Rajon Rondo is a hyper-competitive Connect Four player.

Monday, March 4, 2013

The Best Movie of 2012 In America (Or At Least The Most Enjoyed)

Recently, economist Dave Berri, in talking about the Oscars, pointed out that if we looked simply at revenue, the ‘best’ movie of 2012 was ‘Marvel’s The Avengers’. Essentially, he argued that, if we measured the worth of movies in terms of the utility they provide to customers, then ‘Marvel’s The Avengers’, as the movie in 2012 with the highest revenue, delivered more utility to people than any other film. (It’s not certain whether or not Dave Berri thinks that the movie which delivers the most utility is the ‘best’, but it does seem to be strongly suggested.)

But did ‘The Avengers’ really deliver the most utility? The reason I say this, which is a reason that also occurred to commenters on Berri’s site, is that measuring utility simply by revenue means that a dollar spent on one movie delivers exactly the same utility to the viewer as a dollar spent on any other movie. This is implausible – people certainly have different levels of enjoyment in relation to different movies.

One way to adjust for this is to use a measure of ‘user enjoyment’. In this case, I used the ‘user ratings’ from – given that each movie (at least the highest-grossing ones) has a large sample of users rating it, I reckon this is as good an indication as any of the average level of enjoyment that viewers got from that film. I then multiplied this rating by the $US box office revenue for each of the top 25 highest-grossing movies in the US that were released in 2012.  

Actually, I adjusted the user rating somewhat by multiplying it to the power of three. For example, if ‘Argo’ has a user rating of 8.0, and the latest ‘Twilight’ movie has a user rating of 5.7, then this means that each person, on average, got 2.8 times more enjoyment from watching ‘Argo’ then from watching ‘Twilight’ (whereas it would only be 1.4 times if I left the user rating as is). The result of this is that ‘Argo’ ends up with a higher total utility rating then ‘Twilight’ even with half the box-office take, which seems about ‘right’ to me (though it’s an arguable point).

As it turns out, this doesn’t make too much difference at the very top of the list. ‘The Avengers’ and ‘The Dark Knight Rises’ are clearly #’s 1 and 2, and you would have to put a very high weight on the user rating to get ‘The Dark Knight Rises’ to the top. ‘The Hobbit’, ‘The Hunger Games’, ‘Skyfall’, and ‘Django Unchained’ round out the top six, which in thinking about the movies released in 2012 that have had the largest impact, seems about ‘right’ to me as well.

Total Gross US
User Rating
Utility Rating
Marvel's The Avengers
The Dark Knight Rises
The Hobbit: An Unexpected Journey
The Hunger Games
Django Unchained
The Amazing Spider-Man
Wreck-It Ralph
Madagascar 3: Europe's Most Wanted
Les Miserables
The Twilight Saga: Breaking Dawn Part 2
Dr Seuss' The Lorax
21 Jump Street
Hotel Transylvania
Ice Age: Continental Drift
Safe House
The Vow
Snow White and the Huntsman
Taken 2

I think we can safely say then that ‘The Avengers’ did deliver more total utility/enjoyment than any other 2012 movie to cinema-goers in the US (and probably worldwide). I’m not going to go so far as to say that definitively makes it the ‘best’ movie, but as far as creating total happiness goes it looks to have had no peer.