Get excited football fans, it’s time the annual dispassionate look at which AFL sides are set to rise and fall based solely on the numbers. Whip out the calculators, have your spreadsheets at the ready: it’s time for maths!

The five basic tenants of a story, you know the ones you were taught in primary school (well, I was anyway) evidently apply to information analysis: you need who, what, when, where, why and how.

Numbers are useful, but as I hope I showed last year, they can be limiting when it comes to analysing what goes on in AFL football.

The stats we have, let alone the ones we fans get access to, are at best a basic accounting framework: we know who got what, but not where, when and how. That makes searching for why quite challenging.

Philosophy lectures aside, there are a few pieces of very useful insight we can glean from the basic public information we receive – if we look at it through the right lens. That’s what we’ll be doing today. Most of the tools should be familiar to you by now, but head over to this piece – one of the first I wrote on this website – for a primer.

Pythagorean wins
The first is Pythagorean wins, which is a measure that seeks to work out what a team’s winning percentage would be in a hypothetical universe where the only thing that mattered was points for and points against. It’s a system that’s been shown in every sport to be a better predictor of team quality; indeed, nine of the past ten AFL premiers have been ranked one or two on Pythagorean wins in their premiership years, and the one that wasn’t – the 2006 West Coast side – was ranked third.

A useful piece of information we can glean from these numbers is the difference between Pythagorean wins and actual wins. A positive number – that is, a team didn’t win as many games as their offensive and defensive performance says they would have in this hypothetical universe – says the team may be in for an improvement in the year ahead. The same is in reverse for a negative number: a team that won more games than their Pythagorean wins would generally perform less well the following year.

That’s a good place to start. And wouldn’t you know it, there are quite a few teams that have big deviations between their actual and Pythagorean wins in 2015.

The Fremantle Dockers outperformed their Pythagorean expected wins tally by a sizeable 2.2 wins last year, which would have been enough to knock them down to fifth on the ladder if it was their final record. This hides a peculiar detail about last season’s Dockers though, and one which we should be mindful of when assessing the Dockers prospects in 2016: their first half and second half to the season were remarkable and mediocre, respectively.

In their first ten games, the Dockers went 9-1, with a loss to Richmond in Round 10 the only thing stopping them from a clean sweep before the bye period. They earned eight of their Pythagorean wins at that point, meaning that in the remainder of the seasons they gathered just 6.8 more Pythagorean wins in 12 games. They were, in fact, ninth in the competition in the final 12 games, after being third to Hawthorn and West Coast in the first 10.

Does it mean they’re a candidate for regression? Put it this way, if Fremantle were to play the 2015 season in exactly the same way that they did last year, the chances of them ending up with the same 17 wins are small.

The other big beneficiary of the vagaries of sporting competitions last season was Melbourne, who got to seven wins despite their offensive and defensive output pegging them as a five-win team. That’s an interesting outcome, given the improvement that Melbourne has experienced since Paul Roos took over in 2014. Their 5.3 wins 1.7 more than they achieved in Roos’ first year, which itself was an improvement on the 1.4 they received (oh yes) in 2013. Regression? One hopes not.

Other overachievers included Essendon – it’s likely they won’t be a six win team this year for decidedly non-mathematical reasons – Geelong and Carlton. Each of these teams outperformed their output by one win or more, which is generally a sign that regression could occur. Each face interesting circumstances in the year ahead, particularly the Cats, who would be mighty disappointed if their win tally ended at 11 this season.

The list of underachievers is fascinating. Both Hawthorn and West Coast – last year’s grand final victor and grand final non-victor, respectively – underperformed their Pythagorean wins.

Hawthorn’s home-and-away season was worth an insane 19.5 wins according to this system, which was a full 3.5 less than they achieved. There’s a reason for that very large number, which we’ll get to in a moment. But even when that is factored in, Hawthorn still underperformed by two wins, which seems remarkable given they laid waste to the competition in 2015.

This is where this statistic falls down a little because it struggles to account for really large margins of victory and loss. Hawthorn won six games by a margin of 65 points or more (which was the average game margin, plus one standard deviation), and this cold hearted statistical model can’t understand why consistently large margins of victory like that don’t result in more wins. Just to jump back quickly, this could partially explain the reason behind Carlton’s underperformance: they were beaten by 65 points or more in six outings (although Brisbane also had six floggings, but were within a reasonable bound of their actual wins).

It’s mostly the same reason why West Coast’s Pythagorean wins are similarly larger than their actual wins: they had five victories by more than 65 points.

But what this does show is that they were clearly the two best teams in the competition, and that if they were to repeat their performance again perhaps some of that extra margin accumulated in individual games would be spread across other, less extravagant performances. That would result in more wins, suggesting that they could improve.

The final interesting team here is Collingwood, who were 2.4 wins under their Pythagorean expected total in 2015. They’re another club that experienced the cliched tale of two halves last season: an 8-3 start, in which they were bang on their Pythagorean expected wins total (-0.4), gave way to an apocalyptic 2-9 finish, where they underperformed by close to two wins (-1.7). The data suggests their first half outcomes were reflected in their performance, but in the second they were closer to a 4-7 team than a 2-9 team. In either case, they would have missed the finals, given the benchmark was the 13 win ‘Roos.

I happen to think Collingwood are going to be very good this year, for reasons beyond these entrails which we’ll get to before March 24. But their case does segue quite nicely into the next piece of information that we can use to consider teams primed for growth and decline.

Close wins
This one always raises some eyebrows when it’s brought up: teams that win a disproportionate number of their close games in any one year tend to regress to the mean the following year. A close game in this sense is a game where the final margin is 12 points or less – selected mostly because it’s possible for a team to slam on two goals in a very short space of time, but also because that seems to be a good consensus figure from when I’ve seen this question asked elsewhere.

Over the long run, almost every team wins between 45 per cent and 55 per cent of their games decided by 12 points or less. There are a couple of exceptions: Hawthorn and Geelong both won 58 per cent of their games that were decided by 12 points or less between 2000 and 2015, while Brisbane won just 41 per cent. The Giants have a poorer percentage (37 per cent), but they’ve only played 11 games with that final margin which isn’t a large enough set that we can draw conclusions.

So it’s a fair assumption that a club will, over its lifetime, win about half of its games decided by 12 points or less. On that basis, a club that won significantly more or less than its share in one particular year would be expected to come back to the pack a little in the following year. We can use that information to see whether any clubs’ win tallies were boosted by lots of close wins.

There’s Collingwood, who played in seven games that were decided by 12 points or less, and won just one of them (against Brisbane, in Round 1). That means Collingwood lost six close games in a row in 2015, which seems so unlikely that I decided to have a look into it in a bit more depth.

Since the start of the 2000 season, there’s only been 10 instances of a club losing six or more close games in a row:

Which is to say the Pies’ run of close losses doesn’t happen very often – and almost never in a single season. If Collingwood were to play seven close games in 2016, we would expect them to win a few more; assuming their performance levels are the same their record would be boosted by a couple of wins. Hawthorn – there they are again – could also expect to see a little bit of a record boost too, given they won only one of their five close outings.

Sitting at the opposite end of the spectrum are Fremantle (who won five of their six close games) and Sydney (who won four of five) and Geelong (three and a draw from their four). They could be expected to regress a little based on these numbers alone. However as above, Geelong have shown in the past that they are somewhat immune to the law of averages; they are also currently on a 9.5 close game winning streak – their last home-and-away season close loss was in Round 23, 2013.

These figures go some way to explaining the difference between a team’s Pythagorean expected wins and their actual wins. For example, going back to Collingwood, if the difference between their Pythagorean expected wins (-2.4) is combined with the difference between a 50-50 record in close games and their actual record in close games (+2.5), we find that their modelled wins are almost precisely the same as their actual wins (9.9 versus 10). It’s not perfect – Hawthorn still underperformed by 1.9 wins, and Carlton by 2.3 wins – but it helps.

Fixture change
The last one we’ll look at is a bit less quantitative but is something that I think figures in how a team can be expected to perform in the current year versus the last: the change in the relative strength of their fixture.

Now, before someone reminds me, I have said in the past that you can’t judge the ‘winner’ or ‘loser’ of a particular fixture effectively until the end of the year. An excellent case in point is that the 2014 premier Hawthorn received a slate of games that were, by my estimate, 80 points harder than the Gold Coast Suns. Port Adelaide, who had the hardest slate of games, played a schedule that was 147 points more challenging than Greater Western Sydney, who had the easiest time of it. That doesn’t sound like a lot, but it works out to be equal to the four games worth of average winning margin; it is potentially very significant.

What the table below shows is how a team’s 2016 schedule compares to its 2015 schedule when the measure that we’re using to determine strength or weakness is the Pythagorean expected winning percentage their 22 opponents recorded in 2015. This isn’t perfect – it doesn’t take into account growth or decline of team’s lists, in just one of many flaws – but because we’re simply measuring how a team’s schedule is different, not how each team is different, it’s fair play.

It’s the Greater Western Sydney Giants that can expect to see the biggest ramp up in their schedule difficulty, going from a schedule that saw opponents win an average of 46 per cent of games (ranked 18th of 18 in 2015) to 51 per cent in 2016 (ranked sixth). This would be a function of the Giant’s double ups: out go the Blues, Demons and Saints, and in come the Dockers, Cats and Power (return legs against the Suns and Swans, locked in, probably for all eternity).

That’s not a death sentence for the Giants, though, who we can expect to improve naturally for the second straight season. They blew their 2014 Pythagorean expectation away: it said they were one win worse than their 6-16 record would imply, and yet they recorded an expansion-leading 11-11 record in 2015.

The other team that can expect to see a big lift in their difficulty is Hawthorn. The Hawks double up on Melbourne, North Melbourne, Richmond, Sydney and West Coast, compared to last year’s flukish allocation of the all-disappointing Carlton, Essendon, Geelong, Port Adelaide and Sydney (arguably none of whom met their fullest expectations last season). That sees their schedule rating go from 47 per cent (ranked 16th) to 51 per cent (ranked fifth).

There’s bad news for Adelaide, North Melbourne and Richmond here, too, with these clubs all seeing large increases in their expected schedule difficulty this season. The ‘Roos have been handed the league’s most difficult set of games using this measure, with an average opponent winning percentage of 53 per cent (up from an 11th ranked 48 per cent last season).

How about the beneficiaries? It’s undoubtedly the Port Adelaide Football Club, who go from having one of the most difficult slates of games in recent history (an average winning percentage of their opponents of 55 per cent) to a much more mild 14th ranked draw. The Power face a Dangerfield-less Adelaide and rising Richmond as their lone top eight double ups. That’s a massive turnaround from 2015 when they faced Fremantle, Hawthorn and Sydney twice, as well as eventual top eight finishers Adelaide and the Western Bulldogs.

The other big positive changes flow the way of Geelong – who would be expected to ride back into their rightful place in the finals for any number of reasons – and Essendon. Both clubs go from having average opponent winning percentages of 54 per cent down to 48 per cent.

But the biggest beneficiary of all could be St Kilda, who have an average opponent winning percentage of just 48 per cent baked into their draw, in what projects as the easiest slate for the 2016 season. I’ll have a lot more to say on this mob before the season proper gets underway.

Right, that’ll do for now. As I said at the start there’s a limit to what all of this cold numerical analysis can tell us by way of who may rise and fall in 2016. But history tells us they’re a more than decent starting point.