MAFL 2010 : Round 2

Before I launch into this week's wagering and tipping information, a final reminder: if you want to take part in this year's blog-readers' competition you need to have an entry to me before centre-bounce Thursday night. Details of the competition are in this blog entry.

Entry is free and there are no prizes, which I think has an appealling symmetry to it. Entries can be e-mailed to me at the usual address.

Anyway, onto the footy, which again starts on a Thursday this week but which has no Friday game, it now being traditional for the AFL to avoid games on Good Friday.

Probability Scoring Methods

In Sunday's blog I introduced the three probability scoring methods that I'll be using to evaluate the HELP model's predictive performance this season.

To recap, they were:

The logarithmic score, which assigns a forecaster a score of 2+log(p) where p is the probability that he or she assigned to the winning team.

The quadratic score, which assigns a forecaster a score of 1-(1-p)^2 where p is again the probability that he or she assigned to the winning team.

The spherical score, which assigns a forecaster a score of p/sqrt(p^2 + (1-p)^2), where p is yet again the probability that he or she assigned to the winning team.

Is Luck Alone Enough To Win Your Tipping Competition?

Many of you, I'm sure, have participated in tipping competitions where the leader after a few rounds seems to be unfettered by any knowledge of the game. Frustrating though that can be, some solace can be found by determining how likely it is that their performance can be written off to chance.

Whenever we're making such a determination what we first need to decide is the "level of statistical significance" (or p-value) that we're willing to accept. This level is a probability and reflects our tolerance for rejecting a chance explanation of a result we see when it was in fact due to chance. If, for example, we set our acceptable level of statistical significance to be 5% then we'll rule out chance as the cause of a result if that result would occur less than 5% of the time if someone was actually guessing randomly. The higher we set the p-value the more likely we make it to rule out a chance explanation, and the lower we set it the less willing we are to do the same.

MAFL 2010 : Round 1 Results

It's hard to make money when you're betting solely on favourites.

The Heuristic-Based Fund landed 3 bets from 4 this weekend but the one it lost was the longest-priced and therefore most vital one from a profitability viewpoint, so it finished down 0.6% on the weekend. This leaves those with the Recommended Portfolio down 0.06% for the season - a mere flesh wound at most.

That means strike one for the Shadow Fund. Two more consecutive losses will see it hand over control of the Heuristic-Based Fund to whichever heuristic is best performed at the end of Round 3.

MAFL 2010 : Round 1

We're on.

From a wagering viewpoint, this season has started like most others, with the TAB Sportsbet bookie posting head-to-head odds more than a week before the first game and then leaving them unchanged for over a week. It's as if punters haven't yet realised the season's about to start. Indeed, as I type this, the odds are still what they were Monday a week ago.

MAFL, for its part, has also followed the early season script, wagering lightly, unwilling to risk much until the season's patterns have been established and calibrated. Only one Fund is active and only four bets have been made.

And so the cycle begins again for another season.

Why April's Conceivably Better Than March

It's an unlikely scenario I know, but if the players on the AFL Seniors lists ever got to talking about shared birthdays I'd wager they'd find themselves perplexed.

As chestnuts go, the Birthday problem is about as hoary as they come. It's about the probability that two randomly selected people share a birthday and its longevity is due to the amazement most people express on discovering that you need just 23 randomly selected people to make it more likely than not that two or more of them will share a birthday. I'll venture that few if any of the 634 players on the current Seniors lists know that but, even if any of them did, they'd probably still be startled by what I'll call the AFL Birthday phenomenon.

A Proposition Bet Walks Into a Bar ...

There's time for another quick paradox before the season commences.

Consider the following proposition bet. Each week we'll look at the total points scored in the first game of the round and look at whether the total is even or odd. I win if, across consecutive rounds, the sequence (even,odd,odd) occurs before the sequence (even,odd,even) and you win if the converse occurs. So, for example, if the total scores in the first game of Rounds 1, 2 and 3 were (146, 171, 155) then I'd win. If, instead, they were (132, 175, 162) then you'd win. If no result had been achieved after Round 3 then we'd keep going, starting with the aggregate score for game 1 of Round 4, until one or other of the winning sequences occurred.

The Other AFL Draft

Drafting is a tactic well-known to cyclists and motor-racers and confers an advantage on the drafter by reducing the effort that he or she (or his or her vehicle) needs to expend in order to move.

There's a similar concept in round-robin sports where it's called the carry-over effect, which relates to the effect on a team's performance in a particular game that's due to the team its current opponent played in the previous round. Often, for example, it's considered advantageous to play teams the week after they've faced a difficult opponent, the rationale being that they'll have been 'softened up', demoralised and generally made to feel blah by the previous match.

We Don't Need No 37-cent Piece (But 30- and 45-cent Pieces Might be Nice)

Last night I was reading this Freakonomics blog explaining why a 37-cent piece would make for more efficient US coinage. In the article the question asked was what set of 4 different coin denominations could most efficiently be used to make up any amount between 1c and 99c. Two equally efficient answers were found: a set comprising a 1-cent, 3-cent, 11-cent and 37-cent piece, and one comprising a 1-cent, 3-cent, 11-cent and 38-cent piece. Either combination can be used to produce any total between 1c and 99c using, on average, just 4.1 coins.

Well Australia's different from the US in oh so many ways, and one of those ways is relevant for the present topic: we round all amounts to the nearest 5 cents, having disposed of the 1- and 2-cent pieces in 1991.

So, I wondered, what set of 4 coins would most efficiently meet our needs.

Now Open: This Year's Blog Readers' Competition

Last season a few of you took part in a competition in which participants had to predict the finishing order for all 16 teams and the winner, Dan, was the person whose finishing order was mathematically closest to the actual finishing order at the end of the home and away season. Not only were Dan's selections, overall, closest to the final ladder, but for 3 teams his selections were perfect: he had Geelong finishing 1st, St Kilda 2nd and Melbourne 16th.

A Paradox, Perhaps to Ponder

Today a petite blog on a quirk of the percentages method that's used in AFL to separate teams level on competition points.

Imagine that the first two rounds of the season produced the following results:

Geelong and St Kilda have each won in both rounds and Geelong's percentage is superior to St Kilda's on both occasions (hence the ticks and crosses). So, who will be placed higher on the ladder at the end of the 2nd round?

Using a Ladder to See the Future

The main role of the competition ladder is to provide a summary of the past. In this blog we'll be assessing what they can tell us about the future. Specifically, we'll be looking at what can be inferred about the make up of the finals by reviewing the competition ladder at different points of the season.

Improving Your Tipping

You're out walking on a cold winter's evening, contemplating the weekend's upcoming matches, when you're approached by a behatted, shadowy figure who offers to sell you a couple of statistical models that tip AFL winners. You squint into the gloom and can just discern the outline of a pocket-protector on the man who is now blocking your path, and feel immediately that this is a person whose word you can trust.

Tips for Tipping

You've been forced to enter a tipping competition for a sport you know nothing about and, frankly, have no interest in adding to the list of sports you know something about. The competition is standard in that it rewards you with 1 point for a correct tip and no points for an incorrect tip. Your 15 minutes of research, which represents the entirety of the time you're willing to spend on the endeavour, reveals that the home team consistently wins about 58% of games season after season.

Given that knowledge, which if any of these three strategies is superior:

(a) Match the expected home team/away team mix in your tips, that is, tip the home team 58% of the time

(b) Recognise that you have no basis on which to favour one team over another so tip the home team about 50% of the time

(c) Be lazy and always tip the home team

Make a mental commitment to your answer and try to come up with at least an intuitively appealling logic for it.

Testing the HELP Model

It had been rankling me that I'd not come up with a way to validate any of the LAMP, HAMP or HELP models that I chronicled the development of in earlier blogs.

In retrospect, what I probably should have done is build the models using only the data for seasons 2006 to 2008 and then test the resulting models on 2009 data but you can't unscramble an egg and, statistically speaking, my hen's albumen and vitellus are well and truly curdled.

Then I realised that there is though another way to test the models - well, for now at least, to test the HELP model.