Game Cadence

If you were to consider each quarter of football as a separate contest, what pattern of wins and losses do you think has been most common? Would it be where one team wins all 4 quarters and the other therefore losses all 4? Instead, might it be where teams alternated, winning one and losing the next, or vice versa? Or would it be something else entirely?

The answer, it turns out, depends on the period of history over which you ask the question. Here's the data:

So, if you consider the entire expanse of VFL/AFL history, the egalitarian "WLWL / LWLW" cadence has been most common, occurring in over 18% of all games. The next most common cadence, coming in at just under 15% is "WWWW / LLLL" - the Clean Sweep, if you will. The next four most common cadences all have one team winning 3 quarters and the other winning the remaining quarter, each of which such cadences have occurred about 10-12% of the time. The other patterns have occurred with frequencies as shown under the 1897 to 2009 columns, and taper off to the rarest of all combinations in which 3 quarters were drawn and the other - the third quarter as it happens - was won by one team and so lost by the other. This game took place in Round 13 of 1901 and involved Fitzroy and Collingwood.

If, instead, you were only to consider more recent seasons excluding the current one, say from 1980 to 2008, you'd find that the most common cadence has been the Clean Sweep on about 18%, with the "WLLL / "LWWW" cadence in second on a little over 12%. Four other cadences then follow in the 10-11.5% range, three of them involving one team winning 3 of the 4 quarters and the other the "WLWL / LWLW" cadence.

In short it seems that teams have tended to dominate contests more in the 1980 to 2008 period than had been the case historically.

(It's interesting to note that, amongst those games where the quarters are split 2 each, "WLWL / LWLW" is more common than either of the two other possible cadences, especially across the entire history of footy.)

Turning next to the current season, we find that the Clean Sweep has been the most common cadence, but is only a little ahead of 5 other cadences, 3 of these involving a 3-1 split of quarters and 2 of them involving a 2-2 split.

So, 2009 looks more like the period 1980 to 2008 than it does the period 1897 to 2009.

What about the evidence for within-game momentum in the quarter-to-quarter cadence? In other words, are teams who've won the previous quarter more or less likely to win the next?

Once again, the answer depends on your timeframe.

Across the period 1897 to 2009 (and ignoring games where one of the two relevant quarters was drawn):

• teams that have won the 1st quarter have also won the 2nd quarter about 46% of the time
• teams that have won the 2nd quarter have also won the 3rd quarter about 48% of the time
• teams that have won the 3rd quarter have also won the 4th quarter just under 50% of the time.

So, across the entire history of football, there's been, if anything, an anti-momentum effect, since teams that win one quarter have been a little less likely to win the next.

Inspecting the record for more recent times, however, consistent with our earlier conclusion about the greater tendency for teams to dominate matches, we find that, for the periods 1980 to 2008 (and, in brackets, for 2009):

• teams that have won the 1st quarter have also won the 2nd quarter about 52% of the time a little less in 2009)
• teams that have won the 2nd quarter have also won the 3rd quarter about 55% of the time (a little more in 2009)
• teams that have won the 3rd quarter have also won the 4th quarter just under 55% of the time (but only 46% for 2009).

In more recent history then, there is evidence of within-game momentum.

All of which would lead you to believe that winning the 1st quarter should be particularly important, since it gets the momentum moving in the right direction right from the start. And, indeed, this season that has been the case, as teams that have won matches have also won the 1st quarter in 71% of those games, the greatest proportion of any quarter.

July - When a Fan's Thoughts Turn to Tanking

Most major Australian sports have their iconic annual event. Cricket has its Boxing Day test, tennis and golf have their respective Australian Opens, rugby league has the State of Origin series, rugby union the Bledisloe, and AFL, it now seems, has the Tanking Debate, usually commencing near Round 15 or 16 and running to the end of the season proper.

The T-word has been all over the Melbourne newspapers and various footy websites this week, perhaps most startlingly in the form of Terry Wallace's admission that in Round 22 of 2007 in the Tigers clash against St Kilda, a game in which the Tigers led by 3 points at the final change but went on to lose by 10 points:

"while he had not "tanked" during the Trent Cotchin game in Round 22, 2007, he had let the contest run its natural course without intervention"

That stain on the competition's reputation (coupled, I'll admit, with he realisation that the loss cost MAFL Investors an additional return of about 13% for that year) makes it all the more apparent to me that the draft system, especially the priority draft component, must change.

Here's what I wrote on the topic - presciently as it turns out - in the newsletter for Round 19 of 2007.

Tanking and the Draft

If you’re a diehard AFL fan and completely conversant with the nuances of the Draft, please feel free to skip this next section of the newsletter.

I thought that a number of you might be interested to know why, in some quarters, there’s such a fuss around this time of year about “The Draft” and its potential impact on the commitment levels of teams towards the bottom of the ladder.

The Draft is, as Wikipedia puts it, the “annual draft of young talent” into the AFL that takes place prior to the start of each season. In the words of the AFL’s own website:

"In simple terms, the NAB AFL Draft is designed to give clubs which finished lower on the ladder the first opportunity to pick the best new talent in Australia. At season's end, all clubs are allocated draft selections. The club that finished last receives the first selection, the second last team gets the second selection and so on until the premier receives the 16th selection."

So, here’s the first issue: towards season’s end, those teams for whom all hopes of a Finals berth have long since left the stadium find that there’s more to be gained by losing games than there is by winning them.

Why? Well say, for example, that Richmond suddenly remembered what the big sticks are there for and jagged two wins in the last four games, leaping a startled Melbourne in the process, relegating them to position Spoon. The Tigers’ reward for such a stunning effort would be to (possibly – see below) hand Melbourne the sweetest of draft plums, the Number 1 draft pick, while relegating themselves to the Number 2 pick. Now, in truth, over the years, Number 1 picks have not always worked out better than Number 2 picks, but think about it this way: isn’t it always nicer to have first hand into the Quality Assortment?

Now entereth the notion of Priority Picks, which accrue to those teams who have demonstrated season-long ineptitude to the extent that they’ve accumulated fewer than 17 points over its duration. They get a second draft pick prior to everyone else’s second draft pick and then a third pick not that long after, once all the other Priority Picks have taken place. So, for example, if a team comes last and wins, say, four games, it gets Pick #1, Pick #17 (their Priority pick, immediately after all the remaining teams have had their first pick) and then Pick #18 (their true second round Pick). If more than one team is in entitled to Priority Picks then the Picks are taken in reverse ladder order.

Still with me?

Now, the final twist. If a team has proven its footballing inadequacy knows not the bounds of a single year, having done so by securing fewer than 17 points in each of two successive seasons, then it gets its Priority Pick before anyone else gets even their first round pick. Once again, if more than one team is in this situation, then the tips are taken in reverse ladder order.

So, what’s the relevance to this year? Well, last year Carlton managed only 14 points and this year they’re perched precipitously on 16 points. If they lose their next four games, their first three draft picks will be #1 (their Priority Pick), #4 (their first round pick), and #20 (their second round pick); if they win or even draw one or more of their remaining games and do this without leaping a ladder spot, their first three draft picks will be #3, #19 and #35. Which would you prefer?

I find it hard to believe that a professional footballer or coach could ever succumb to the temptation to “tank” games (as it’s called), but the game’s administrators should never have set up the draft process in such a way that it incites such speculation every year around this time.

I can think of a couple of ways of preserving the intent of the current draft process without so blatantly rewarding failure and inviting suspicion and rumour. We’ll talk about this some more next week.

*****

In the following week's newsletter, I wrote this:

Revising the Draft

With the Tigers and the Dees winning last week, I guess many would feel that the “tanking” issue has been cast aside for yet another season. Up to a point, that’s probably a fair assessment, although only a win by the Blues could truly muffle all the critics.

Regardless, as I said last week, it’s unfair to leave any of the teams in a position where they could even be suspected of putting in anything other than a 100% effort.

I have two suggestions for changes to the draft that would broadly preserve its intent but that would also go a long way to removing much of the contention that currently exists.

(1) Randomise the draft to some extent. Sure, give teams further down the ladder a strong chance of getting early draft picks, but don’t make ladder position completely determine the pick order. One way to achieve this would be to place balls in an urn with the number of balls increasing as ladder position increased. So, for example, the team that finished 9th might get 5 balls in the urn; 10th might get 6 balls, and so on. Then, draw from this urn to determine the order of draft picks.

Actually, although it’s not strictly in keeping with the current spirit of the draft, I’d like to see this system used in such a way that marginally more balls are placed in the urn for teams higher up the ladder to ensure that all teams are still striving for victory all the way to Round 22.

(2) Base draft picks on ladder position at the end of Round 11, not Round 22.

Sides that are poor performers generally don’t need 22 rounds to prove it; 11 rounds should be more than enough. What’s more, I reckon that it’s far less likely that a team would even consider tanking say rounds 9, 10 and 11 when there’s still so much of the season to go that a spot in the Finals is not totally out of the question. With this approach I’d be happy to stick with the current notion that 1st draft pick accrues to the team at the foot at the ladder.

Under either of these new draft regimes, the notion of Priority Picks has to go. Let’s compensate for underperformance but not lavish it with silken opportunity.

****

My opinion hasn't changed. The changes to the draft for the next few years that have been made to smooth the entry of the Gold Coast into the competition probably mean that we're stuck with a version of the draft we have now for the next few years. After that though, we do have to fix it because it is broken.

The Differential Difference

Though there are numerous differences between the various football codes in Australia, two that have always struck me as arbitrary are AFL's awarding of 4 points for a victory and 2 from a draw (why not, say, pi and pi/2 if you just want to be different?) and AFL's use of percentage rather than points differential to separate teams that are level on competition points.

I'd long suspected that this latter choice would only rarely be significant - that is, that a team with a superior percentage would not also enjoy a superior points differential - and thought it time to let the data speak for itself.

Sure enough, a review of the final competition ladders for all 112 seasons, 1897 to 2008, shows that the AFL's choice of tiebreaker has mattered only 8 times and that on only 3 of those occasions (shown in grey below) has it had any bearing on the conduct of the finals.

Historically, Richmond has been the greatest beneficiary of the AFL's choice of tiebreaker, being awarded the higher ladder position on the basis of percentage on 3 occasions when the use of points differential would have meant otherwise. Essendon and St Kilda have suffered most from the use of percentage, being consigned to a lower ladder position on 2 occasions each.

There you go: trivia that even a trivia buff would dismiss as trivial.

The Decline of the Humble Behind

Last year, you might recall, a spate of deliberately rushed behinds prompted the AFL to review and ultimately change the laws relating to this form of scoring.

Has the change led to a reduction in the number of behinds recorded in each game? The evidence is fairly strong:

So far this season we've seen 22.3 behinds per game, which is 2.6 per game fewer than we saw in 2008 and puts us on track to record the lowest number of average behinds per game since 1915. Back then though goals came as much more of a surprise, so a spectator at an average game in 1915 could expect to witness only 16 goals to go along with the 22 behinds. Happy days.

This year's behind decline continues a trend during which the number of behinds per game has dropped from a high of 27.3 per game in 1991 to its current level, a full 5 behinds fewer, interrupted only by occasional upticks such as the 25.1 behinds per game recorded in 2007 and the 24.9 recorded in 2008.

While behind numbers have been falling recently, goals per game have also trended down - from 29.6 in 1991, to this season's current average of 26.8. Still, AFL followers can expect to witness more goals than behinds in most games they watch. This wasn't always the case. Not until the season of 1969 had there been a single season with more goals than behinds, and not until 1976 did such an outcome became a regular occurrence. In only one season since then, 1981, have fans endured more behinds than goals across the entire season.

On a game-by-game basis, 90 of 128 games this season, or a smidge over 70%, have produced more goals than behinds. Four more games have produced an equal number of each.

As a logical consequence of all these trends, behinds have had a significantly smaller impact on the result of games, as evidenced by the chart below which shows the percentage of scoring attributable to behinds falling from above 20% in the very early seasons to around 15% across the period 1930 to 1980, to this season's 12.2%, the second-lowest percentage of all time, surpassed only by the 11.9% of season 2000.

(There are more statistical analyses of the AFL on MAFL Online's sister site at MAFL Stats.)

Does The Favourite Have It Covered?

You've wagered on Geelong - a line bet in which you've given 46.5 points start - and they lead by 42 points at three-quarter time. What price should you accept from someone wanting to purchase your wager? They also led by 44 points at quarter time and 43 points at half time. What prices should you have accepted then?

In this blog I've analysed line betting results since 2006 and derived three models to answer questions similar the one above. These models take as inputs the handicap offered by the favourite and the favourite's margin relative to that handicap at a particular quarter break. The output they provide is the probability that the favourite will go on to cover the spread given the situation they find themselves in at the end of some quarter.

The chart below plots these probabilities against margins relative to the spread at quarter time for 8 different handicap levels.

Negative margins mean that the favourite has already covered the spread, positive margins that there's still some spread to be covered.

The top line tracks the probability that a 47.5 point favourite covers the spread given different margins relative to the spread at quarter time. So, for example, if the favourite has the spread covered by 5.5 points (ie leads by 53 points) at quarter time, there's a 90% chance that the favourite will go on to cover the spread at full time.

In comparison, the bottom line tracks the probability that a 6.5 point favourite covers the spread given different margins relative to the spread at quarter time. If a favourite such as this has the spread covered by 5.5 points (ie leads by 12 points) at quarter time, there's only a 60% chance that this team will go on to cover the spread at full time. The logic of this is that a 6.5 point favourite is, relatively, less strong than a 47.5 point favourite and so more liable to fail to cover the spread for any given margin relative to the spread at quarter time.

Another way to look at this same data is to create a table showing what margin relative to the spread is required for an X-point favourite to have a given probability of covering the spread.

So, for example, for the chances of covering the spread to be even, a 6.5 point favourite can afford to lead by only 4 or 5 (ie be 2 points short of covering) at quarter time and a 47.5 point favourite can afford to lead by only 8 or 9 (ie be 39 points short of covering).

The following diagrams provide the same chart and table for the favourite's position at half time.

Finally, these next diagrams provide the same chart and table for the favourite's position at three-quarter time.

I find this last table especially interesting as it shows how fine the difference is at three-quarter time between likely success and possible failure in terms of covering the spread. The difference between a 50% and a 75% probability of covering is only about 9 points and between a 75% and a 90% probability is only 9 points more.

To finish then, let's go back to the question with which I started this blog. A 46.5 point favourite leading by 42 points at three-quarter time is about a 69.4% chance to go on and cover. So, assuming you backed the favourite at $1.90 your expected payout for a 1 unit wager is 0.694 x 0.9 - 0.306 = +0.32 units. So, you'd want to be paid 1.32 units for your wager, given that you also want your original stake back too.

A 46.5 point favourite leading by 44 points at quarter time is about an 85.5% chance to go on and cover, and a similar favourite leading by 43 points at half time is about an 84.7% chance to go on to cover. The expected payouts for these are +0.62 and +0.61 units respectively, so you'd have wanted about 1.62 units to surrender these bets (a little more if you're a risk-taker and a little less if you're risk-averse, but that's a topic for another day ...)