So often in the commentary for an AFL game we hear it said that one team or the other "has the momentum going into the break". This blog sets out to examine this claim - how we might interpret it quantitatively and, given that interpretation, whether or not it's true.

A Working Definition of Momentum

In the sense that the term's often used, momentum means temporary advantage, so a team that "has the momentum" should be more likely to do better in some respect while it retains this momentum than it would otherwise do without it. It's an open question how long such an advantage might last; conceivably it could persist for the remainder of the game or, instead, might have the half-life of an elementary particle and be observable only in retrospect and by inference.

For this blog I'm interested only in momentum whose effects can be detected by observing the competing teams' scoring over the length of an entire quarter, and the existence of which can be based on one team's outscoring of the other in an earlier quarter or quarters.

Differentiating Momentum From Superiority

Momentum is surely a transitory thing. If a team has momentum from the start of the game and all throughout it, I think they're best described as the "better team" rather than as the "team with the momentum". I don't think anyone would attribute Black Caviar's 22 consecutive wins, for example, to her "having momentum".

So, to differentiate momentum from superiority for a given AFL contest, I'll consider only those games where both teams have demonstrated an ability to outscore their opponents over the course of an entire quarter. As a consequence of this requirement I can search for evidence of momentum only in 3rd and 4th quarters, since I need the data from at least the first two quarters of any game to establish that one team is not simply better than the other, even if only on the day.

One aspect of momentum that I'll explore is whether it's a binary phenomenon that manifests only as an ability to outscore one's opponent whether by 1 point or 100, or if it exists along a continuum, so that a team can be said to have degrees of momentum, which manifest as an ability to outscore one's opponent by a larger amount when a team has more of it.

Hypotheses to Test

Firstly, let's form some hypotheses to test for momentum in the third quarter (Q3).

H1: If momentum exists then, in games where Team A outscored Team B in Q1, and Team B outscored Team A in Q2, Team B should outscore Team A in Q3 because Team B "had the momentum" at the end of Q2.

H2: If momentum exists along a continuum then, in games where Team A outscored Team B in Q1, and Team B outscored Team A in Q2, Team B should outscore Team A in Q3 by an amount which is positively related to the amount by which it outscored them in Q2.

H3: If momentum exists along a continuum then, in games where Team A outscored Team B in Q1 and Team B outscored Team A in Q2, Team B should outscore Team A in Q3 by an amount which is positively related to the lead that Team B has established at the end of Q2.

To test for momentum in Q4 we'll use similar hypotheses but consider only those games where: 

• Team A outscored Team B in Q1 but was outscored by Team B in both Q2 and Q3. Team B will be the team deemed to "have the momentum".
• The lead established by either team at the end of Q3 is less than 4 goals. This is to exclude those games where one or other of the teams might have, consciously or otherwise, given up at the end of Q3, potentially contaminating the information that we can glean from the scores in the final term

Note that, for all hypotheses, we consider a tied quarter as: 

• ruling out the game from consideration if the result of that quarter is being used to determine if momentum exists at the end of either Q2 or Q3
• as a half win if we're using that quarter to determine whether such momentum was translated into outscoring in a subsequent quarter (ie in Q3 or Q4, depending on which set of hypotheses we're testing)

The Evidence for Momentum in Q3

Data relevant to H1 appears in the table below in which I've grouped football seasons into epochs as a way of determining if momentum has been a persistent, a recent, an ancient, or a mythical phenomenon.

As an example of how to read this table, consider the first row. It records the fact that, across seasons from 1897 to 1905 there were 309 games in which the team that outscored its opponents in Q1 was outscored by them in Q2. This represents 49% of all games from this epoch.

Of those 309 games, the team that scored the greater number of points in Q2 (and hence "had the momentum") also scored the greater number of points in Q3 only 38% of the time. That means the team without the putative momentum outscored the team with it 62% of the time. That looks far more like regression to the mean to me than it appears to support any notion of momentum, at least if our crude measure of manifested momentum is outscoring one's opponent.

In no epoch is it true that teams with momentum going into Q3 outscore their opponents more than 50% of the time and, across all of VFL/AFL history, teams with momentum entering Q3 have won only 39% of third terms.

(As a side note I'd point out the sharp reduction in the proportion of eligible games in the three most-recent epochs. This means that we're witnessing fewer games in which one team outscores the other in Q1 and is then outscored by them in Q2, a result that is entirely consistent with the view I've expressed in earlier blogs that the competition is becoming less competitive.)

Hypothesis H1 is then clearly refuted.

The evidence for H2 is more equivocal.

On the left is the data for the entire history of VFL/AFL and it shows that: 

• overall, the team claimed as having momentum going into Q3 tends to score fewer points in Q3 than does its opponent, which is further evidence in favour of regression to the mean and against momentum
• broadly, the more a team outscored its opponent in Q2, the more it was outscored by its opponent in Q3

If we narrow our historical perspective, however, we do find some trace evidence for the existence of momentum amongst teams with higher levels of outscoring in Q2 (but not the highest). The data in the middle of the table relates to seasons from 1980 to 2012 and shows that teams that outscored their opponents by between 20 and 40 points in Q2 tended to outscore their opponents in Q3 by a point or two. Teams that outscored their opponents by 41 points or more in Q2 were, however, on average outscored by their opponents in Q3, though this might be due to a reduction in the motivation levels of these teams having established a comfortable lead by half-time.

On the right is the data for an even more-recent period of time, from 1996 to 2012, and it provides similar data to that for the period 1980 to 2012 but shows greater levels of outscoring in Q3 by teams with momentum and that had outscored their opponents by between 20 and 40 points in Q2.

One way of controlling for the possible effects of differences in motivation levels across different teams with momentum is to adjust for the lead that the team with momentum had established by the end of Q2. The following table provides the data to do this, and provides what we need to explore H3.

Here we find that, across the entire history of VFL/AFL, the evidence is that teams with momentum at the end of Q2 are outscored by teams without momentum regardless of the lead that the team with momentum has (or doesn't have) at the end of Q2, but the level of outscoring by the team without momentum declines as the lead of the team with momentum increases.

The data for more-recent expanses of history also shows that the level of outscoring by the team without momentum declines with the size of the lead of the team with momentum, but it does so to such an extent that there is now evidence for momentum amongst teams that led at the end of Q2. In other words, if the team that outscored its opponent in Q2 also led at the end of Q2 then it tended to outscore its opponent in Q3. The amount by which it outscored its opponent in Q3 depended on the size of the lead it had up to a point - up to about a 30 point lead - but for leads larger than this motivational aspects appear to impinge and the level of outscoring declines (or even changes sign). 

The Evidence for Momentum in Q4

We move now to considering the evidence for momentum based on scoring in Q4. As a reminder, we're now claiming that a team has momentum if it has outscored its opponent in Q2 and in Q3 having been outscored by them in Q1. To mitigate the possibly contaminating effects of games that had effectively been decided by the end of Q3 - and we've seen above that there is evidence for reduced levels of team motivation in such games - we include only those games where the lead, for either team, is under 4 goals.

Due to the stringency of the eligibility requirements, only about 15% of games are included in the analysis.

What we find is that for every epoch but the most recent one (which suffers from a paucity of eligible games) the evidence for momentum is strong. Teams that outscored their opponents in Q2 and Q3 having been outscored by them in Q1 (and that do not lead or trail their opponents by more than 23 points at the end of Q3), outscore their opponents in Q4 about 55% of the time.

The trend in the rate of outscoring has been declining across successive epochs since reaching its apex in the 1960-1968 epoch, so it's hard to know whether the 48% figure so far recorded for the most-recent epoch is or is not evidence for the disappearance of the momentum effect entirely.

Next we'll review the evidence for momentum after grouping teams on the basis of the level of their outscoring in Q3.

We first consider the period 1897 to 2012 and find that, overall, the evidence is in favour of the existence of momentum in Q4 for the teams we've included. Teams with alleged momentum at the end of Q3, on average, outscore their opponents in Q4 by about 3 points.

The data for smaller and more-recent subsets of history provides similar evidence for the existence of momentum in Q4.

Finally, we'll group teams with momentum on the basis of the lead they'd established, if any, at the end of Q3. (Remember that we've capped leads at under 4 goals.) 

Looking at the entire expanse of VFL/AFL history and across teams with different sized leads at the end of Q3, the evidence is firmly in favour of the existence of momentum. Even the teams that trailed by as much as 11 to 20 points at three-quarter time, despite having outscored their opponents in Q2 and Q3, on average outscore their opponents in the final term by just over 1 point.

The evidence remains largely positive as we narrow our historical focus, the only potentially disconfirming evidence being that related to teams with momentum that trail by 11 to 23 points at the end of Q3. There has been relatively few of them but they have, collectively, been outscored by their opponents on average. 

Conclusion

What to make of all this then?

Here's my take: 

• Based on the data for the entirety of VFL/AFL history, momentum does not appear to exist in Q3 for teams that outscored their opponents in Q2 having been outscored by them in Q1. On the contrary, there appears to be a regression towards the mean such that the team that scored higher in Q1 tends to be the higher scorer in Q3.
• There is some evidence, however, that momentum effects may have been present in games played more recently - say over the past 30 years or so - but only those teams that outscored their opponents in Q2 and, in so doing, established a lead or almost did so.
• Momentum does appear to exist in Q4 for teams that have outscored their opponents in Q2 and Q3 after having been outscored in Q1. Whether such momentum is best characterised as in-game momentum or just a slow start by the superior team is a question for another day, but the fact that, at least more recently, teams with momentum going into Q4 that still trail at the end of Q3 do not tend to exhibit momentum, lends some weight to a "superior team" interpretation.

It would be interesting to assess in-game momentum on much shorter timescales - say by determining whether a team that has just scored is more or less likely to be the next scorer - but for that I'd need the score logs for a reasonably-sized sample of games. These logs do exist online but not in a format that facilitates data capture. Maybe during the off-season ...

Also, finding some way to control for relative team strengths, say by using MARS Ratings or pre-game bookmaker prices, would be beneficial but, at present, I only have this data for relatively recent seasons. Another task during the off-season then might be to generate MARS Ratings for the entire history of VFL/AFL.