For reasons that aren't even evident to me, I decided to revisit the issue of "when losing leads to winning", which I looked at a few blogs back.
In that earlier piece no distinction was made between which team - home or away - was doing the losing or the winning. Such a distinction, it turns out, is important in uncovering evidence for the phenomenon in question.
Put simply, there is some statistical evidence across the home-and-away matches from 1980 to 2008 that home teams that trail by between 1 and 4 points at quarter time, or by 1 point at three-quarter time, tend to win more often than they lose. There is no such statistical evidence for away teams.
The table below shows the proportion of times that the home team has won when leading or trailing by the amount shown at quarter time, half time or three-quarter time.
It shows, for example, that home teams that trailed by exactly 5 points at quarter time went on to win 52.5% of such games.
Using standard statistical techniques I've been able to determine, based on the percentages in the table and the number of games underpinning each percentage, how likely it is that the "true" proportion of wins by the home team is greater than 50% for any of the entries in the table for which the home team trails. That analysis, for example, tells us that we can be 99% confident (since the significance level is 1%) that the figure of 57.2% for teams trailing by 4 points at quarter time is statistically above 50%.
(To look for a losing leads to winning phenomenon amongst away teams I've performed a similar analysis on the rows where the home team is ahead and tested whether the proportion of wins by the home team is statistically significantly less than 50%. None of the entries was found to be significant.)
My conclusion then is that, in AFL, it's less likely that being slightly behind is motivational. Instead, it's that the home ground advantage is sufficient for the home team to overcome small quarter time or three-quarter time deficits. It's important to make one other point: though home teams trailing do, in some cases, win more often that they lose, they do so at a rate less than their overall winning rate, which is about 58.5%.
So far we've looked only at narrow leads and small deficits. While we're here and looking at the data in this way, let's broaden the view to consider all leads and deficits.
In this table I've grouped leads and deficits into 5-point bands. This serves to iron out some of the bumps we saw in the earlier, more granular table.
A few things strike me about this table:
- Home teams can expect to overcome a small quarter time deficit more often than not and need only be level at the half or at three-quarter time in order to have better than even chances of winning. That said, even the smallest of leads for the away team at three-quarter time is enough to shift the away team's chances of victory to about 55%.
- Apparently small differences have significant implications for the outcome. A late goal in the third term to extend a lead from say 4 to 10 points lifts a team's chances - all else being equal - by 10% points if it's the home team (ie from 64% to 74%) and by an astonishing 16% points if it's the away team (ie from 64% to 80%).
- A home team that leads by about 2 goals at the half can expect to win 8 times out of 10. An away team with such a lead with a similar lead can expect to win about 7 times out of 10.