Does an Extra Day's Rest Matter in the Home and Away Season?

Whenever the draw for a new season is revealed there's much discussion about the teams that face one another only once, about which teams need to travel interstate more than others, and about which teams are asked to play successive games with fewer days rest. There is in the discussion an implicit assumption that more days rest is better than fewer days rest but, to my knowledge, this is never supported by empirical analysis. It is, like much of the discussion about football, considered axiomatic.

In this blog we'll assess how reasonable that assumption is.

DAYS BETWEEN GAMES BY TEAM, HOME AND AWAY

Firstly, let's look at the data for the home-and-away seasons from 1999 to 2012 in terms of the number of days between successive games for the participating teams. 

For the analysis I've grouped the days between games into 4 "buckets": 6 or fewer days between games, exactly 7 days between games, exactly 8 days between games, and 9 or more days between games. The following table gives a sense of how this grouping divides the contests across the seasons.

For example, 323 games from the home-and-away seasons of 1999 to 2012 pitted two teams that each had played their previous game 6 days or fewer prior to the current game. By comparison, only 107 games pitted two teams on the back end of 8 days or more of rest.

This table demonstrates how assiduously the AFL have prevented teams with little rest meeting teams with much rest. For example, only 17 Home teams have met an opponent that's had 8 days or more rest (ie played 9 days or more prior to the upcoming clash) when they themselves have had 5 days or fewer rest (ie played 6 days or fewer prior to the upcoming clash).

Conversely, Away teams with 9 days since their previous contest have met Home teams with 6 days or fewer since their previous contest on only 20 occasions.

An inspection of the off-diagonal elements of this table reveals that, generally, Home teams have been asked to play on less rest than the Away teams they face, but that the difference is only marginal.

(Incidentally, the fewest number of days between one game and the next for any team is 4, which is a fate that's been imposed on Collingwood and Essendon twice each as a result of their insistence on meeting on ANZAC day.)

Looking at the profile of days between games by team when playing at home yields the following chart.

The teams that have more often played at home on few days rest are Adelaide, Carlton, Collingwood, the Kangaroos, Port Adelaide, St Kilda and the Western Bulldogs, while the teams that have less often played at home with few days rest are the Brisbane Lions, Geelong, Melbourne and Sydney. Most notably, the Gold Coast and GWS have rarely played at home after having had 8 or more days since their previous encounter; Fremantle and the Western Bulldogs have also relatively rarely found themselves in this position.

Turning next to days rest before playing away from home we find that Adelaide, Essendon, Geelong, Hawthorn and West Coast have, proportionately, most often been asked to play away within 6 days of their previous encounter. The Gold Coast and GWS are again notable here in terms of the relative infrequency with which they've been asked to back up playing away so soon after a previous clash. The Brisbane Lions, Fremantle and the Roos have also rarely been asked to play away on 5 days rest or fewer.

That's all interesting enough, but does it have any bearing on game outcomes?

DOES REST MATTER?

There are two ways that more rest might manifest in team performance: as higher victory margins or as higher winning rates. To quantify the effects of rest in terms of these two performance algorithms, I've built a couple of statistical models.

(I did something similar in terms of assessing the importance of days rest in Finals in an earlier blog, though there I looked only at victory margin. I found then that the number of days rest for the Home team had a small, positive but statistically insignificant effect on the eventual game margin, and that the number of days rest for the Away team had a slightly larger, negative [ie more days rest was detrimental to the Home team margin] and statistically significant effect on the eventual margin.)

In the first model, the target variable is the margin of victory of the Home team and, in the second, it's the result, Win or Loss, for the Home team. In both models the regressors are: 

• The Interstate Status of the contest from the Home team's perspective
• The number of days since the Home team last played
• The number of days since the Away team last played
• The log odds ratio of the Home team
• The MARS Ratings of the Home and Away teams
• The average for and against record per game for the past 16 rounds

(Specifics of the definitions of these variables appear in the footnotes of the table below.)

Due to the inclusion of the always-important log odds ratio and the relative suspicion with which I treat the bookmaker data I have for seasons prior to 2006, I've fitted these models only to the home-and-away data for seasons 2006 to 2012.

Though not reported here, I also ran models including Venue Experience for the Home and Away teams, but these did not prove to be statistically significant (nor sufficiently interesting to talk about, save this paragraph) and so were subsequently excluded.

Consider first the results shown on the left, which pertain to a model with the Home team victory margin as the target.

We find that the Interstate Status variable is statistically significant. The coefficient implies that Home teams playing in their home State when their opponents are out of their home State tend to score almost 5 points more than they otherwise would at a neutral venue facing the same team.

Also, we find that the coefficient on the Home team's pre-game log odds ratio is statistically significant, as are the coefficients on the Away team's MARS Rating and the Home team's average for and against performance for the most recent 16 rounds in the current competition. As something of an aside, it's interesting to note that these variables still manage to achieve statistical significance despite the withering shadow of the bookmaker-derived log odds ratio, also present in the model.

Turning next to the variables we're mostly concerned about in this blog, relative to the points scored when the Home team is playing after 5 days or fewer rest we find that Home teams tend to score fewer points on more days rest, to a statistically significant level when they're on 8 days or more rest. This is counter to the prevailing wisdom.

Similarly, the more rest the Away team has, the greater the expected victory margin of the Home team -though here, none of the coefficients are statistically significant. Once again, this flies in the face of pundit opinion.

The coefficients on the right of the table relate to the model where the target variable is the result for the Home team, win or loss (it's a binary logit we're fitting, and drawn games are excluded), rather than the margin of victory. Nothing in this column substantively contradicts the results just presented - there are some changes of sign, but none of the variables changing in this way are also statistically significant.

One might conjecture that days rest is not, on its own, the important feature to consider but that what matters instead is the interaction between days rest and interstate status for the teams' current or previous encounters. I've fitted a number of additional models including such interaction terms and found that they contribute little, if any, additional explanatory power and that the newly-introduced coefficients do not generally achieve statistical significance.

Based on these results, a reasonable person could come to only one conclusion: days rest broadly doesn't matter and, if it does, less is better than more.

A TEAM-BY-TEAM VIEW

Though we've concluded that days rest is largely an irrelevance when we consider all teams at once, it's conceivable that rest is more important, perhaps much more important, for some teams than for others. To quantify this, ideally we'd fit the same models that we fitted earlier to subsets of the data for each team individually, or we'd include each team in interaction terms. But we've relatively few data points for each team and so risk overfitting if we to proceed in this manner.

Instead, let's assume that each team's days rest when playing at home or away is orthogonal to (ie independent of) the strength of the teams that it faced in those clashes and whether or not the contest was deemed an Interstate clash, and proceed by simply calculating the average victory margin for each team when playing at home or away, cross-tabbed by the number of days since the team's last clash.

On the left we can see each team's average victory margin when playing at home on the back end of various length rests. If the prevailing wisdom is correct for a particular team then we should see the average margin increasing at the length of the rest increases. 

Broadly (and generously) this is the case only for the Lions, Collingwood, Geelong, the Roos, Port Adelaide, St Kilda, Sydney and the Dogs. What's particularly noticeable is the tendency for teams having had 9 days or more since their last contest to perform less well, on average, than when they've had exactly 8 days since their last clash. Only seven teams are better with 9 days or more since their last game than they are with exactly 8 days (hence the negative and statistically significant coefficient tabulated earlier).

(Do note, however, how relatively rare is the phenomenon of 9 days or more since the last game - see the fourth column of the second-to-last block of data in the table, which shows, for example, that Adelaide have enjoyed this much rest prior to a home game on just 19 occasions.)

The second block of data records each team's average victory margin when playing away after various rests. Here too we should see increasing average margins as rest length grows if prevailing wisdom counts for anything. Once again being generous, we can list Fremantle, Geelong, Hawthorn, the Roos, St Kilda and West Coast as the only teams to which such wisdom applies.

Long rests once more appear to be detrimental to performance: there are nine teams with worse records for away games played after 8 days rest or more than for away games played after exactly 7 days rest. Note once more, however, the relative paucity of games played after such a long break; the data for this appears in the rightmost column of the table above.

SUMMARY AND CONCLUSION

My take on all this is that: 

• Overall, in the home-and-away season, the number of days rest that a team has between successive games is largely irrelevant to the number of points it scores or whether or not it wins
• If anything, longer rests are worse than shorter ones, regardless of whether the upcoming game is at home or away
• A handful of teams seem to do better on longer rests when playing at home or away: Geelong, the Roos and St Kilda.
• Other, small handfuls of teams do better playing either at home or away - but not both - on longer rests
• Whether or not travel is required during the rest period is also an irrelevance

 (EDIT: Shortly after posting this blog I was struck by the possibility that the bookmaker's prices might incorporate an element to account for the days rest that each team has enjoyed. If this were the case then, by including the log odds variable, ostensibly as a way of controlling for the relative strengths of the competing teams, I'd also potentially be introducing additional collinearity and reducing the likelihood of finding the days rest variables statistically significant.

So, here are the results of the two regression models excluding the log odds variable, with the original results also provided for comparative purposes:

The changes in the coefficients on the days rest variables are small and the patterns of significance are unchanged, so we've no reason to alter our original conclusion. Coefficients on all other variables in the model are affected however, in terms or size and statistical significance, suggesting that bookmaker prices incorporate elements to account for the Interstate Status of each contest and, as we'd expect, the relative team strengths. In particular it seems that bookmaker prices incorporate more information about the strength of the Home team than they do information about the strength of the Away team, as evidenced by the larger effect on the coefficients on these variables when the log odds variable is omitted.)