# Revisiting the Empirical Evidence for the Predictability of Conversion Rates: An All-Time VFL/AFL Perspective

The empirical world is almost always more complex than the theoretical one, which makes life more interesting but statistical modelling more difficult. As I've noted before, swings and roundabouts ...

In a couple of recent posts (here and here) we looked at theoretical evidence relating to the hypothesis that Scoring Shots are more often a better guide to team superiority than are final Scores. That evidence tended to favour the hypothesis but was crucially dependent on the assumption that weaker teams convert scoring opportunities at the same rate as stronger ones.

That assumption is not entirely without merit. This post, based on TAB and score data, and written in early 2014, provides strong empirical support, as does this post from much later in that same year, although I did note in this latter post that "stronger teams tend to have marginally higher conversion rates".

Both of those analyses used TAB bookmaker prices to determine relative team strengths and were, therefore, constrained to consider only the period for which I had reliable bookmaker data: 2006 to the then-present day, which was the end of season 2013 for the first post and virtually the end of season 2014 for the second.

Today we'll revisit this analysis using MoSSBODS Team Ratings instead of TAB prices to determine relative team strengths, which will allow us to perform the analysis for the entire history of the VFL/AFL, and not just for the period from 2006 onwards.

The chart below records the proportion of games in which MoSSBODS Favourites converted at a higher rate than their opponents, for Favourites of varying relative strengths (left to right) and for a range of VFL/AFL Eras (top to bottom). Points coloured red are statistically significantly different from 50% (two-tailed test at 10% level), while those coloured black are not. The size of a point reflects the number of games on which is is based.

The first thing to note is that every point on this chart lies above 50%, which means that Favourites of any and all relative strengths are likely to convert at a higher rate than their opponents. For very mild Favourites, however, we can't be statistically confident that the true probability of them out-converting their opponents lies above 50%; for very strong favourites we can be quite confident. Teams that MoSSBODS has rated 12 or more Scoring Shot Favourites have registered higher Conversion rates than their opponents about 60% of the time or more, in every Era.

Also, it seems that the likelihood of the Favourite recording the higher Conversion rate tends to increase, in every Era, with higher levels of favouritism. That's broadly consistent with what we found in those 2014 posts, though one difference between our analysis here of the 2000-2015 period and the analysis of the 2006-2013 period in those earlier posts, is that we've now found Favourites of all relative abilities converting at a higher rate than their opponents. In the earlier posts we found that mild Underdogs converted at higher rates marginally more often than their opponents.

Speculating about reasons why stronger teams might tend to convert at higher rates than their opponents, one might reasonably hypothesise that either or both of the following statements are true:

• Offensively superior teams tend to generate Scoring Shots that are inherently more convertible into goals
• Defensively superior teams tend to allow Scoring Shots that are inherently less convertible into goals

The charts below explore this idea, the chart on the left recording the proportion of games in which the MoSSBODS Offensively superior team (defined as the team for which the MoSSBODS Offensive Rating for that team less the MoSSBODS Defensive Rating for its opponent is higher) recorded the higher Conversion Rate, and that on the right recording the proportion of games in which the Defensively superior team (defined as the team for which the MoSSBODS Defensive Rating for that team less the MoSSBODS Offensive Rating for its opponent is higher) recorded the higher Conversion Rate. Note that, in determining Offensive and Defensive superiority we ignore Venue effects, which we did not when we determined Overall superiority earlier.

We see here evidence to support both statements. Only 1 of the 24 points on each of the charts lies below 50%, which suggests that both Offensive and Defensive superiority is associated with relatively elevated Conversion Rates. There's also evidence in both charts for an increasing likelihood of superior Conversion as teams become relatively more Offensively and Defensively superior, although statistical significance is attained more often in relation to Defensive superiority.

### CONCLUSION

Across VFL/AFL history there is solid evidence that the better team (as assessed using MoSSBODS) in a contest is more likely to convert Scoring Shots at a higher rate than their opponents, especially when the better team is rated substantially higher.

This fact should be taken into account when considering those earlier posts about the theoretical evidence for the relative efficacy of Scoring Shots versus Scores for determining underlying relative ability. Put simply, in games between mismatched opponents, both statistics are probably equally informative (and, in many games, will provide the same ordering anyway).

(Note: I did explore the relationship between MoSSBODS'-assessed relative team abilities and the likelihood that Scoring Shots or Scores will more often reflect the "correct" team ordering, but it proved very difficult to identify statistically significant differences. If anything, I'd say that Score is probably the better metric for stronger Favourites, but it's hard to be definitive.)

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