Last night I was thinking about the results we found in the previous blog post about upsets and mismatches and wondered if the historical pattern of expected game margins was borne out in the actual results. On analysing the data I found that there were a lot more victories of 10 Scoring Shots or more in magnitude than MoSSBODS had predicted. In most seasons, at least one-third of the games finished with a victory margin equivalent to 10 Scoring Shots or more, which was usually two or three times as many as MoSSBODS had predicted.
My snap assessment was that MoSSBODS was probably too conservative, too unwilling to predict large victory margins. To test this hypothesis, I decided to look at the performance of the TAB Bookmaker over the period 2006 to 2015 (using, for convenience, points rather than Scoring Shots).
The table at right summarises the results of the analysis, the Expected Absolute Margin data for the rows based on the TAB Bookmaker's handicap in the line market, and the Actual Absolute Margin data columns based on the actual results for each game. We can see from this table that, for example, of the 616 games in which the TAB handicap implied an expected victory margin of less than two goals (in absolute terms), only 173 actually finished with a margin of this magnitude.
In fact, most games with an Expected Absolute Margin of two goals or less actually finished with an Absolute Margin of six goals or more, and this is also the case for games with Expected Absolute Margins of two to less than four, four to less than six, and six or more goals.
We can see just how much more prevalent six goals or larger margins are by converting the data in this first table into row percentages, which I've done in the second table, at left, and which reveals that between about 30% and 65% of all games from each row finished in a victory of six goals or more. In aggregate, although only 17% of games had a TAB handicap implying a six goals or greater victory was expected, 43% of games actually finished with such a result. If we consider a blowout game as one with such a margin, then it seems that blowout results occur at about 2.5 times the rate that the Bookmaker expects, as was the case for MoSSBODS predictions.
Now MoSSBODS might be conservative and tend to produce expected margins nearer zero than is warranted, but a bookmaker can't afford to show any systematic biases, so there must be something else going on here.
And, of course, there is. If we assume, as we usually do, that the result of a game from the AFL competition can be reasonably modelled as a Normal variable with a mean equal to some pre-game, unbiased expected estimate of the margin and some (probably fixed) variance, we can calculate the theoretical likelihood of witnessing a game finishing with a margin in some specified range given some assumption about the game's true expected margin and variance or standard deviation.
I've done this for the table at right, using for the mean in each row the average absolute margin for games from one of the rows in the table above, and assuming a fixed 36 point standard deviation for all games. Theoretically then, games with a true Expected Margin of 6.9 points - which are proxies for the games in the top row of the table above - can be expected to produce an actual absolute margin of 36 points or more about 33% of the time.
The correspondence between the percentages in this table of theoretical values and the empirically determined percentages in the previous table are striking.
So, what causes the preponderance of larger absolute margins? It comes because of the relatively large proportion of the Normal distribution that lies in the tails beyond both -36 and +36 point margins, even for games with quite small expected margins. Games with an expected margin of +6.9 points, for example, have about a 12% chance of producing an actual margin of -36 points or less and a 21% chance of producing an actual margin of +36 points or more. Being the only unbounded category also helps bolster the proportion of games falling in the 36+ Actual Absolute Margin bucket.
The empirical finding that blowout results - defined as victories by six goals or more - are more likely then we'd expect, even if our pre-game expectations are unbiased, is therefore supported by theoretical considerations. Changing the definition of "blowout", while altering the ratio of actual to expected blowouts, doesn't change the underlying result, as we can see in the tables below for which I've redefined blowout as a victory margin of 10 or more goals. Here we find that blowouts are 5 times more prevalent than we expect (and we still find a good fit between the empirical and theoretical results).
We can use the theoretical Normal approximation to make a couple of final observations about blowouts, which is that they will be more prevalent in seasons where:
- pre-game expected absolute margins are higher (somewhat obviously)
- the variability of final margins about their expectations is larger
On this last observation, note that in the previous blog I included a final chart that suggested the variability of final margins has been declining since about 1990, perhaps plateauing in the past few years. This downward trend, if it resumes and if it is not offset by an increase in the spread of team abilities, should reduce the number of blowouts in future seasons - albeit it at the cost of reducing the expected number of upsets.
Even with a 32 point standard deviation and a season consisting solely of games with pre-game expected margins of just 12 points, however, we'd still expect about 1 game in 12 to finish with a 60 point or larger margin. Randomness will continue to ensure that we'll see unattractive contests every week, even between apparently closely-matched opponents.