Here it is. A mathematical explanation of why there are 13 to 14 home and away games involving Richmond at the MCG each year.
Aside from Richmond, there are anything between three to five MCG co-tenants.
Wikipedia lists Melbourne, Collingwood, Essendon, Hawthorn and Carlton, but it also lists Essendon and Carlton as tenants of Marvel Stadium.
So this is a variable number. Let's call X the number of co-tenants a team has.
The calculation can actually be applied to any team, not just Richmond.
It ignores minor anomalies such as:
1. Away games against non-co-tenant Geelong which end up at the MCG anyway.
2. Away games against co-tenant Hawthorn in Tasmania.
3. The fact that this distribution is less random for non-Victorian teams because they always play their co-state team twice every year.
This answers the question "Given the current structure of the AFL, what is the statistically expected number of games a team can expect to play at its home ground, based on the number of co-tenants it has?"
There are fractional numbers here which make it sound ridiculous but that does not alter the fact that the result is a valid statistical average value.
A team's games fall into four categories.
1. Co-tenants that they play twice. On average there are 5*X/17 of these teams, and twice as many games all of which will be at the MCG - so that's 10*X/17.
2. Other teams they play twice. There are (17-X)*5/17 of these teams, twice as many games, and half of them will be at the MCG - that's (17-X)*5/17.
3. Co-tenants that they play once. There are 12*X/17 of these teams, the same number of games, and they are all at the MCG - so that's 12*X/17.
4. Other teams they play once. There are (17-X)*12/17 of these and half of the games will be at the MCG so that's (17-X)*6/17.
Adding them up and doing some algebra gives the magic formula of 11*(X/17+1).
So, if you think we have three co-tenants, then Richmond should average 12.94 MCG games per year.
If you think it's four, then we should have 13.59 per year.
But really it's five - Richmond haven't played Carlton at Marvel since 2006 and we've never played Essendon there.
So the number is 14.24. We should be getting 14 games a year and even 15 every fourth year.
If Richmond are getting any less than 14 games at the MCG in a year, then we should be the ones complaining.
Aside from Richmond, there are anything between three to five MCG co-tenants.
Wikipedia lists Melbourne, Collingwood, Essendon, Hawthorn and Carlton, but it also lists Essendon and Carlton as tenants of Marvel Stadium.
So this is a variable number. Let's call X the number of co-tenants a team has.
The calculation can actually be applied to any team, not just Richmond.
It ignores minor anomalies such as:
1. Away games against non-co-tenant Geelong which end up at the MCG anyway.
2. Away games against co-tenant Hawthorn in Tasmania.
3. The fact that this distribution is less random for non-Victorian teams because they always play their co-state team twice every year.
This answers the question "Given the current structure of the AFL, what is the statistically expected number of games a team can expect to play at its home ground, based on the number of co-tenants it has?"
There are fractional numbers here which make it sound ridiculous but that does not alter the fact that the result is a valid statistical average value.
A team's games fall into four categories.
1. Co-tenants that they play twice. On average there are 5*X/17 of these teams, and twice as many games all of which will be at the MCG - so that's 10*X/17.
2. Other teams they play twice. There are (17-X)*5/17 of these teams, twice as many games, and half of them will be at the MCG - that's (17-X)*5/17.
3. Co-tenants that they play once. There are 12*X/17 of these teams, the same number of games, and they are all at the MCG - so that's 12*X/17.
4. Other teams they play once. There are (17-X)*12/17 of these and half of the games will be at the MCG so that's (17-X)*6/17.
Adding them up and doing some algebra gives the magic formula of 11*(X/17+1).
So, if you think we have three co-tenants, then Richmond should average 12.94 MCG games per year.
If you think it's four, then we should have 13.59 per year.
But really it's five - Richmond haven't played Carlton at Marvel since 2006 and we've never played Essendon there.
So the number is 14.24. We should be getting 14 games a year and even 15 every fourth year.
If Richmond are getting any less than 14 games at the MCG in a year, then we should be the ones complaining.