Scottish Football: More European Speculation

Recently I posted some subjective odds for which Scottish clubs would represent the country in next year's European tournaments. As I did last year, I will provide something more objective.

I will use the same criteria as last year.

• All teams have equal chances
• Each match (except the Scottish Cup final) has a 1/3 chance of ending in a draw.
• All non-draws have a goal differential of 1.
• If two teams are tied on points and goal differential, the team that is currently ahead will stay ahead.

If I wanted better odds, I would bother to program in the odds from Fivethirtyeight for all upcoming matches. But I think this is close enough.

Since the Scottish Cup final is Celtic-Hearts, we have the following situation. If Celtic wins, the top 4 in the league make it to Europe. If Hearts win, it's the top 3, plus Hearts...unless Hearts also finishes third, in which case the 4th place team makes it too. That is exceedingly unlikely, but I had to program for it.

Celtic:

• Chance of being Champions League representative: 99.5%
• Chance of being Europa League representative: 0.5%
• Chance of missing out on Europe: 0%

Rangers:

• Chance of being Champions League representative: 0.5%
• Chance of being Europa League representative: 99.4%
• Chance of missing out on Europe: 0.1%

Kilmarnock:

• Chance of being Champions League representative: 0%
• Chance of being Europa League representative: 71.5%
• Chance of missing out on Europe: 29.5%

Aberdeen:

• Chance of being Champions League representative: 0%
• Chance of being Europa League representative: 67.0%
• Chance of missing out on Europe: 33.0%

Hibernian:

• Chance of being Champions League representative: 0%
• Chance of being Europa League representative: 10.1%
• Chance of missing out on Europe: 89.9%

Hearts:

• Chance of being Champions League representative: 0%
• Chance of being Europa League representative: 51.6%
• Chance of missing out on Europe: 48.4% 

In words, if Celtic wins the Scottish Cup, it will probably be Celtic, Rangers, Kilmarnock and Aberdeen. If Hearts wins, it will probably be Celtic, Rangers, Hearts and whichever one of Kilmarnock and Aberdeen takes 3rd place. Hibernian has an outside chance of taking a spot away from Kilmarnock or Aberdeen.