Scottish Football: More European Speculation

Before the Scottish Cup semi-finals, I posted some subjective odds for who the Scottish representatives will be in Europe. Now that we know the finalists (Celtic and Motherwell), I thought I should make the odds a little more objective. Let's make a bunch of questionable assumptions:

• All teams have equal chances. (Probably true-ish if you ignore Celtic.)
• 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.

These are all bad, but probably not too bad. Let's code this up and see what happens. I'm going to do some rounding to make things make a little more sense.

Celtic:

• Chance of being Champions League representative: 99.95%.
• Chance of entering Europa League in second round: 0.025%.
• Chance of entering Europa League in first round: 0.025%.
• Chance of missing out on Europe: 0%.

Rangers:

• Chance of being Champions League representative: 0.025%.
• Chance of entering Europa League in second round: 24%.
• Chance of entering Europa League in first round: 65%.
• Chance of missing out on Europe: 11%.

Aberdeen:

• Chance of being Champions League representative: 0.025%.
• Chance of entering Europa League in second round: 19%.
• Chance of entering Europa League in first round: 57%.
• Chance of missing out on Europe: 14%.

Hibs:

• Chance of being Champions League representative: 0%.
• Chance of entering Europa League in second round: 6%.
• Chance of entering Europa League in first round: 45%.
• Chance of missing out on Europe: 49%.

Kilmarnock:

• Chance of being Champions League representative: 0%.
• Chance of entering Europa League in second round: 0.4%.
• Chance of entering Europa League in first round: 10%.
• Chance of missing out on Europe: 90%.

Hearts:

• Chance of being Champions League representative: 0%.
• Chance of entering Europa League in second round: 0%.
• Chance of entering Europa League in first round: 0.007%.
• Chance of missing out on Europe: 99.993%.

Motherwell:

• Chance of being Champions League representative: 0%.
• Chance of entering Europa League in second round: 50%.
• Chance of entering Europa League in first round: 0%
• Chance of missing out on Europe: 50%

Another way of looking at it, here are the projected finishes:

1. Celtic 100%
2. Rangers 48% Aberdeen 39% Hibs 12% Kilmarnock 1%
3. Aberdeen 39% Rangers 34% Hibs 24% Kilmarnock 3% 
4. Hibs 49% Aberdeen 21% Rangers 15% Kilmarnock 14% Hearts 0.02%
5. Kilmarnock 79% Hibs 14% Aberdeen 3% Hearts 2% Rangers 2%
6. Hearts 98% Kilmarnock 2% Hibs 0.04%