Scottish Football: Three To Go

I have updated my crude simulation after this weekend's games. The new probabilities are:

1. Celtic 99.6% Rangers 0.4%
2. Rangers 99.6% Celtic 0.4%
3. Aberdeen 67.4% Kilmarnock 30.9% Hibs 1.8%
4. Kilmarnock 59.1% Aberdeen 31.1% Hibs 9.6% Hearts 0.2%
5. Hibs 76.1% Hearts 12.7% Kilmarnock 9.7% Aberdeen 1.5%
6. Hearts 87.1% Hibs 12.6% Kilmarnock 0.3%

In words, Celtic failed to clinch the title, but is almost certain to. Rangers clinched no worse than 2nd (and a European place). The race for 3rd and 4th is still basically Aberdeen and Kilmarnock, with Aberdeen 2-1 favorites to nab 3rd, and Hibs having an 11% chance of sneaking in there. The difference between 3rd and 4th will matter if Hearts shocks Celtic for the Cup.

Scottish Football: Four Matches To Go

I will once again use my crude simulation to update the top half of the Scottish Premiership as each set of matches goes by.

1. Celtic 98.8% Rangers 1.2%
2. Rangers 97.4% Celtic 1.2% Aberdeen 1.2% Kilmarnock 0.2%
3. Aberdeen 64.1% Kilmarnock 33.0% Hibs 1.5% Rangers 4.1% Hearts 0.01%
4. Kilmarnock 58.8% Aberdeen 32.9% Hibs 7.9% Hearts 0.4% Rangers 0.03%
5. Hibs 71.6% Hearts 18.7% Kilmarnock 7.9% Aberdeen 1.8%
6. Hearts 80.8% Hibs 19.0% Kilmarnock 0.1% Aberdeen 0.003%

So, in words. Celtic failed to clinch, thus opening up the chances they won't win. (Although if this simulation were weighted by team rating, the chance would be almost zero.) Rangers came very, very close to clinching a European place. If a 1-in-3700 sequence of events happens in the league, and Hearts wins the Cup, they're left out. Aberdeen's defeat of Kilmarnock put them in the driver's seat for the 3rd slot and guaranteed Europe. Hibs' draw left them slipping out of the European places, and Hearts loss means that the Cup is almost certainly the only way they get into Europe.

[This post was updated after I discovered a coding error that made slight changes in the probabilities.]

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.