Scottish Football: Two Matches to Go

There are two matches (per team) left in the Scottish Premiership, and it's time for a new program.

That's because there are only 4 games left that can affect the European participation. With only 3 possible outcomes for each game, that's 3⁴=81 total possibilities. It's better to exhaust over all the possibilities versus randomly simulating them.

To recap, Celtic has sewn up first place, Kilmarnock is locked into 5th, and Hearts is guaranteed 6th. Aberdeen has 69 points, Rangers has 68, and Hibernian has 66. Aberdeen has Rangers and Celtic remaining, Rangers has Aberdeen and Hibs, and Hibs has Hearts and Rangers. It is either the case that second place gets a first-round bye for Europa League qualifying while the other two don't, or second and third get in the Europa League while fourth doesn't. So the outcome matters.

Rangers has goal differential of +26, Aberdeen +18 and Hibs +17. I am therefore going to assume Rangers wins any tiebreakers. If Aberdeen and Hibs both end up with 70 points, Aberdeen will end up with a negative differential in their last two games, with Hibs positive. In other cases, I will throw up my hands.

Of the 81 possible outcomes...

• 29 have Aberdeen, Rangers, Hibs
• 24 have Rangers, Aberdeen, Hibs
• 14 have Aberdeen, Hibs, Rangers
• 5 have Rangers, Hibs, Aberdeen
• 3 have Hibs, Aberdeen, Rangers
• 2 have Hibs, Rangers, Aberdeen
• 2 have Rangers, and then a tiebreaker
• 2 have a tiebreaker and then Rangers

If we assign the remaining tiebreakers randomly (why not?), that gives:

1. Celtic 100%
2. Aberdeen 54% Rangers 37% Hibs 9%
3. Rangers 38% Aberdeen 36% Hibs 26%
4. Hibs 67% Rangers 23% Aberdeen 10%
5. Kilmarnock 100%
6. Hearts 100%