Monday, May 07, 2018

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%

Tuesday, May 01, 2018

Scottish Football: Three Matches to Go

Well, last weekend's matches determined a couple of things. Celtic clinched the league, and thus the Champions Cup berth. Kilmarnock will do no better than fifth, and is thus out of Europe. (Whew.) Hibs, Aberdeen and Rangers are the Europa League entrants, if Celtic wins the Cup. In that case, all that is left to be determined is who gets the first-round bye.

If Motherwell wins the Cup, they're in Europe (with the first-round bye), and one of Hibs, Aberdeen and Rangers loses the game of musical chairs. It's not entirely clear whom. Here's what my simulation shows:
  1. Celtic 100%
  2. Aberdeen 60.5% Rangers 21.3% Hibs 18.2%
  3. Rangers 39.8% Hibs 33.0% Aberdeen 27.2%
  4. Hibs 48.7% Rangers 38.9% Aberdeen 12.3%
  5. Killie 99.6% Hearts 0.4%
  6. Hearts 99.6% Killie 0.4%

Here is where a weakness in my simulation comes in. Rangers and Hibs have both faced Celtic already; Aberdeen is up next. The projected higher finish for Aberdeen does not reflect that harder road ahead.