This Tuesday, San Marino lost in Warsaw to a Polish team that finished with a comfortable 5-0 victory. Coupled with the other group result of Montenegro 1-1 England, San Marino sits in a rather precarious position.
San Marino is not mathematically eliminated. But their chances are so slim it's truly remarkable.
Here is the table as it currently stands:
| Team |
Pld |
W |
D |
L |
GF |
GA |
GD |
Pts |
| Montenegro |
6 |
4 |
2 |
0 |
14 |
3 |
11 |
14 |
| England |
6 |
3 |
3 |
0 |
21 |
3 |
18 |
12 |
| Poland |
5 |
2 |
2 |
1 |
11 |
6 |
5 |
8 |
| Ukraine |
5 |
2 |
2 |
1 |
6 |
4 |
2 |
8 |
| Moldova |
6 |
1 |
1 |
4 |
3 |
10 |
-7 |
4 |
| San Marino |
6 |
0 |
0 |
6 |
0 |
29 |
-29 |
0 |
With four games left, it is mathematically possible for San Marino to still achieve the 12 points needed to qualify for the next round (recall that the top spot gets automatic qualification, and the top eight number two teams (of nine groups) play a head to head round to determine four more teams that qualify).
What is not immediately obvious, however, is just how hard that would be. Here are the remaining matches in this group:
June 7: Montenegro vs. Ukraine
June 7: Moldova vs. Poland
Sept 6: Ukraine vs. San Marino
Sept 6: England vs. Moldova
Sept 6: Poland vs. Montenegro
Sept 10: Ukraine vs. England
Sept 10: San Marino vs. Poland
Oct 11: Moldova vs. San Marino
Oct 11: Ukraine vs. Poland
Oct 11: England vs. Montenegro
Oct 15: England vs. Poland
Oct 15: San Marino vs. Ukraine
Oct 15: Montenegro vs. Moldova
Eight of these games have obvious results if we want San Marino to go on to the next round: England has to lose their last four, and San Marino has to win their last four. Plugging those results into the table, we get:
| Team |
Pld |
W |
D |
L |
Pts |
| Montenegro |
7 |
5 |
2 |
0 |
17 |
| San Marino |
10 |
4 |
0 |
6 |
12 |
| England |
10 |
3 |
3 |
4 |
12 |
| Poland |
7 |
3 |
2 |
2 |
11 |
| Ukraine |
8 |
3 |
2 |
3 |
11 |
| Moldova |
8 |
2 |
1 |
5 |
7 |
Forcing England to lose all of their games brings Poland and Ukraine within one point of the 12 point best that San Marino can still mathematically achieve. And the five match-ups that haven't yet been accounted for are:
June 7: Montenegro vs. Ukraine
June 7: Moldova vs. Poland
Sept 6: Poland vs. Montenegro
Oct 11: Ukraine vs. Poland
Oct 15: Montenegro vs. Moldova
Since Ukraine and Poland play each other, that match must end in a draw, AND they have to outright lose the rest of their games. That gives us:
| Team |
Pld |
W |
D |
L |
Pts |
| Montenegro |
9 |
7 |
2 |
0 |
23 |
| San Marino |
10 |
4 |
0 |
6 |
12 |
| England |
10 |
3 |
3 |
4 |
12 |
| Poland |
10 |
3 |
3 |
4 |
12 |
| Ukraine |
10 |
3 |
3 |
4 |
12 |
| Moldova |
9 |
3 |
1 |
5 |
10 |
And the last game left is Montenegro vs. Moldova. And Moldova can't win that one, or they leap frog San Marino as well.
That means of the thirteen remaining matches, all thirteen have to have specific results or else San Marino is eliminated. To top it all off, San Marino would have to overcome a 49 goal deficit to win the tie-breaker and make it to the qualification round.
Let's re-cap.
In order for San Marino to qualify for the second round of UEFA qualifying, every single one of the following things has to happen:
1) June 7: Montenegro beats Ukraine, AND
2) June 7: Moldova beats Poland, AND
3) Sept 6: Ukraine loses to San Marino, AND
4) Sept 6: England loses to Moldova, AND
5) Sept 6: Poland loses to Montenegro, AND
6) Sept 10: Ukraine beats England, AND
7) Sept 10: San Marino beats Poland, AND
8) Oct 11: Moldova loses to San Marino, AND
9) Oct 11: Ukraine draws Poland, AND
10) Oct 11: England loses to Montenegro, AND
11) Oct 15: England loses to Poland, AND
12) Oct 15: San Marino beats Ukraine, AND
13) Oct 15: Montenegro does not lose to Moldova, AND
14) San Marino overcomes a goal deficit of 49 in four games, AND
15) San Marino finishes top 8 (of 9) amongst the second place finishers
And more to that last point, the current projected cut-off is 12.5 points, so even if San Marino were to finish second in their group, chances are they would finish 9th amongst the second place finishers.
Wow.
So, what are the odds of such a thing actually happening? Well, if I steal the current ratings from
www.eloratings.net and plug them into my Elo rater (it's not a perfect fit, admittedly, I don't use the exact same model as eloratings.net does, but it'll work as a fairly good approximation), I can approximate the odds of specific results. The current Elo ratings are:
1924 England
1741 Ukraine
1659 Montenegro
1650 Poland
1351 Moldova
860 San Marino
The calculated probabilities are in the following table, and the desired results are hi-lighted:
| Home |
Away |
H-Elo |
A-Elo |
E[X] |
W |
D |
L |
| Montenegro |
Ukraine |
1659 |
1741 |
0.51 |
0.3449 |
0.3332 |
0.3219 |
| Moldova |
Poland |
1351 |
1650 |
0.23 |
0.1125 |
0.2368 |
0.6507 |
| Ukraine |
San Marino |
1741 |
860 |
1.00 |
0.9938 |
0.0049 |
0.0013 |
| England |
Moldova |
1924 |
1351 |
0.98 |
0.9644 |
0.0281 |
0.0075 |
| Poland |
Montenegro |
1650 |
1659 |
0.61 |
0.4566 |
0.3159 |
0.2276 |
| Ukraine |
England |
1741 |
1924 |
0.37 |
0.2140 |
0.3105 |
0.4755 |
| San Marino |
Poland |
860 |
1650 |
0.02 |
0.0060 |
0.0229 |
0.9711 |
| Moldova |
San Marino |
1351 |
860 |
0.97 |
0.9440 |
0.0439 |
0.0121 |
| Ukraine |
Poland |
1741 |
1650 |
0.74 |
0.6107 |
0.2570 |
0.1323 |
| England |
Montenegro |
1924 |
1659 |
0.89 |
0.8176 |
0.1354 |
0.0470 |
| England |
Poland |
1924 |
1650 |
0.89 |
0.8254 |
0.1301 |
0.0445 |
| San Marino |
Ukraine |
860 |
1741 |
0.01 |
0.0035 |
0.0138 |
0.9827 |
| Montenegro |
Moldova |
1659 |
1351 |
0.91 |
0.8525 |
0.1112 |
0.0362 |
The the odds of all of these results going San Marino's way (which is simply ascertained by multiplying all the hi-lighted probabilities together) is 0.00000000000000000237823.
Or about 1 in 420 quadrillion.
And that's a very lower bound, conservative estimate, since we haven't even taken into consideration that San Marino has to beat each of their opponents by about twelve goals each.
A person has better chances at winning the
Mega Millions lottery jackpot... twice.
So San Marino isn't mathematically eliminated yet, but no matter what odds your bookie gives you, don't take that bet.
