Scotland Overturn the Odds In Rome.

The 2014 Six Nations made a brief, but compelling reappearance to the centre of the sporting stage over Friday night and Saturday afternoon. Three match weekends into a five weekend series has seen each of the six nations suffer at least one defeat. Although Ireland still hold a significant advantage by virtue of their points differential, they still have to travel to France on the final Super Saturday.

A comprehensive defeat for France in Wales and a much smaller one for Ireland at Twickenham leaves four of the six countries with ambitions to lift the trophy in mid March, but the most relieved coach will be an Australian born Scott.

Italy have gradually developed into worthy, if inconsistent members of Europe's premier international rugby competition, swapping occasional stunning wins against the top tier nations, with large margin defeats. However, they have become natural rivals with Scotland for the wooden spoon.

Since the competition grew from five sides to six in 2000, Italy have recorded 11 wins to Scotland's 18, well below the 37 win total posted by the next highest ranked side, Wales. So a match against Scotland, especially in Rome has increasingly become the game that Italy target to secure at Six Nations victory.

For much of the first half in the Stadio Olimpico, the narrow favouritism enjoyed by Italy, combined with the slight lack of overall quality throughout each team was reflected in a scoreboard that advanced only intermittently through penalty goals. An Italian try just before the interval appeared to give the home side the decisive score as they stretched their lead to 10 points. A deficit that almost always proves insurmountable. Not only does the trailing side require two at least two score to draw ahead, they must also prevent their opponents from adding to their score.

However, a flurry of second half try scoring from Scott Johnson's side edged Scotland in front, but they couldn't keep Italy off the scoreboard and as the clock reached the final minute they trailed 20-18 and heroic failure beckoned.

In the plot above, I've charted how the win/loss and draw probabilities fluctuated throughout the 80 minutes of the game. To add context and declutter the horizontal axis, I've listed the scoreline and various match events in the table below. As with football, scores are obviously the main factor in shifting in game probabilities, but pitch position also sways likelihood, although not as dramatically as in the NFL.

Time Elapsed.	Scoreline.	Comments.
0	0-0	Italy were 4 point favs at kickoff
3	0-0	Attacking lineout to Scotland
4	0-0
10	0-0
14	3-0	Penalty for Italy (Allan)
20	3-0
23	3-3	Penalty for Scotland (Laidlaw)
29	3-3
31	6-3	Penalty for Italy (Allan)
35	6-3	Scotland Attacking
36	6-3	Defensive Scrum to Italy
37	6-3	Attacking Scrum to Italy
38	6-3
40	13-3	Converted Try for Italy (Allan)
45	13-6	Penalty for Scotland (Laidlaw)
55	13-11	Unconverted Try for Scotland (Dunbar)
60	13-11
63	13-11	Scotland Attacking
65	13-11	Defensive scrum Italy
67	13-18	Converted Try for Scotland (Dunbar)
70	20-18	Converted Try for Italy (Furno)
75	20-18	Scotland Attacking
77	2018
79	20-18	Attacking Scrum Scotland
80	20-21	Drop Goal for Scotland (Duncan Weir)

Except for a brief few minutes late in the game when they took a five point lead, Scotland were underdogs right up until Duncan Weir's towering drop goal  16 seconds from the clock turning red. Although Scotland were well placed around the Italian 22 as they trailed with time expiring, the discipline of the Italian defence and a referee who was unlikely to penalise for anything but a blatant infringement, meant that they had to create their own score.

Two points down and with three on offer for a successful drop goal made their choice almost automatic. As they continually took the ball into contact, the chance of a fatal knock-on become all too real, so they had to trust to a kick that was further out than ideal.

Drop goals aren't successful anywhere near as often as comparable penalty kicks or conversions, a generic conversion rate of around 30% would be typical, although some are attempted under advantage when the player effectively has a shot to nothing.

Creating a goal expectancy model for drop goals follows the same route as those for goal expectation for shots in football. Matching the outcome of the attempt to the pitch coordinates from where the kick originated provides a baseline with which to measure any subsequent drop goal opportunities.

Weir was well outside the Italian 22 line, but shy of the 10 meters line and he had a nice line of backs innocently impeding any attempt by the Italians to charge the kick down. So his kicking action was relatively relaxed and although he was to the left of the posts, that aided the natural arc of his right footed kick.

As he caught Cusiter's pass and prepared to swing his boot, his and Scotland's chances of success probably hung around 26%. The odds favoured the hosts, but Weir provided a magnificent finish to a fine contest during one of the best overall weekends in Six Nations history.