Omar's figures hint at the apparent fairness of this bargain because the number of home and away teams progressing without the need for a penalty shootout is reasonably equal. This is what we would expect if the quality of the home sides in the second leg was equivalent to that of the visitors over the course of the sample.
A theoretically based approach to the problem involves modelling the outcome of an extra 30 minutes between two equally matched sides to see if their chances of progressing in the extra time period is roughly equal. 1.4 goals per 90 minutes would be a typical goal expectancy for the home side compared to 1.0 for the visitors. However, over a 30 minute period these values would be greatly reduced. Figures of 0.57 goals and 0.41 would be typical values for the goal expectations of each team over final 30 minutes of the 90 in such a match up. So if both teams played in a similar manner to a normal game, these are the kind of goal expectancies we would see in extra time.
At the end of 90 minutes of the second leg, each team will have had an equal amount of playing time on their own turf to have built up a winning advantage. Therefore it is desirable that the extra thirty minute format shouldn't unduly favour one side over and above the difference in ability between the sides. So for two equally matched sides, the chances of progressing should be as near to 50/50 as possible.
Once extra time is reached, the home side has two routes to winning the tie. They can take and maintain a lead in extra time or they can keep the game scoreless and then progress on penalties. The away side has the same opportunities to reach the next phase, but also can progress with a score draw in the additional 30 minutes of play.
Chances Of An Equally Matched Home Side Progressing From Extra Time in the UCL.
|Team.||Win in ET||Draw ET period 0-0.||Win Shootout.||Overall Chance of Progressing.|
Chances Of An Equally Matched Away Side Progressing From Extra Time in the UCL.
|Team.||Win in ET||Draw ET period 0-0.||Score Draw in ET.||Win Shootout.||Overall Chance of Progressing.|
We can get a reasonable estimate of the chances of these individual outcomes occurring from a Poisson based calculation on the decayed pregame goal expectancy of our generic, equally talented home and away sides. For the shootout I've assumed each side has an equal chance of winning the penalty kick contest.
Either by accident or design, by allowing the away side the opportunity to still score an away goal in the additional 30 minute period, UEFA have almost entirely eliminated the home side's advantage of playing a larger proportion of the tie on home turf. The rules as they stand excellently perform the task of adding an extra half hour of potentially dramatic open play action, while still remaining fair to both sides.