Group stage of UEFA Champions league is played in autumn with four teams in each group playing home and away. Matches can end in a draw. The Knock-out stage begins after the winter break and as the name suggests, draws need to be resolved. The two-leg format uses away goals as an initial tiebreaker. Imagine two teams drawing 1-1 after both legs. Assume both sides scored in the same match. In that case the team scoring away wins; otherwise penalties will decide the outcome.
Essentially an away goal carries more weight than a goal scored at home. I mentally add 0.01 for every away goal. So if Team B scores away, I record the score as 0 – 1.01. If Team A equalises then the score reads 1 – 1.01. In the second leg, a goal by Team A makes the score 1.01 – 2.01. A equaliser by Team B means that the tie is level at 2.01 – 2.01 with both teams having scored once each – home and away. Any goal scored beyond this point will decide the tie.
The choice of .01 as a weight is fair. It is highly unlikely that one team will score 100 away goals. If that happened .01 * 100 would amount to an extra goal. The weight is notional and another value like 0.001 will suit as well. Its value does not matter. The key is to remember that some goals are more equal than others and this has been widely accepted.
The UEFA Champions League Final is not two-legged. So away goals do not come into play in the finals. Could we get another element to decide the tie as long as a team manages to score in regular time?
I think a notional weight called ε with a value of say 0.000001 can help decide a tie without resolving to penalties. Only one ε exists and it is always attached to the most recent goal.
How does it work? Assume that in a one-legged knock-out event, Team A scores in the opening minute. The score reads 1 – 0. Team A may defend this goal or attack further to increase the advantage. Team B has no choice and must find an equaliser.
Using ε the same score will notionally be saved as 1.000001 – 0. Now Team B needs to score just 1 goal to swing the tie in its favour. A goal by Team B will change the score to 1 – 1.000001 as ε is now assigned to the more recent goal by Team B.
Team A will no longer try to defend that solitary goal as the risk of conceding a goal will knock them out. Both teams will try to score a goal if any team leads by a solitary goal. This change will make the game more competitive and attractive. And the penalty shoot-out is avoided.
One scenario still remains unaddressed. What if the score remains 0-0 at full time? In that case we can use The Advantage. It is the brainchild of Henry Birtles:
This is how The Advantage works. With the teams tied at 90 minutes, The Advantage comes into play. This entails a shoot-out before extra-time has started. Birtles proposes a cut-down version of three spot-kicks per side or an immediate sudden-death shoot-out to keep the process brief and help the players stay loose and ready to carry on.
Once one side has The Advantage, the teams then go on to play extra-time. The team winning at the end of the 30 minutes extra-time wins. The Advantage will only be applied if they are still tied at the end of 120 minutes.