Now that football (soccer) leagues are back in play, let us consider the old question of how to get more goals scored. As the play has become more defense oriented, it is obvious that attack needs to be encouraged, thereby increasing the risk. Quite obviously, to reward risk taking, it must be that the expectation of a return from wining and losing must be higher than that of a draw. This can be achieved by awarding three points instead of two for a win, a practice that is now almost uniformly adopted, and Isabelle Brocas and Juan Carrillo confirm from a theoretical point of view that this is a good way to increase risk taking.
The latter paper also recommends to have a 20-minute golden goal extra time in case of a draw: the first to score wins. I am not quite sure I follow the intuition there. Knowing that there is this extra-time, it gives less incentives to play offensively during the regular time. This is at least my observation of NHL hockey games.
What else could encourage offensive play? One could go the American football way, which is to basically regulate when a team can only play offense. But soccer is too fluid for that. But ice hockey can be very exciting when teams are short-handed due to a timed penalty. Having fewer players, even temporarily, is a disadvantage that can lead to have more goals scored. But more importantly, the fear of time penalties would lead defenders to be less aggressive (face it, yellow cards are not much of a threat), thus opening the play to attackers.
That said, one can still discuss whether more goals are really needed. If a game can be decided by a single goal, and this goal could happen at any moment and not necessarily be scored by the dominating team, this can also make a game exciting.
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