The NHL made one change to the icing rules in order to decrease the number of icings, the rule was quite simple: if you ice the puck you cannot change the players on the ice, but the opposing team can change lines (so a tired line vs. a fresh line). The concept was good, but was less effective given the fact that a number of times an icing would include a commercial break giving both sides a two minute break. The results were stunning however, the new rule decreased icings by 50% (10 per game to 5 per game).
In order to understand scoring after an icing, one should to understand the offensive zone face-off: first off, there’s a 55% chance of winning an offensive zone face-off. From there, there’s likely around a 66% chance of shooting, with a 70% chance of hitting the net. If the puck does hit the net it has around a 10% chance of going in, this all equals around 2.5% chance of scoring off an offensive zone face-off.
Was this decrease in icings warranted? It would be hard to answer that question, due to the fact that players in more disadvantageous (on the ice for two minutes) situations would avoid icing the puck. However if you look at goals after icings (30 seconds or less after an icing) you have 215 in 2005-2006 vs. 304 in 2003-2004, which is actually only about 30% less, it did have an effect on scoring, as a percentage though it was 2.5% vs. 3.1% with a standard deviation of about 0.2%, however it is only a 25% increase in terms of percentage from years past. Scoring increased by 25% resulting in teams to decrease icing the puck by 50%. Would you be better off icing or not icing is the tricky question that I can’t answer.