For an water polo officiating class we were asked, "which is more damaging, a counter or an exclusion?" Here is the analysis:
Given:
A good team scores on 15% of normal possessions, 50% of counters, and 50% exclusions. (Note: for normal possessions, I am averaging the 6 goals of 30 possessions with the "rarely better than 10%).
Find - which is more damaging:
A contra at the start of possession would be worth (+0.50 goals) to the offended team and the offending team loses (-0.15 goals). The offended team gains (+0.35 goals) per possession. A contra at the end of the possession would be worth nothing since the shot clock is expiring anyway. On average a contra is worth (0.35+0)/2 = 0.175 goals to the offended team.
An ejection at the beginning of the possession would be worth ((exclusion-normal)+0.50-0.15 = 0.35 goals) and the offending team loses nothing. An ejection at the end of the possession, the offending team loses a possession (-0.15) and the offended team gains a possession (+0.50 goals). This gives a 0.65 goal advantage to the offended team. On average, then, the ejection is worth (0.65 + 0.35)/2 = 0.5 goals to the offended team.
Results:
Therefore, an exclusion is 2.85 time more damaging than a counter. Q.E.D.
