John Guiney, chief of the Meteorological Services Division at NOAA's National Weather Service, Eastern Region, offers this answer.
The proposition that waves always break in odd-numbered groups may be more anecdotal than fact. Perhaps the best way to approach this question is to provide some information on ocean waves and the processes that lead to their growth, travel and demise as breaking waves along the coast.
Wind produces all the waves in the world's oceans. There are two primary types of waves: wind waves and swells. Wind itself forms and sustains the former, which tend to propagate in the direction of the wind that forms them. Three factors govern the size and extent of wind waves: wind speed, the distance the wind blows across the water (also referred to as the fetch) and the length of time it blows. But once wind waves leave the area where the wind generated them, they are known as swells. Swells can propagate freely across the ocean independent of wind direction. is referred to as the wave's period. A swell with a period (the time it takes for a wave's crest and trough to pass a given point) equal to or greater than about 15 seconds can propagate across the ocean surface for thousands of miles with little loss of size or energy until it reaches shallow water in the coastal zone and breaks.
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Over distance and time, waves that move at nearly the same speed keep pace with one another and form a group. Wave measurements usually show a tendency for large waves to group together--often referred to by scientists as "groupiness." Normally, the number of waves in a group range anywhere from three to 15 or more, and it typically consists of smaller waves in the lead, larger waves in the middle and smaller waves again at the rear. This is because waves in the rear tend to move forward, build in size and then diminish as they reach the front. Although individual waves move at twice the speed of the group, they are bound to it by the energy they all share. Eventually, they travel at the group speed, which is defined as half the individual wave speed, in deep water.
This state of affairs only changes when wave groups encounter shallow water. When this occurs, the group speed and the individual wave speed become the same. As waves move into more shallow water, their speed decreases while their steepness, or height, increases. Here they are also influenced by the shape of the ocean floor itself. At roughly a depth of 1.3 times the wave height, the wave breaks and results in surf.
When watching the surf at the beach, you will notice that the waves are loosely grouped in periods of high waves alternating with periods of low ones, and that there are waves breaking that are larger than the surrounding waves. This can be caused by sand-bars. Waves that pass over a bar break and reorganize into new, smaller waves as they enter deeper water beyond the bar. Local winds and terrain effects can also influence waves at the coast and how or where they break. Surfers typically refer to wave groups in the surf zone as a set. These sets occur from every few minutes to once every half hour or more, depending on how far the waves have traveled to reach the coast. Hence, although waves do break in groups or sets, there is no evidence to suggest that the number of waves in a given group is anything but random.
