QUESTION: How can hull shape prevent broaching and pitch-poling which occur during heavy weather sailing?
ANSWER: By carefully balancing the ends of a yacht hull's shape so the hull trims level even while heeling during heavy weather sailing.

Sea Kindly Balanced Ends

The LCB acts like a fulcrum. As the LCB moves aft on this wide transom racing yacht, the hull pitches down to compensate. An acceptable option for a racing hull with a racing crew, but this is not a sea kindly hull shape for serious offshore cruising hulls.

The moderate transom width on a Caliber assures a stable course even when the winds and seas build up. The Caliber hull will tend to gently heel while maintaining a level trim. In other words, the bow does not automatically lower as the wind and heel increase. It is difficult to broach a balanced hull design.
From “Seaworthy Offshore Sailboat” by John Vigor
               “Imagine a boat shaped like an old-fashioned flat iron-- almost triangular in shape, pointed in front and wide at the back. Now think what happens when that boat heels under sail. The bow end sinks slightly because it has little buoyancy; the stern end rises much more because it has excess buoyancy.
              Now that the stern has less grip on the water than the bow has, the stern tends to be blown downwind through the water and the boat weathercocks into the wind, pivoting from the bow. This is called griping [broaching].”
From “Rough Weather Seamanship” by Roger Marshall
               “The stern shape is critical to the boat’s behavior. A boat with a large, fat stern and fine bow will tend to sail bow-down as it heels, which can cause the rudder to lift out of the water slightly and become less efficient. The boat may also be more prone to broaching in heavy weather [...]”
From “Modern Cruising Under Sail” by Don Dodds
               “If the stern gets too wide it can create turbulence; it also adds wetted surface when hard on the wind at larger angles of heel. As I discussed earlier, stability problems have been blamed on excessive width in the stern.”
From “Seaworthy Offshore Sailboat” by John Vigor
               “Designers of oceangoing cruisers try to balance the ends of a boat by keeping the submerged areas fore and aft roughly equal at all stages of heel. This results in a boat that is easily balanced by varying the areas of sail fore and aft of the mast. Such a boat obeys the helm easily and quickly in all conditions without excessive strain on the rudder. It is a great safety feature”