B737 FLT CREW REPORTS CAPT'S WINDSHIELD FAILURE AT FL380 AND DIVERSION. DURING TAXI IN ACFT DEPARTS PAVED SURFACE BUT IS ABLE TO CONTINUE TO GATE WITH NO DAMAGE.

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FERRY FLT (2 PLTS; NO OTHER CREW OR PAX) FROM ZZZ1 TO ZZZ2 DEPARTED ZZZ1 AT XA45. 1 HR INTO THE FLT AT FL380 AND AROUND .730 MACH; A LOUD 'POP' WAS HEARD AND CAPT'S FORWARD WINDSHIELD CRACKED WITH A COMPLETE SHATTERED APPEARANCE. ACCOMPLISHED CHKLIST AND INITIATED DSCNT TO 14000 FT MAINTAINING LOW CABIN PRESSURE DIFFERENTIAL. XFERRED ACFT CTL TO FO AND COMMUNICATED SITUATION TO COMPANY. AGREED WITH DISPATCHER TO DIVERT TO ZZZ. DECIDED TO MAINTAIN 14000 FT RATHER THAN LOWER TO ENSURE ENOUGH FUEL FOR DIVERT. GOOD WX AND VISIBILITY THROUGHOUT FLT AND FO'S VISUAL APCH AND LNDG ON RWY XXL. STILL NIGHT CONDITIONS AT XC30 AT TOUCHDOWN AND TAXI OFF. I TOOK BACK CTL DURING ROLLOUT AS I COULD SEE THE GREEN CTRLINE LIGHTS OK AND THEN INSTRUCTED BY TWR TO CROSS RWY XXR. AFTER XING WE WERE NBOUND WHEN THE CTRLINE LIGHTS ENDED AND WE SAW OUR PARKING RAMP AHEAD. THE FO BEGAN CHANGING RADIOS FOR RAMP ENTRY AND AS WE SLOWLY CONTINUED FORWARD IN MY MIND WITH THE LIMITED VISIBILITY I THOUGHT TXWY CONTINUED ON. IT DIDN'T AND WE ROLLED OFF THE PAVEMENT INTO THE GRASS. I REALIZED WHAT HAD HAPPENED AND STOPPED THE ACFT. THE GND WAS FIRM AND TXWY LIGHTS AHEAD RECESSED SO I KNEW WE COULD CONTINUE. FO NOTIFIED ATC GND OF OUR SITUATION AND ASKED PERMISSION TO CONTINUE WHICH WAS GRANTED. REMAINDER OF TAXI WAS UNEVENTFUL TO OUR GATE. POSTFLT WALKAROUND REVEALED NO ACFT DAMAGE AND CTL TWR TOLD ME THEIR INSPECTION OF TXWY LIGHTS REVEALED NO DAMAGE AS WELL. CONTRIBUTING FACTORS ARE LIMITED VISIBILITY; FATIGUE AND NIGHT CONDITIONS. I CONSIDERED HAVING THE ACFT TOWED ONCE CLR OF RWY; AND WOULD HAVE HAD THERE BEEN PAX ON BOARD; BUT MY DESIRE TO 'ACCOMPLISH THE MISSION' LED ME TO BELIEVE I COULD OVERCOME MY FATIGUE AND WINDSHIELD DAMAGE TO FINISH THE JOB. ALSO; MY FAMILIARITY WITH ZZZ CAUSED ME TO SEE SOMETHING THAT WASN'T THERE.