If we played 15 home games a season from 1897 to 1901 (the Albion finished bottom that year. Ha) when we played 17 homes games, the that is 145 matches. From 1906 when we started playing 19 home games a season until the league was suspended at the end of the 1915 season, so another 171 games, giving us 316 so far.
We then had 21 home league games from 1919 up to 1995, minus 6 years for the war, so that is around 1540 games, providing a new total (give or take) of 1856.
It has been 18 seasons with 19 home league games, giving us another 342. Therefore, ignoring the FA Cup and from 1960 on, the League Cup, I would guess we've played a minimum of 2198 league games at the home of football.
I would also add that we have more than likely seen over 2000 top flight games of football at B6.