Do In Reality line mares do well over jumps?
According to the Hannoverian people, jumping ability is highly heritable compared to other traits. It has a numerical value of 40 compared to other traits that have numerical values of less than 20. (If you're interested in the numbers, you can go to the American Hanoverian Society website and read their article about the heritability of various traits.)
The Man O'War line has a very long history of producing great jumps racers. From Battleship, who was the first American owned and trained horse to win the Aintree Grand National, up through Relic whose lines are still found in in France even today for jump racing. It all seems to go back to Rock Sand in the distant past, and Rock Sand was certainly used in multiple close crosses in the Man O'War family and connections. War Relic is the primary source of the jumping line today, and he's 3x3 in In Reality.
A Valid Expectations mare would be a good choice, since you really want French lines for stamina and jump. Once again, going back into the far, far past, the French Dollar line and the Le Sancy lines and Roi Herode all produced exceptional jumping horses, both for racing and for show. Since Running Stag has already got the Tourbillon line on the bottom, you could easily linebreed to reinforce "the jump". His German lines bring in the other great source of "the jump", which is Hampton/Bay Ronald.
Of course, the other really good choice for jump racing would be a Northern Baby mare. His offspring have been successful at jumps racing both here and in Europe. [/quote]