In chapter 12 of The Just Men of Cordova (1917) by Edgar Wallace, the author was describing the situation of two horses, Nemesis and Timpolino, in the betting on horse racing:
The previous day, on the opening of the racing season, his stable had run a horse in a selling plate, and it was encouraging that this animal, though carrying top weight, beat his field easily. It was this fact that had brought Nemesis to the position of short-priced favourite.
Gresham himself had very little money upon her; he did not bet very heavily, though he was credited with making and losing fabulous sums each year. He gained nothing by contradicting these rumours. He was sufficiently indifferent to the opinions of his fellows not to suffer any inconvenience from their repetition.
But the shortening of price on Nemesis was a serious matter for the connection of Timbolino. They could not cover their investments by “saving” on Nemesis without a considerable outlay.
I found by searching, and through this link, that the one, who "saves" in betting, makes something like "reserve betting" on another horse, to insure he won't lose all his investment. But I still don't get the meaning of this bolded statement. And what's the connection between the team of Timpolino and the betting on Nemesis?