Mr. Sappleton plays a very small role in "The Open Window." He is mainly one of the imaginary "ghosts" who appear heading for the open French window towards the end of the story and frighten Framton Nuttel so badly that the poor man goes running out of the house and down the country road. In plotting his story, Saki must have decided that he wanted to get all the men out of the way so that he would only have to deal with three characters: Framton, Vera, and Mrs. Sappleton. However, the author had to show the presence of the entire family, so he conceived the idea of having the three men all out hunting, and this gave him the idea of having Vera use them for her ghost story. She describes them in some detail to Framton, including the following.
Poor dear aunt, she has often told me how they went out, her husband with his white waterproof coat over his arm, and Ronnie, her youngest brother, singing 'Bertie, why do you bound?' as he always did to tease her, because she said it got on her nerves.
The white waterproof coat will serve to identify Mr. Sappleton. No doubt he is the member of the family to whom Framton's sister's letter of introduction was addressed. His only dialogue is the following.
"Here we are, my dear," said the bearer of the white mackintosh, coming in through the window, "fairly muddy, but most of it's dry. Who was that who bolted out as we came up?"
Mr. Sappleton's role is to frighten poor Framton as well as to serve as a spokesman for the other two hunters. His dialogue establishes beyond a doubt that he is not a ghost but just an ordinary country squire who has been out hunting. Vera has done such a good job of creating her story and acting horrified when the three men appear in the gathering dusk that the reader needs to be informed of the true facts. The men were never sucked into any bog. Vera just made up a story as a practical joke, and then she enhanced its effect by playing a role in her own little drama. Mrs. Sappleton cries:
"Here they are at last. Just in time for tea, and don't they look as if they were muddy up to the eyes!"
Framton turns toward Vera to give her a look of sympathetic understanding, but:
The child was staring out through the open window with a dazed horror in her eyes.
This goggle-eyed look further serves to identify the three men as the ones who were supposedly killed by being sucked into a bog. Mrs. Sappleton's description of her husband and two brothers as looking "as if they were muddy up to the eyes" is important to the deception because their muddy condition, along with her husband's statement that they are all "fairly muddy," suggest they could look is if they had just managed somehow to pull themselves out of that bog after being entombed in it for three years.