Should the Washington Nationals Rest Scherzer, Risking Home Field Advantage?

The Washington Nationals have clinched a wild card spot, but are only one game up on the Milwaukee Brewers for home field advantage in the NL Wild Card game. The Brewers have been red hot, with a 19-4 record in the month of September. 

Meanwhile, the Nationals have one of the best rotations in baseball, with Max Scherzer and Stephen Strasburg ranking #2 and #3 in the NL, respectively, in pitcher WAR this season.

Scherzer is their best pitcher. And he's currently in line to start the last game of the regular season on Sunday. However, that would burn him for the one-game playoff next Tuesday. So which is more valuable? Scherzer pitching in the NL Wild Card game, or the Nationals retaining home field advantage?

My colleague answered this question via FiveThirtyEight's pitcher ratings:

Using 538's Elo rating, they have Scherzer (30) as worth 11 more points than Strasburg (19). However, they have HFA listed at 24 points, which is actually doubled to 48 points if you take the HFA away from WAS and give it to MIL. So Strasburg at home is worth 43 points and Scherzer on the road is worth 6 points, a difference of 37 points! So they theoretically should keep Scherzer on normal rest this week as long as HFA is still on the line.

Per the Elo formula and FiveThirtyEight's ratings, the Nationals would be 54.4% favorites on the road with Scherzer, and 59.7% favorites at home with Strasburg. So they should maximize their chances at retaining home field.

I checked this using my play-by-play MLB simulator, assuming that the Brewers' top arm, Brandon Woodruff, would start in either wild card scenario. I found similar results: the Nationals win 57.5% of the time on the road with Scherzer, and 59.9% of the time at home with Strasburg. Both pitchers are really good! So home field is the deciding factor.

And for the Brewers to maximize their chances of winning, they have to chase either pitcher early: Scherzer's average start in Milwaukee is 6.08 innings in a Brewers win, but 6.49 innings in a Nats win. Strasburg's average start in Washington is 5.79 innings in a Brewers win, but 6.25 innings in a Nats win.