I seem to have forgotten that in the nightmare Padres scenario (where they lose tomorrow and the Rockies, Mets, and Phillies all win) they will have to play and win two games, not one, to get in the playoffs. Meanwhile, the Mets and Phillies need only win one game (or two out of three) and the Rockies need to win just one.
How does this change San Diego's fortunes from an odds perspective, and does this mean they should start Jake Peavy tomorrow?
If the Padres start Peavy Sunday:
They should win the game 57.2% of the time, clinching automatically. The 42.8% of the time they lose, they still get in automatically any time the Rockies lose and at least one of the Mets and Phillies lose. This happens (27.3% * 42.8%) = 11.7%, for a total of 68.9% uncontested playoff berths.
The remaining 31.1%, they end up in at least one tiebreaker game. I won't bore you with the math here, but without the benefit of starting Peavy or Chris Young, they will emerge with a total percentage of:
80.7% Wild Card
If the Padres start Tomko Sunday:
Their chances of winning the game Sunday go down to 45.1%, and they win uncontested a total of 60.1% of the time. They get a huge boost in their first tiebreaker game, getting to start Peavy instead of Tomko. Again, lots of boring math gets skipped here, but the result:
80.0% Wild Card
However, this is not the end of the discussion. By adjusting Peavy's schedule, the Padres also adjust his availability for the NLDS. If they start him Sunday, they are assured of getting two starts out of him in their division series, provided they're willing to start him on three days' rest again in NLDS Game 2. However, if they let him rest on the Sabbath, 60% of the time they'll get him on full rest for two starts since they avoid any tiebreaker games. The remaining 20% of their playoff appearances, Peavy will get only one NLDS start.
Research tends to indicate that starting on three days' rest doesn't negatively impact performance that much, so I'd probably start Peavy (or Heath Bell) on Sunday. However, just because I would start Peavy on three days' rest twice in a row does not mean Bud Black will. Without that assumption, I think sacrificing .7% in Wild Card equity is worth getting Peavy rested for two games in the division series, so it looks like Black is making the right call given his own limitations.