Diamondbacks Playoff Odds Revisited

About three weeks ago, shoewizard wrote a Fanpost looking at the Diamondbacks' play-off odds, which Baseball Prospectus then rated at an unimpressive 3.6%, as we sat four games back of the Giants. Here's what he wrote:

Giants at 58-43 have a .574 Win %. If they maintain that pace the rest of the season they finish 93-69. The D Backs at 54-47 have a .535 Win %. To finish with 94 wins they have to go 40-21 the rest of the way, which is a .656 Pace! So the Giants better slow down or we have no chance.

Ask and ye shall receive. Since then, we've gone 12-6, while San Francisco has gone 6-12, and we are now two games ahead of them as a result. Let's revisit the numbers the rest of the way, now the boot is on the other foot...

Scenario 1: Diamondbacks maintain current Win % (.555).
At that pace, we would go 90-72. To finish with 91 wins, the Giants would need to go 27-16 the rest of the way. That's a .628 W%: Only the Phillies have managed that in the NL; the second-best W% is the Atlanta Braves .588. To put those 27 wins further into context, the Giants have achieved that number only over their last 53 games, having gone 27-26. That's ten more than they have left to play.

Things are made more interesting by the fact that we have six games left against the Giants. With Arizona currently in the lead, simply playing the Giants even in those contests would work in our favor, since it would mean six fewer games in which San Francisco would catch up. Let's assume, for the purposes of thought, that the D-backs play .555 baseball over the 37 games against non-Giants. That would give us 20.5 additional wins, putting us on 86.5 wins before playing SF. The list below shows what the Giants would need to do in their 37 non-Dbacks games to beat us, based on the result of their games against us.

• If we go 6-0 (92.5 wins), SF has to go 29-8
• If we go 5-1 (91.5 wins), SF has to go 27-10
• If we go 4-2 (90.5 wins), SF has to go 25-12
• If we go 3-3 (89.5 wins), SF has to go 23-14
• If we go 2-4 (88.5 wins), SF has to go 21-16
• If we go 1-5 (87.5 wins), SF has to go 19-18
• If we go 0-6 (86.5 wins), SF has to go 17-19

The Giants current W% of .538 is 20-17 over 37 games. So if they did that in the match-ups against other teams, we could lose both series, going 2-4, and still win the West. We no longer need to beat them head-to-head. Simply holding our own, at the current paces for both sides, will be sufficient. Of course, defeating them would make their task close to impossible, requiring them to win two out of every three games against everyone else.

Scenario 2: Diamondbacks maintain current Pythagorean W% (.520).
The Diamondbacks have, to some extent, over-performed. Based on their runs scored and allowed, the Pyhtagorean W% says they would be expected to have won about four games less than they have. This is largely due to Arizona's excellent record of 22-13 in one-run games; those are generally thought to be a random outcome. Now, the Giants have over-performed to an ever greater degree - Pythag projects them to have won six less games - but let's assume just that Arizona drops back to .520. That would be 22 wins, giving them 88. To reach 89, the Giants would still need to go 25-18. That .581 W%, is still well ahead of their current .538.

Repeating the exercise described above for the Giants series, what do we find? .520 over 37 non-Giants games is a 19-18 record, putting them at 85 wins, plus the games against San Francisco

• If we go 6-0 (91 wins), SF has to go 28-9
• If we go 5-1 (90 wins), SF has to go 26-11
• If we go 4-2 (89 wins), SF has to go 24-13
• If we go 3-3 (88 wins), SF has to go 22-15
• If we go 2-4 (87 wins), SF has to go 20-17
• If we go 1-5 (86 wins), SF has to go 18-19
• If we go 0-6 (85 wins), SF has to go 16-21

It really doesn't make very much difference - San Francisco only has to win one game less, if the Diamondbacks were to regress to their Pythagorean record. And going 2-4 head-to-head would still leave the Giants needing to improve on the current, "lucky" [per Pythagoras] W% in order to come out on top.

Scenario 3: Diamondbacks play .500 ball.
As a final estimate, let's say Arizona simply plays even down the stretch, splitting the remaining 43 games. That's 21.5 wins, taking them to 87.5. To reach 88, the Giants still need to go 24-19, which works out at a .558 W%, twenty points better than they've done to date. And crunching the numbers as before, for the head-to-head games: 18.5 wins in the 37 non-Giants encounters = 84.5 wins, so:

• If we go 6-0 (90.5 wins), SF has to go 27-10
• If we go 5-1 (89.5 wins), SF has to go 25-12
• If we go 4-2 (88.5 wins), SF has to go 23-14
• If we go 3-3 (87.5 wins), SF has to go 21-16
• If we go 2-4 (86.5 wins), SF has to go 19-18
• If we go 1-5 (85.5 wins), SF has to go 17-20
• If we go 0-6 (84.5 wins), SF has to go 15-22

This is slightly more favorable for San Francisco, in that if we play .500 ball against the rest of the league, and go 2-4 against them, the Giants only need an 19-18 record elsewhere to take the division.

Conclusion
The boot is truly on the other foot now. It's San Francisco who need to be saying, "The Diamondbacks better slow down, or we have no chance." And yet, despite all this, Baseball Prospectus still gives the Giants a 74.4% chance of winning the division. Can we say "thoroughly discredited," children? I know I can... CoolStandings.com, on the other hand, has Arizona at 62.2% favorites for the NL West, which seems much more credible.

However, there are still 43 games left and we've seen how quickly things can turn. A bad patch for Arizona could certainly switch the tables back in San Francisco's favor, just as the Giants' implosion over the past three weeks has done so for the Diamondbacks. But, for now, the good news is that we no longer need to improve or hope for our rival to start losing, because both have already happened. Simply playing the way we have been, going forward, will likely be enough to take the Arizona Diamondbacks to the NL West title.