In prior years, the various versions of Baseball Prospectus’s Playoff Odds Reports were slow to respond to changes in lineups. All of them required the team to start playing differently-sometimes as a result of trades or injuries-before any change would be seen in the playoff odds of the various contenders, and those changes would be pretty seriously depressed by the weight of all the games that had come before.

This year, as a direct result of changes in the way we’re running our depth charts, for one of the versions we have done away with any feedback from actual team performance in setting the win percentage that drives the playoff odds program.* The PECOTA-based version of our playoff odds is being entirely set by our projections of player performance. The rates of player performance come from the pre-season PECOTAs, but modified to include some information about how the player has performed so far this year, which Eric Seidman discussed in an Unfiltered post last week. The volume of performance is set by the depth charts, which ultimately means by me, since I’ve taken the final say on all changes to the depth chart master program. For the PECOTA-based playoff odds, a trade or injury has an immediate impact on the team’s expected performance-we can anticipate the change in team performance without waiting for the signal to appear, and its effects on the post-season odds is immediate.

In order to try to isolate the effect of roster changes on the results, we took the assigned playing time distributions from July 23-the day before the Matt Holliday trade-and pasted them into the current set of the depth-chart program. I had to do that; I made some changes to the routine in the last week, affecting how pitchers who switched between starting and relieving would be treated, making them somewhat better when relieving, and we certainly didn’t want changes because of that to affect these results. Those results, which are projections based on week-old lineups, were then run through the standings projection routine starting today, so that the results of games played in the interim would not affect these results, although you can certainly argue that they should be affected if the traded player appeared in them. I’ll plead that the desire to explore the changes in the lineups demands that the two sets of projections be run from identical data sets, which is why I’m not simply looking up the odds for today, and the odds a week ago, and taking the difference.

It turns out that the best team in terms of improving their chances at a playoff spot is the Cardinals, who essentially replaced a Chris Duncan/Rick Ankiel combo projected to hit for about a .260 Equivalent Average (EqA) with Matt Holliday, projected to hit about .315. That’s worth 15 runs on the rest of the season. They also picked up Julio Lugo, a significant upgrade at the plate from Brendan Ryan for at least part-time play; having Lugo and Ankiel as your main spares allows some addition by subtraction, with the ripple effect of their jettisoning some of the fringe players on the roster. The Cardinals’ expected record jumped by 18 points as a result of all the moves, and their playoff chances increased from 59 to 69 percent.

The team that had the biggest change in its expected winning percentage however-a 42-point gain, well over twice what the Cardinals added-is the Florida Marlins. Their only trade was to bring in Nick Johnson from the Nationals, but he essentially replaces Emilio Bonifacio in the lineup, meaning you’re replacing a .220-ish EqA with a .300ish EqA. The picture is complicated by internal changes in the pitching staff that happened at the same time-ditching Andrew Miller for now, getting Matt Lindstrom back from the DL-that also helped to inflate their expected win total. Still, having the best win-percentage increase only gets them a four-point gain in their playoff odds, from just three percent to seven percent, which was also the fourth-largest improvement by any club. The system still likes the Phillies and Braves a lot more than it does the Marlins, and it doesn’t see many opportunities for outdoing those two teams.

The single best player to move during the deadline was Cliff Lee, picked up by the Phillies. They also picked up Ben Francisco, who will be a useful outfield backup, and didn’t give away anyone that was part of their playoff run. That combination netted the Phils a 23-point gain their expected record, the third-best mark in the majors. Their odds gain was just slightly enough for second place, as they went from a 70 to a 76 percent chance of making the playoffs, a gain entirely concentrated in their chance of winning the division; their wild-card chances actually dropped.

The second-best team from an added wins perspective, and just barely missing the second-best odds gain, was the Tigers. Jarrod Washburn provides most of the lift, providing Detroit a big upgrade from Lucas French in the rotation, but they also benefit from Carlos Guillen‘s return from the DL (in part because that forced Josh Anderson out to Kansas City). Another part of the lift is that they still have nine games with the Indians, who rank as the largest casualty of deadline moves-the Tigers pick up more than two-thirds of an expected win just in those games against Cleveland. In all, they moved up 25 points in record and six points-from 29 to 35 percent-in their chances.

Next we see the San Francisco Giants. They combined an 18-point gain in win percentage with a four-point gain in their playoff chances, but they are still outsiders; the gain was only from 13 to 17 percent. Their big moves were upgrades at first and second base, with Ryan Garko and Freddy Sanchez moving in. The fact that they get this kind of result from bringing in Garko and Sanchez, who can’t really be considered to be big-name players, points out just how desperate the Giants were, particularly at second-Emmanuel Burriss, Matt Downs, and Kevin Frandsen combined for a .187 EqA this year. Still, the Rockies and Dodgers are significant obstacles for them to overcome, and someone to improve on Ryan Sadowski in the fifth starter spot would have been nice.

The most prolific trader, the Red Sox, show modest gains in both their record (+16 points) and their odds (two points); once you’re at 90 percent, like the Sox were, their isn’t much room left to grow. Adding Casey Kotchman and Victor Martinez were fine add-ons, but the Sox weren’t exactly suffering at those positions this year, and they did give up some decent players like Justin Masterson to get them. Still, the playoff odds overwhelmingly point to a Yankee/Red Sox playoff tandem, one winning the division and the other winding up with the wild card.

As for everyone else, and all that activity? No one else gained in the standings.

On the flip side, the biggest losers in terms of record is considerably different from the biggest losers in terms of odds. The biggest losers in record tended to be teams who were already all but eliminated from playoff contention already: the Indians, Pirates, Athletics, and Nationals had a combined 0.7 percent chance of making the playoffs before the trading started, and they dropped all the way to 0.1 percent afterwards. That’s an all-but-unnoticeable ripple in the ooze at the bottom of the pond. The Indians’ projected record dropped a staggering 50 points to “lead” everyone.

The biggest playoff odds losers were the teams who were in contention but stood pat at the deadline while their competition made moves to improve. The playoffs are very nearly a zero-sum game, where if you make it, I don’t. Those gains that the Cardinals, Phillies, and Tigers ran up had to come from somewhere. They came, respectively, from the Braves (who dropped from 46 to 39 percent), the Cubs (dropping from 52 to 45 percent), and the White Sox (from 55 to 50 percent).

Wait a minute, the White Sox, losers? They didn’t stand pat; they picked up Jake Peavy, who if he wasn’t hurt would contend with Lee for the title of “best player traded.” Their expected record also improved by nine points, largely due to their remaining games with the Indians. However, it is possible, from a making-the-playoffs perspective, that they might have done better not making the trade: Peavy is injured and going to miss about half of what’s left of the season, while two of the players they gave up, Richard and Poreda, were useful members of the team now, and their expected contributions over two months were likely to exceed what Peavy can do in one.

Paradoxically, though, Peavy almost certainly strengthens the team in the playoffs, assuming they get in. For the sake of argument, let’s unreasonably assume that the Sox have a 50 percent chance of winning each playoff series. If he raises that by even two points, to 52 percent, he just raised their chance of winning the World Series, even with the drop in making the playoffs. The math:

Win Series with Peavy = .50 (make playoffs) * .52 ^ 3 (three rounds of playoffs) = .070
Without Peavy : .55 (make playoffs) * .50 ^3 (three rounds) = .069

Is that significant? No, but it is interesting, at least to some of us.

*: Well, mostly. Changes in player performance do lead to changes in the player’s projection, so some measure of the team’s performance is still going to sneak in through that back door.

A version of this story originally appeared on ESPN Insider Insider.

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Without doing any math, I would guess that Washburn would be the player that most increased his new team's chances of winning the series. Is that even remotely accurate?
So what do you think of Peavy in a bandbox?
Any chance we can get the list of how much each team's playoff odds and expected winning percentage?
It seems to me that Kenny Williams took on quite a financial burden to give his team a 0.1% greater chance of winning the World Series.
Yeah, hs should have ehecked the PECOTAs before he did that.
The 0.1% figure assumes that Peavy improves the team's chances of winning any particular playoff series from 50% to 52%. That's an arbitrary assumption, chosen to make a point. Peavy's actual impact from a World Series perspective could well be greater.
As a Nats fan, I'm also curious about how the deadline dealing affected the Nats (and others) chances in the "Bryce Harper Sweepstakes," i.e., the odds of getting next year's #1 draft pick. Maybe the Royals traded for Betancourt to try to catch the Nats. If Strasburg fails to sign with the Nats, what are the odds the Padres (his home town team) have the first or third pick next year? Lots of interesting questions down at the bottom as well.