At 4:40 p.m. Eastern Time on Wednesday, J.P. Ricciardi’s self-imposed deadline to trade Roy Halladay will pass. At that point, the afternoon’s Blue Jays/Mariners tilt will be underway, and Toronto’s scheduled starter, by way of their general manager’s thinking, will no longer have a potential trade hanging over his head. Artificial deadlines are made to be broken, however, particularly by those who play as fast and loose with their public statements as Ricciardi. Inevitably, he’ll be fielding calls on his ace right up until 4 p.m. Eastern on Friday, the official non-waiver trading deadline, because Halladay would be a critical addition to the playoff chances of at least 10 teams.

Over the past few weeks, we’ve taken several looks at possible destinations and scenarios for dealing Halladay. Today’s approach calls upon the recent work done by BP Idol finalist Matt Swartz. In the service of an article focusing on the economic impact of taking on Halladay’s contract, Swartz used the binomial theorem to estimate a distribution for the expected remaining win total of each team, matched it to the team’s current playoff odds, and recalculated the distribution and odds given the bump that the addition of Halladay would provide over the course of the remaining season. The size of said bump is built upon the assumption that Halladay is worth 6.0 WARP, or six wins above a replacement-level fifth starter over the course of a full season; depending upon the remaining schedule for each team, that’s roughly a 2.3-win upgrade at the moment.

Here’s how the field of contenders (and pretenders) changes with the addition of Halladay, with numbers through close of play on Monday, and odds refigured by Swartz:

Team        Pct3    W-L    Pre%  Post%  RHFactor
Mets        .490   47-51    3.1   10.2   3.29
Mariners    .498   51-48    4.8   14.1   2.94
Brewers     .461   49-50    6.1   16.9   2.77
Astros      .459   50-49    6.6   18.0   2.73
Marlins     .482   51-48    9.6   23.8   2.48
Giants      .478   53-46   11.9   27.9   2.34
White Sox   .505   51-49   25.2   46.8   1.86
Braves      .535   51-48   26.9   49.3   1.83
Rays        .584   54-46   34.0   57.2   1.68
Rangers     .524   55-42   35.5   59.3   1.67
Twins       .519   50-50   36.6   59.8   1.63
Tigers      .490   52-46   37.9   61.4   1.62
Cubs        .502   52-45   44.5   67.9   1.53
Cardinals   .517   54-48   52.8   74.2   1.41
Rockies     .540   54-45   59.2   79.8   1.35
Red Sox     .563   58-40   66.0   84.5   1.28
Angels      .532   58-40   71.9   88.2   1.23
Phillies    .520   57-40   79.7   92.5   1.16
Yankees     .582   61-38   86.0   95.4   1.11
Dodgers     .581   62-37   98.8   99.8   1.01

To define terms, Pct3 is a team’s third-order winning percentage, their Pythagorean winning percentage after adjusting for scoring environment, run elements, and quality of opposition; WL is the team’s actual record, Pre% is their current percentage chance of making the playoffs as per the plain vanilla version of our Playoff Odds report (as opposed to the one based on PECOTA), Post% is their estimated chance of making the playoffs with that 2.3-win upgrade, and RHFactor or “Roy Halladay Factor” is their Post%/Pre%.

The Mets, for example, would more than triple their chance of making the playoffs, either by winning the NL East or Wild Card. Even so, they’d be left with a 1-in-10 shot, still very long odds. The five teams ranked below them here (or above them in terms of current playoff odds) would more than double their chances at an October berth, but from among that group only the Giants would have even a 1-in-4 shot after his addition, and the last thing they need is starting pitching. For such teams, emptying the minor league system to acquire Halladay in the service of such a longshot is a terrible idea, not that any of those six are seriously entertaining the notion.

At the other end of the spectrum are the teams whose chances of making the postseason wouldn’t increase by very much at all, a class in which the Phillies, who have pursued Halladay the most heavily out of the need to patch their struggling rotation, now find themselves. Back when I first addressed the prospect of the defending World Champions trading for Halladay, the Phils were 44-38, leading the NL East by two games, but with four teams within 4½ games. Their odds of making the postseason stood at 52.8 percent, but their rotation’s ERA was a bloated 5.02, second to last in the league. Since then, they’ve gone 14-2 and increased their division lead to seven games thanks in part to a 3.12 rotation ERA. While acquiring Halladay would surely improve their chances once they make the postseason, their immediate need isn’t so acute.

In all, nine teams would increase their chances of making the playoffs by between 35 and 86 percent by acquiring Halladay, the worst of whom, the White Sox, would wind up just shy of a 50-50 shot. Of those nine, the NL teams have demonstrated less need for pitching; the Braves, Rockies, Cubs, and Cardinals rank first, third, fourth, and sixth in the league in starting pitcher ERA, and they round out the top five in SNLVAR behind the Giants as well. Among those teams, the Cubs, for whom Ted Lilly and Ryan Dempster recently traded DL and rotation slots, would be a logical fit, at least if their farm system weren’t so bereft of upper-level talent and the ownership situation so messy.

The AL teams in that sweet spot have more pressing rotation needs. The Twins (12th in rotation ERA, 10th in SNLVAR) just lost Kevin Slowey for the season, leaving three starters with ERAs above 5.00 in Scott Baker, Glen Perkins, and Francisco Liriano. The Rays (ninth in rotation ERA, eighth in SNLVAR) have David Price (5.60 ERA) and Scott Kazmir (6.22 ERA even after a strong start against the Yankees on Tuesday night) significantly underperforming. The Rangers’ rotation (sixth in both categories) has the league’s lowest strikeout rate and worst strikeout-to-walk ratio, not to mention Derek Holland (6.13 ERA) taking poundings that tax the bullpen. Even the Tigers, who rank second in both categories, have Armando Galarraga and Rick Porcello with ERAs creeping towards 5.00; the latter’s been bombed for 19 earned runs in 18 2/3 innings over his last four starts.

Though their relative boost wouldn’t be as big, one could make the case that the Red Sox (seventh in both categories) and Angels (10th in rotation ERA, 12th in SNLVAR) belong in the discussion, too, given the state of their starting pitching. The Sox now have John Smoltz getting rocked, while Daisuke Matsuzaka and Tim Wakefield are on the DL; the Angels have Joe Saunders and Ervin Santana struggling to regain last year’s form, with ERAs of 5.02 and 7.29, respectively.

Counting those two teams, that makes for 11 legitimate contenders for whom the acquisition of Halladay would more significantly boost their playoff push than for the Phillies, the current favorites to land him. Whether any of them have the will and the wares to entice the Blue Jays remains to be seen, but don’t be surprised when the phones keep ringing past Wednesday afternoon.

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