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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.

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Mountainhawk
7/29
Read that the Phillies scouts have left Seattle before seeing Halladay pitch, and they have essentially finalized a deal with Cleveland: Cliff Lee + unknown for Knapp, Carrasco, Marson, and Donald. I wonder how much return on Halladay the Blue Jays just lost if this is true, and the strongest pursuer of his services is out.
Mountainhawk
7/29
Deal pending medical record review: Cliff Lee and outfielder Ben Francisco for Class A right-hander Jason Knapp, Class AAA right-hander Carlos Carrasco, shortstop Jason Donald and catcher Lou Marson, according to major-league sources.
prs130
7/29
The chart is kind of silly... nobody is trying to get Halladay for the purpose of making the playoffs. As a Phillie fan, I want that second bullet specifically for the postseason. I'm pretty confident (79.7% sounds about right) that the Phils can outslug mediocre opponents for the next two months and win a weak division. What I really want is that second bullet to use against the Dodgers & Cards.
rowenbell
7/29
A more refined approach to this type of analysis could focus on the change in the likelihood of advancing to the World Series, taking into account the heightened utility of a Halladay-type pitcher in short-series playoff baseball.
padresprof
7/30
The chart is exactly the answer to the question MOST GMs are asking - how much will this trade increase my team's probability of making the playoffs. The Dodgers, Yankees and maybe the Phillies don't need to ask this question, but most teams do. The next part is to ask - given this probability, does it make economic sense? Teams have to pay for him and evaluate the loss of potential income from the players they give up. And yes, this calculation includes the potential gain of moving through the playoffs to the WS.
padresprof
7/30
And this calculation is essentially what Matt Swartz performs in his article: http://www.baseballprospectus.com/article.php?articleid=9263
stately
7/29
Umm...why don't you just list the teams in reverse order by their current odds of reaching the playoffs, because that's what this list is. Obviously teams with a high probability of reaching the playoffs have less room for improvement. This calculation is absurd. Maybe you should subtract pre from post? That would certainly give us a better idea of the impact of adding Halladay to one of these teams. Otherwise this exercise is pretty useless.
jjaffe
7/29
Most of the margins via subtraction wind up in a very narrow band, with eight teams gaining between 20-24 percent. Particularly after a criticism of a previous piece involving using subtraction and playoff odds, I found this way to be more instructive; that a team's odds would nearly double seemed like an idea worth expressing. YMMV, I guess.
birkem3
7/29
But at the same time, how much would a team like the Pirates gain from acquiring Halladay? Would their playoff odds be 30x higher with Halladay?
Mountainhawk
7/29
Probably not. Adding 2 wins to the Pirates would actually have negative value if it moved them down in the draft a couple of spots.
birkem3
7/29
By gain, I was merely referring to their playoff odds.
jjaffe
7/29
The Post/Pre number isn't the be-all and end-all of the story. If you read the article, you'd see that I dismissed the idea that any of the top six teams - the ones greater than 2x - acquiring him because their odds would still be so slim. That goes for the Pirates several times over.
NathanJM
7/29
Yeah I think you have the right idea in the article, it just isn't apparent in the table, so why bother calculating it? It's a great idea to try and come up with an RH factor though! We're just thinking of ways to improve it I think :)
NathanJM
7/29
Yeah I have to agree, the divide-by calculation doesn't make much sense. That said, neither does the subtration (although the subtraction would lead to more-useful information about who is probably going to be more-motivated to make a move?) What would be interesting to see (and maybe it is in this chart, just not very visibly) is just by how much a team landing Halladay improves their playoff chances...not just by comparing their straight odds with/without but also showing how the odds of their competitors decreases within the division & wild card. You could then find the team that stands to gain the greatest marginal benefit (either widening their lead in their division or narrowing the gap to catch up). For added fun you could even re-set replacement level to the appropriate 5th starter. For instance a closely-competitive division like the AL central has a bunch of team that are in pretty close contention (Twins, Sox, Tigers). Although any of them landing Halladay wouldn't increase their odds too much, by how much would it separate them from the pack? A similar thing could be done to look at changes in odds once IN the playoffs (much harder to do w/o knowing the playoff teams, but maybe you could make a rough approximation by re-setting replacement level to be the 3rd starter or something.) It might not play directly toward explaining the current teams going after him, but it would be interesting to see.
DrDave
7/29
Um, subtracting the before from the after is exactly what you want -- it already factors in your opponents' change in odds. Think of it as having a board-game-type spinner, with a dial divided into "playoffs" and "go home". Adding Roy Halladay replaces a portion of "go home" with a new section labeled "playoffs because of Roy". Subtracting the before odds from the after odds tells you how big that new section is. As others have noted, using the ratio is particularly uninformative when dealing with small probabilities. Knowing that a certain behavior triples your risk of cancer sounds bad -- until you learn that it takes the odds from 1:30000 to 1:10000. The question you should care about is "what are the chances that this behavior will cause me to get cancer?", and that's what subtraction answers.
jjaffe
7/29
Interesting point. In the interest of providing people with that particular flavor, here are the subtractive numbers: Rangers 23.8 Tigers 23.5 Cubs 23.4 Rays 23.2 Braves 22.4 White Sox 21.6 Cardinals 21.4 Rockies 20.6 Red Sox 18.5 Angels 16.3 Giants 16.0 Marlins 14.2 Phillies 12.8 Astros 11.4 Brewers 10.8 Yankees 9.4 Mariners 9.3 Mets 7.1 Dodgers 1.0
aaronbailey52
7/29
The last thing the Giants need is a starting pitcher, yet they have an RH factor over 2? Was this chart based on the average 5th starter's stat line, or on precisely who Halladay would replace? Clearly either the comment is wrong, or this chart is way too loosey goosey for anything more than the most casual of uses.
jjaffe
7/29
"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." FYI, Jonathan Sanchez is at 0.0 WARP1 right now, Ryan Sadowski at 0.1.
jjaffe
7/29
And Johnson's out until September, leaving both in the rotation and Zito as the #3 unless they make a deal.
Richie
7/29
I thought the 'Secret Sauce' flatout proved Halladay-type starters don't have any heightened utility in post-season series, no more so than comparably-gifted position players.
jjaffe
7/29
You've overstated that considerably. The Sauce findings in BBTN showed that the quality of the top three starters (as measured by VORP) doesn't have any statistically significant impact in predicting playoff outcomes. To my knowledge, Nate Silver and Dayn Perry didn't test for the impact of a single ace. Even so, a pitcher such as Halladay who's able to help raise a team's strikeout rate -- one of the three key factors in the Sauce -- will improve a team's chances.
llewdor
7/29
Isn't this the wrong way to look at it, though? Sure, some teams don't need Halladay to reach the post-season, but what does Halladay do to their Secret Sauce numbers? Acquiring Halladay might be done with an eye to winning in the postseason, not just getting there.
jjaffe
7/30
While Secret Sauce rankings have some predictive value, they don't really translate into a head-to-head measure which lends itself to a game-by-game based odds analysis the way our Playoff Odds do. Since there aren't many teams with a #5 starter averaging 6.8 EqK9, the chances are Halladay would raise their strikeout rates, but only by a microscopic amount. If you figure he throws 100 innings for the new club with 2 K more per nine over the #5 guy he's replacing, that's only 22 extra strikeouts over the remainder of the season. Spread that across a full season load of around 1450 innings, that's a net addition of 0.13 K/9 - worth no more than a couple points in the Sauce rankings, certainly not enough to tell us much definitively about a team's increased chances in the postseason. The bottom line is that any short series is such a crapshoot that the addition of a single player may not wind up providing much predictive value, at least without knowing the context of a given matchup. If you can figure out a way to quantify that, knock yourself out, but failing that, please, don't sit there and tell me I've gone about this the WRONG way.
padresprof
7/30
I'm wondering if the comments on this page criticizing the article reflect an ingrained view that single games can be predicted sufficiently well enough that people can predict winners with near perfect accuracy. Essentially, that the random element found within sporting events can always be argued out of the equation. We see this often in the writeups of individual games. For example - the reason the Rays lost 3 to 2 is because the team didn't come up with the key hit. Hence there are no clutch players on the team. So the goal of BP should be to predict the outcome of every game rather than giving us probabilities. That is why BP is always doing it the wrong way. "sarcastic :) "