You have a choice. I’ll give you $100 right now, or you can let me flip a coin. If it lands on heads, I’ll give you $250. But if it lands on tails, I’ll give you $20. I’m using a fair coin, so the expected value of flipping the coin is $135 based on the 50/50 odds it lands on heads or tails. If you like risk or are a risk-neutral person, it’s an easy decision to take your chances with the coin because the odds are strongly in your favor. If you’re a risk-averse person, however, you’re more likely to take the sure thing because $135 isn’t a whole lot more than $100, and $100 is a whole lot more than $20.

Let’s add another wrinkle. It’s the same choice, but if you choose the coin flip, you have to wait a month. The dollar amounts are the same, but now there’s a time component. To get the value of the coin flip, you need to apply a discount factor to the $135. For some people, that discount factor is pretty close to one, but it might be much lower if you’re strapped for cash and the $100 would dramatically improve your life in the present.

Major league players face a much higher stakes version of this decision when their club comes to them with a contract extension. Do they take a sure thing now, or do they wait and gamble on themselves? While we’re focusing a lot on the 2015-2016 free-agent class this month, there are eight players who could have been free agents for the first time this year but instead chose to cash out early by signing extensions. Did they make the right decision?

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After having typically appeared in the very hallowed pages of Baseball Think Factory, Dan Szymborski’s ZiPS projections have been released at FanGraphs the past couple years. The exercise continues this offseason. Below are the projections for the Texas Rangers. Szymborski can be found at ESPN and on Twitter at @DSzymborski.

Other Projections: Atlanta / Cincinnati / Kansas City / Philadelphia / Pittsburgh / Toronto.

Batters
The Texas Rangers outperformed their Base Runs record by seven wins this past season, resembling on the peripheral level more a league-average club than a division-winning one. That’s not to discredit their accomplishment, at all. It does, however, begin to explain how a team that won 88 games and returns literally all its positional starters — how such a team could look so ordinary by way of computer algorithms.

It certainly isn’t an advantage for Texas that they have a considerable portion of their payroll allocated to four merely decent players. Elvis Andrus, Shin-Soo Choo, Prince Fielder, and Josh Hamilton are expected to earn roughly $88 million collectively this year and yet to produce fewer than six wins as a group. That’s approximately $15 million per win — or nearly double the current estimated win valuation of the market.*

None of this, of course, is to impugn Adrian Beltre, who famously once played both Daedalus and Icarus in a community theater production of Ovid’s Metamorphoses.

*Note: I’ve neglected to mention here that a portion of Fielder’s and nearly all of Hamilton’s contracts are being subsidized by other clubs. Naturally, that changes the dollars-per-win calculus. What it doesn’t change is the projections themselves.

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Though baseball’s Winter Meetings seem like the playground of the front office executive, there is one other baseball man who’s ubiquitous: the manager. Semi-required to attend media events and an annual luncheon, most of the sport’s managers descend on the meetings to make their mark.

For the most part, they field questions about next year’s lineup, and try to deflect queries about front-office moves. They’ll do a little reminiscing about last year, and a little looking forward to next year. It’s a bit of a dance, since most of the reporters are looking to find out how the roster is going to look on paper, and the person in front of them is mostly in charge of putting that roster on the field.

Still, it’s a great moment to get access to many managers at once. This past August, I asked a collection of players and writers how Bruce Bochy and Joe Maddon — managers with distinctly different approaches and pasts — could both find great success. I thought it would make sense to ask the managers gathered here about their craft, as well.

What has changed about managing? How are the demands on the modern manager different than they once were?

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Zack Greinke is one of the best pitchers in major league baseball, and as a result, he had no shortage of suitors before ultimately signing a contract in excess of $200 million. In addition to money, the Diamondbacks also surrendered their first-round pick next year, the 13th overall selection. While it would not be quite true to say that Greinke cost “only money,” the Diamondbacks did not give up a single active player in order to acquire Greinke.

Cole Hamels, both the same age as Greinke and roughly as effective over the course of his career, was traded over the summer. Hamels’ cost was not “only money,” as the Texas Rangers gave up six players, including three high-end prospects (and Matt Harrison’s contract), for Jake Diekman and the opportunity to pay Cole Hamels around $100 million over the next four years. While the costs come in different forms, we can compare the two to see how the trade market this past summer compared to this offseason’s free agent market for Greinke.

The Los Angeles Dodgers prioritized Cole Hamels at the trade deadline, but subsequently missed out by refusing to part with their best prospects. The team then prioritized bringing Greinke back, only to be outbid by division rival Arizona. The cost for both players was high, and it is difficult to say whether the Dodgers made a mistake passing on both players, but we should be able to compare the costs for both to see if the Dodgers could have kept a comparable pitcher for less than the amount Greinke received in free agency.

As far as comparisons go, Greinke did have a better year in 2015, but their cumulative WAR graphs (shown below) reveal two remarkably similar careers in terms of value.

In addition, both players are projected to do well next season. By Steamer, Greinke is set for a 4.2 WAR while Hamels comes in a bit behind at 3.6 WAR for the 2016 season. Using those projections as the baseline for future production, we can get an estimate for their value over the next few years. With deferrals, Greinke’s deal turns out to be $194.5 million over six seasons, per Ken Rosenthal. Given the consistency of both Greinke and Hamels, for the purposes of this analysis, we will assume the players will age well.

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On July 7th, 2006, a 23-year-old righty made his major league debut against the Tigers. He entered the game in relief and immediately began putting up 99s on the radar gun. It wasn’t enough, however, to prevent Chris Shelton from singling to shortstop and beating out the throw. Brandon Inge also wasn’t afraid of the velocity, as he hit a ground-rule double to center. The young righty was now flustered. He hit Curtis Granderson to load the bases. He paced around the mound, gathered himself, and then rallied to strike out Placido Polanco, get a weak grounder from Ivan Rodriguez, and strike out Magglio Ordonez to end the threat.

On that day, Mark Lowe began a journey that started with the Mariners and continued on to the Rangers (in the Cliff Lee deal), and then the Dodgers, Angels, Nationals, Rays, Indians, Mariners (again), and Blue Jays. And now, almost ten years later, the Tigers have signed him with a two-year deal to be their setup man. It’s been quite a trip for him.

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Before every game, we publish estimated game odds. The odds consider the identities of the starting pitchers, and as the first pitch draws closer, the odds update to factor in the actual starting lineups. I’m not saying it’s an infallible system or anything, but it’s a neat little feature we have, even if it doesn’t get all that much use. And though this is by no means a rigorous test, consider the top 100 most seemingly lopsided games from the season past. Based on the calculated odds, the favorites in those games should’ve won 70 times. The favorites actually won 71 times. So things check out.

The favorite won the game with the single most lopsided odds. Max Scherzer and the Nationals were projected to have 78% odds against Sean O’Sullivan and the Phillies. The favorite also won the next-most lopsided game, and the next-most lopsided game, and the next-most lopsided game, and the next-most lopsided game. The five games with the most imbalanced odds all went to the team expected to win. We find our first upset in sixth. Which would then qualify this as the season’s greatest upset, taking into consideration only pre-game odds. It was an upset when the Royals rallied past the Astros in the playoffs, but that wasn’t a lopsided game at the start. It only became that way later. The biggest upset, considering pre-game outlook? We rewind to June 17, and we go to Los Angeles.

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The Mariners needed a center fielder after they sent Brad Miller and Austin Jackson packing over the past year. They had an extra reliever, maybe, after they acquired Joaquin Benoit from the Padres last week. And, even given all the flaws in their new (probably platoon) center fielder, it’s hard not to like such a low-risk, high-reward move. Even if you value relievers highly.

But these are the things you have to talk about when you try to evaluate the trade that sent center fielder Leonys Martin and reliever Anthony Bass to the Mariners and reliever Tom Wilhelmsen and outfielder James Jones to the Rangers.

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Since we don’t have much more than velocity readings from Japan, it can be difficult to rely on anything but scouting reports when evaluating pitchers coming over from Nippon Professional Baseball. And now that 27-year-old Kenta Maeda is once again rumored to be coming to America through the posting system, we’re once again left wondering how to place him in context.

We have his Japanese strikeout and walk rates, which we can compare to recent postings to find comparable countrymen. We also have his velocity readings and a general sense of the quality of his pitches that we can use to compare him to pitchers beyond just ones that have come from Japan. We even have one game of PITCHf/x data to help us look at the movement of his pitches.

And the few comparable players we produce might be the best we can do from out here in the public sphere.

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During the fifth inning of Game Two, as Alcides Escobar attempted to bunt against Jacob deGrom, Harold Reynolds decried the current state of bunting in professional baseball. Even after he admitted that hard throwers are hard to bunt on, he went on a mini tirade: “I know it’s hard to get one down against a guy that throws this hard, but I’ve never seen this bad of bunting. Ever. Ever! In baseball, just across the board. I know Escobar can handle the bat, but we see this every night. They have to move the runner. Not just the Royals, but across the board.”

The moment was probably lost for a couple reasons. For one, Escobar decided to swing-away after two failed bunt attempts, and promptly tied the game with a single to center. There was too much excitement to think too deeply about the state of bunting in our game. Now we have a second to breathe, though.

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You’re in a pickle, see. The Devil wants to take your soul, and he’s pretty intent on doing it, but he’ll leave you be on one condition: in the span of one hour, you are to teach him everything there is to understand about the game of baseball. Up to this point the game’s been over his head, and he’d like to know what it’s all about, but he also has only so much patience, especially with you. If you can convey to him that special essence of the sport, you’re free to go, spared an eternal damnation. If not, you lose. You know what’s at stake. Of course you do. Your mind races.

Or, your mind would’ve raced. Before Wednesday, before Game 5 between the Rangers and the Blue Jays. You would’ve thought about explaining the rules. You would’ve thought about reviewing certain eras, and certain Hall-of-Fame players. You would’ve thought about going through the physical motions. But now — now — this is an easy situation to fix. You show the Devil Game 5’s seventh inning. He’s gotta have the Internet somewhere. You show him the entirety of the seventh inning, from start to finish. When it’s done, and the second bench-clearing incident is broken up, you’ve got six minutes to take questions.

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