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?

Before we go any further, we have to recognize we can’t actually determine if they made a good decision or a bad decision, we can only estimate about how much money they gained or lost by signing their deals. We have no way of knowing how risk averse players are or how large their discount factor is. Leaving $50 million on the table seems like a really bad call, but if locking in a big payday early and getting an influx of cash greatly improved a player’s family’s quality of life, it was probably a fine decision.

Using Baseball-Reference’s contract pages, I identified eight players who currently have between 6.000 and 7.000 years of service time who were not free agents this winter and have never been free agents (i.e. previous non-tenders are excluded). In other words, these are players who would have hit the market for the first time after 2015 had they not signed contract extensions earlier in their careers.

Our task is to consider how much they would have earned this winter and to compare that to what they will be paid over the rest of their current deal. We’ll also see if any of the players made more money during their arbitration window than we would have expected if they went year-to-year. Keep in mind my estimates are just that — estimates. I’m trying to fit the years and salaries into the context of the market so far, but there are a couple of players who would stand out as unique free agents.

I’ve broken the players down into two categories based on whether signing the extension was good/neutral or bad for their overall financial well-being. Obviously, as you’re reading this, remember that a dollar secured in 2013 has more valuable than one in 2016. But I won’t make any precise estimates for that because each player has their own ideas about risk and the time value of money. To the list!

Good/Neutral Extensions

Derek Holland

Extension: $28.5 million (2012-2016), $11 million option for 2017, $11.5 million option for 2018

Coming off a three-win campaign in 2011, Holland gave the Rangers one pre-arbitration season, three arbitration seasons and one free-agent season for $28.5 million, prior to 2012. That works out to a slight raise in 2012 based on the league minimum, and $16 million during his three arbitration years. Given his very strong 2013 campaign, it’s probably safe to say he would have done slightly better in arbitration had gone on a year-to-year contract.

He’ll make $10 million in 2016 and has team options for $11 million and $11.5 million for 2017 and 2018, respectively, coming down the pike. This is a hard contract to judge given that options depend heavily on his health in the future. He’s only thrown 95 innings since the start of 2014, which makes it seem like he’d have been in line for a one-year deal to rebuild his value this winter. It would probably have come in around the value of his 2016 salary. If we assume that’s the case, the options have negative value because if he pitches poorly or is hurt they won’t get picked up. If he pitches well enough for those options to get exercised, it means he’d be in for a more lucrative deal going into 2017.

As a result, Holland probably lost a few million dollars by signing the deal, but he guaranteed himself life-changing money at 25 years old and didn’t cost himself very much by signing away his twenties to the Rangers.

Jon Niese

Extension: $25.5 million (2012-2016), $10 million option for 2017, $11 million option for 2018

This is a fun one because it’s basically the same extension we just discussed for Holland. In terms of performance, Niese has been more reliable with less of a ceiling. He’s pretty consistently been a 2 WAR pitcher, but he’s coming off his worse season and has never looked like a potential No. 2 starter like Holland. I’d wager his arbitration years are largely a push, and if he were a free agent this winter I think that he’d sign something in the three-year, $36 million to three-year, $42 million range. It might seem like $12 million to $14 million is a lot to pay for Niese, but Mike Pelfrey got $8 million per year and J.A. Happ got $12 million per year, so this is the right neighborhood.

This puts Niese’s 2016 salary slightly below what he would have earned as a free agent with the same holding true for the options. If the options were guaranteed, he’d be looking at a three-year, $30 million deal for 2016 through 2018. That’s relatively close to his market value, so he essentially gave the Mets the decision over 2017 and 2018 for the upfront money. All told, this might be a slight loss for Niese in raw terms, but certainly not a large enough one to suggest it was foolish to sign the deal.

Cameron Maybin

Extension: $25 million (2012-2016), $9 million option for 2017

Maybin is an interesting case because he cashed in at exactly the right time, but he only guaranteed himself a relatively small amount as far as baseball money is concerned. Maybin got his extension, covering one pre-arb year, three arb years and a free-agent year right after his 4.3 WAR season in 2011. He was worth 2.2 WAR in 2012 but he’s been less impressive for a variety of reasons since then.

Again, the arbitration seasons seem pretty fair and his $8 million salary seems in line with what he would earn as a free agent this winter. The only question is whether he’d get a multi-year deal or if he’d go for a one-year deal with a team that had plenty of at bats for him in order to rebuild his value. It wouldn’t be a shock for him to get two years and $16 million or three years and $24 million, given his natural ability and potential upside. No one is investing a ton of money in Maybin, but the Red Sox paid almost $7 million a year over two years to get Chris Young, and Maybin is in a similar tier.

Given that, it seems Maybin potentially cost himself a little money by signing the extension. Still, given that he would have been a non-tender candidate over the last couple years if it hadn’t been for the extension, the guaranteed money evens things out. This one could go either way, but it’s certainly close enough to put it in the neutral category.

Rick Porcello

Extension: $82.5 million (2016-2019)

This is a unique one because it bought out free-agent years exclusively. The Porcello contract was controversial last winter because it looked like a deal that rewarded one good ERA season with ace money. The reality is Porcello’s peripherals had been trending in a good direction, and his fielding independent numbers suggested he was an above-average starter. Additionally, Porcello is only entering his age-27 season, which is much younger than many free-agent pitchers so it’s likely the Sox were buying his peak rather than his decline. Finally, $20 million simply isn’t ace money anymore as shown by the contracts signed by Jordan Zimmermann and Jeff Samardzija this offseason.

In fact, those contracts appear to be rather informative. Zimmermann received five years and $110 million despite a previous Tommy John surgery. Porcello is three years younger and hasn’t gone under the knife. He hasn’t been as good, but he has three years to catch up, and he’s a somewhat similar pitcher. Samardzija is interesting because he got five years and $90 million despite having a very poor platform season. To me, these two deals suggest five years and $100 million would be entirely reasonable for Porcello this winter.

I know that’s going to send some people rushing to the comments section, but teams have moved beyond judging pitchers with ERA and clearly have the ability to put several bad first-half starts in perspective. If we say it’s a five-year, $100 million deal, Porcello left some cash on the table. But he insured himself against catastrophic injury and will reach free agency again when he’s very young, suggesting he could probably do just fine in 2020.

Bad Extensions

Alcides Escobar

Extension: $10.5 million (2012-2015), $5.25 million option for 2016, $6.5 million option for 2017

For our purposes, we can go ahead and assume Escobar’s 2017 option gets picked up. At $6.5 million, the only way the Royals decline it is if he tears his ACL or something next October. Given that, Escobar gave the Royals his arbitration years for $9 million and then gave away his first two free-agent years for about $12 million.

Even if you don’t think much of Escobar and think arbitration wouldn’t net him full credit for his defense, the extension clearly went the Royals way. Let’s say he lost $5 million or so in arbitration. The real loss is that he’s effectively signed to a two-year, $12 million deal for 2016 and 2017 when he likely could have grabbed something between three years, $33 million and four years, $52 million if he were a free agent. Perhaps Porcello technically left more money on the table, but Escobar left a similar amount on the table and did so without guaranteeing himself a big payday.

Granted, it’s hard to fault Escobar for taking the deal given that he signed his contract before he had done much offensively. The dollars favor the Royals, but it’s a much clearer decision in hindsight than it was at the time.

Gio Gonzalez

Extension: $42 million (2012-2016), $12 million option for 2017, $12 million option for 2018

This one is a little simpler. Gonzalez earned some extra money up front but he’s essentially signed to a three-year, $36 million deal from 2016 through 2018 that is built on team options but could be declined if he has Tommy John surgery or another serious injury. Jordan Zimmermann seems like a good enough comparison here. Gonzalez isn’t quite at Johnny Cueto’s level but he’s been more durable, so somewhere in the five-year, $110 million range seems perfectly fine.

In raw dollars, that’s about a $75 million difference. Even if we tacked on two years at the market rate, he’s still more than $30 million short and none of the money beyond 2016 is guaranteed. Gonzalez has made plenty of money already in his career, but in terms of maximizing his earnings, his 2012 extension was a big mistake.

Wade Davis

Extension: $12.6 million (2011-2014), $7 million option for 2015, $8 million option for 2016, $10 million option for 2017

Let’s get crazy. So arbitration was probably a wash given that Davis didn’t start earning saves until this past season. But if we pick it up in the present, Davis belongs to the Royals for two years and $18 million. Recall that Pelfrey got two years and $16 million and Darren O’Day got four years and$31 million. It’s pretty safe to say Davis would make a ton of money this winter as a free agent coming off two otherworldly relief seasons.

This is a hard one to figure given the way reliever valuations are changing, but I’ll put four years, $64 million out there as a guess. Consider what Craig Kimbrel makes and how much the Padres got for him in a trade and it doesn’t seem crazy that teams would pay Davis $16 million per season to anchor their pen. Maybe that’s way off and it’s more like four years, $50 million, but either way, that’s a lot of money left on the table for a guy who plays one of the most volatile positions in the game and could find himself on the shelf in short order.

Andrew McCutchen

Extension: $51.5 million (2012-2016), $10 million option for 2017, $11 million option for 2018

This could probably be an article on its own. Madison Bumgarner and Chris Sale are signed to some team-friendly deals but this one takes the entire bakery. McCutchen is one of the five or 10 best players in baseball, and the Pirates are getting his first three free agent seasons for $41 million. It wouldn’t be outrageous to suggest McCutchen is worth $41 million per season. In fact, if we ask the contract estimator to put together a 10-year deal for McCutchen, it gives us this!

Andrew McCutchen’s Contract Estimate — 10 yr / $370.2 M Year Age WAR $/WAR Est. Value 2016 29 5.7 $8.0 M $45.6 M 2017 30 5.7 $8.4 M $47.9 M 2018 31 5.2 $8.8 M $45.9 M 2019 32 4.7 $9.3 M $43.5 M 2020 33 4.2 $9.7 M $40.8 M 2021 34 3.7 $10.2 M $37.8 M 2022 35 3.2 $10.7 M $34.3 M 2023 36 2.7 $11.3 M $30.4 M 2024 37 2.2 $11.8 M $26.0 M 2025 38 1.5 $12.4 M $18.0 M Totals 38.8 $370.2 M Assumptions Value: $8M/WAR with 5.0% inflation

Aging Curve: +0.25 WAR/yr (18-27), 0 WAR/yr (28-30),-0.5 WAR/yr (31-37),-0.75 WAR/yr (> 37)

Ten years and $370 million. Think about that. Now he’d probably negotiate an opt-out and the total value would drop to $330 million or something, but no matter what, his current deal is a steal.

We can acknowledge he’ll be a free agent after 2018, so it makes sense to look at the first three years of any new deal for a more direct comparison. McCutchen would probably have earned somewhere around $100 million between 2016 and 2018 and that’s before you factor in the idea that he’s risking injury and decline by not being able to lock in years four through 10 today. McCutchen insured himself against serious injury or dramatic underperformance when signed the extension, but it came at a steep price. Maybe he wouldn’t get a team to offer $370 million, but it’s hard to imagine he’d get anything less than $30 million per season over nine or 10 years.

*****

In total, the lesson of this year’s would-be free agents is that it’s difficult for players to come out ahead on these deals. The players are taking guaranteed money to acquire security, but once you get to the point where a team is willing to offer you an extension, you’re probably beyond the point at which you’re not going to make tens of millions of dollars playing baseball, no matter what.

The other way to look at this is that teams should probably be more aggressive in offering these deals. If you look at these eight contracts together, the teams came out way ahead and none of the deals were massive losses for the clubs. Of course this is a single year and it may not be representative, but given that we have a nice sampling of player types it does lend some support to the idea.

Finally, it’s a good reminder that players with two or more years of service time are going to be offered contract extensions this spring. Six of the eight players on this list got their deals at two-plus, and only one of them was post-arb. If you’re looking to get a good return on your investment, extend a pre-arb player because they will take discounts in their free-agent years and offer team options to lock in several million dollars now. If you’re a good player, it might be a smart idea to resist that security if you’re looking to hit the jackpot.