Dellin Betances made medium-level news a week ago when he lost his arbitration case. He’d been asking for $5 million — less, for example, than Trevor Rosenthal had made in his first crack at arbitration the season before. The Yankees, meanwhile, submitted a $3 million figure. The case went to arbitration, and the Yankees won. Randy Levine then took the medium-sized news and turned into big news by acting like a fool. While the $2 million difference might not seem like a big deal for Betances when he’s still guaranteed to receive $3 million, the affect on Betances’ finances in the coming years will be significantly greater.

Arbitration isn’t exactly the simplest of systems. Teams submit blind amounts, and if the parties can’t agree on a deal beforehand, they go to hearing. The FanGraphs glossary explains the process in slightly more detail, but if the player and team go to hearing, the arbitration panel decides on either the team’s figure or the player’s figure, with no option to choose a number in between. This makes the arbitration a winner-take-all scenario. If arbitrators could choose a number in the middle, settlements would be even more likely, simplifying the process and lead to far less debate. They can’t, though, and that means that arbitration decisions have a significant impact.

Also relevant is how service time fits into the process. Players’ salaries gradually increase based on service time, rendering the previous season’s salary quite relevant, as it represents the starting point for a raise. A few different researchers have gone through and figured out exactly how much salaries increase during arbitration. (Here’s a good one, for example.) As a general rule, though, it comes to something like a 50% increase in salary every year. Small differences, especially early in the arbitration process, compound to make bigger differences over time.

Once again this year, Sean Dolinar published a handy arbitration visualization that documents all the players who exchanged numbers with their respective clubs. The graphic includes the results of the arbitration hearing (if applicable), whether the teams settled on a one-year deal or reached a long-term deal. Here are the players, excepting those who reached long-term deals:

The last column in the chart indicates whether the player qualified a Super-2 player and therefore reached arbitration a year earlier than the rest of players in the same class. Next to Shelby Miller, I’ve written “No-Sort of,” which seems to require some explanation. Shelby Miller is not a Super-2 player, but even though he does not yet have four years of service time, this is second crack at arbitration. Service time is based on years and days in the majors, not seasons or games, etc. Heading into last year, Miller had three years and 30 days of service time. After struggling mightily last season, Miller was demoted by Arizona in mid-July. They waited until August 31 to call him back up, and by the end of the season, he’d compiled three years and 166 days of service time, six days short of the 172 necessary to constitute a full year. As a result, he’ll be eligible for free agency after 2019 instead of the 2018 season, and the Diamondbacks will receive another year of Miller’s service.

Seven players included in the above table won their arbitration cases. The table below indicates the amounts by which they won. As noted above, however, arbitration decisions tend to have a compound effect. To reflect that compound effect, I’ve attempted to estimate the total effect of this year’s victory on a player’s total arbitration process.

To reach that estimate, I’ve given each of the seven relevant players 50% raises for future arbitration (including 2017). As I said, players can change their future awards significantly with their play, for better or worse, but this should provide a baseline of what winning the arbitration could mean. (Note: I’ve rounded the numbers to just one decimal place for sake of ease.)

2017 Arbitration Winners 2017 Money Won Total Money Won Marcus Stroman $0.3 M $2.4 M Collin McHugh $0.5 M $2.4 M Wilmer Flores $0.4 M $1.9 M Khris Davis $0.4 M $1.7 M Brad Brach $0.5 M $1.3 M Jake Odorizzi $0.3 M $1.3 M David Phelps $0.3 M $0.7 M SOURCE: http://www.fangraphs.com/blogs/2017-mlb-arbitration-visualization/

Marcus Stroman only netted $300,000 this season; however, this was just his first shot at arbitration. As a Super-2 player, he’ll go through the process three more times. His relatively small amount adds up for him.

Before we get to the losers, let’s take a look at those players who settled after exchanging numbers. Most of the time, teams settle before they even exchange numbers. Even after exchanging numbers, though, some parties choose to settle. The table below shows how much both sides would have risked if they had gone to hearing instead of settling. (Once again, figures are round to tenth of a million.)

These are losses both sides could have felt. There was likely strong incentive for both sides to settle Drew Pomeranz’s case, as arbitration would offer significant risks and uncertainty. There’s the question of why teams would ever not just settle instead of going to a potentially contentious arbitration agreement. Generally speaking, teams will settle around the midpoint. If a team always settles, however, there’s an incentive on the player side to submit a higher figure than they otherwise would, to raise the midpoint. If a team threatens to go to hearing, the player’s side is more likely to come in with a lower figure — one with which they reasonably believe they could win arbitration. In order to force the player’s side into this belief, the team actually has to go to hearing from time to time. For some teams, this matters. For others, they might not care too much over a few hundred thousand dollars or even a couple million dollars when it comes to an arduous arbitration case where they’re forced to demean and belittle the accomplishments of their own players.

So here are the guys who went to arbitration and lost. As I mentioned earlier, players can change their valuations through their play on the field. The numbers below are only a baseline, but they are still a baseline.

2017 Arbitration Losers 2017 Money Lost Total Money Lost Dellin Betances $2.0 M $9.5 M Chase Anderson $0.4 M $3.3 M Taijuan Walker $0.4 M $2.8 M Caleb Joseph $0.3 M $2.4 M Michael Wacha $0.4 M $2.0 M Shelby Miller $0.4 M $1.9 M Fernando Abad $0.7 M $0.7 M Tony Watson $0.4 M $0.4 M SOURCE: http://www.fangraphs.com/blogs/2017-mlb-arbitration-visualization/

So that’s how Dellin Betances might have lost far more than $2 million in losing his arbitration hearing. This makes Randy Levine’s gloating all the more unreasonable, but it does help explain why the Yankees were willing to risk an arbitration hearing in the first place. The potential savings for the team aren’t insignificant, even for a team as rich as the Yankees. They completely bungled the PR aspect of the situation, but financially they made out.