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Baseball Game Theory: An offseason simulation

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Which players would you pick?

Rich Schultz/Getty Images

If MLB held a league-wide redraft in which every player across all organizations were available, and each GM could select five players to 'steal' from other teams, what would your list look like?

The catch?

If you and another GM select the same player, he remains with his current team.

This is the scenario that my old college roommate posed to me last week. After thinking about it for some time, I realized I didn't have a great answer, or at least one that I was confident in. The possibilities were endless, and I could always rationalize at least one other faux-GM picking a player that I had settled on.

Surely two franchises would go after Mike Trout; but what if everyone thought that, and after 150 selections he was still on the board, untouched. That chance would be too great to take, and just in case, using a pick on Trout might be worth it, even at the risk of wasting a vote.

What this boiled down to was game theory in a baseball environment. This idea was initially posted on Reddit, and while the jumping off question is the same, the SB Nation simulation had slightly different stipulations.

The Rules

1) Any player is fair game. Free agents, minor leaguers, and big leaguers. The pool of players is restricted to those that are, or have been in MLB organizations already. This means that recently defected players, or soon to be posted players are off limits.

2) GM's are prevented from picking a player that's already in their organization. Teams like the Cubs and Mets would have had an enormous advantage over the other 28 teams, as they simply could have cast votes for their respective core five's and blocked anyone else from having a chance. While it's still difficult to secure a player like Kris Bryant, or Jacob deGrom, allowing a team to submit votes for their own players would have made it impossible.

3) If a team successfully steals a player, his current contract comes with them. So if a team were to acquire Giancarlo Stanton, they would have to be able to afford his salary.

4) The most important rule; no communication between GM's. While SB Nation's previous GM simulation was built upon a dialogue between different teams, allowing GM's to talk to each other about their picks would have completely defeated the point of the exercise.

Teams had just over two days to complete their lists, and after much internal deliberation, we had 150 picks. As you'll see in the table below, there were a number of different strategies. Some GM's chose to load up on prospects, while others swung for the fences in trying to acquire elite talent. Some even tried to predict who they would lose, and targeted players that they could use as replacements.

Overall, 92 players were moved; two teams got all five players they selected; eight got four; eleven got three; eight got two; and one team wound up with only one player.

Of the 150 total picks, 58 were for the same player, which translates to 38.6 percent of the vote not counting.

In the table below, red text signifies that a player was selected at least twice, making the pick null and void. The table is arranged according to the team that picked the player, not the team that lost the player.

Team 1st pick 2nd pick 3rd pick 4th pick 5th pick
Arizona Adam Eaton Corey Seager Kelvin Herrera Jacob deGrom Josh Harrison
Atlanta Jorge Soler Yan Gomes Yordano Ventura Carlos Rodon AJ Pollock
Baltimore Cody Allen Trevor May Yan Gomes Jean Segura Kole Calhoun
Boston Nick Markakis Evan Longoria Trea Turner Stephen Strasburg Ben Zobrist
Chicago (NL) Gerrit Cole Andrew Heaney David Dahl Brendan Rodgers Carson Fulmer
Chicago (AL) Xander Bogaerts Troy Tulowitzki Trea Turner Michael Brantley Raisel Iglesias
Cincinnati Todd Frazier Danny Salazar Kyle Schwarber Adeiny Hechavarria Matt Duffy
Cleveland Paul Goldschmidt Matt Duffy Mookie Betts Marcell Ozuna Hector Rondon
Colorado Jose Abreu Kevin Gausman Lucas Giolito Paul Goldschmidt Steven Matz
Detroit Jung Ho-Kang Garrett Richards Carlos Rodon Corey Seager Yan Gomes
Houston Freddie Freeman Max Kepler Alex Colome Jerad Eickhoff Adam Conley
Kansas Addison Russell Starling Marte Gerrit Cole Jose Quintana Jake Odorizzi
Los Angeles (NL) Craig Kimbrel Gerrit Cole Corey Kluber Scooter Gennett Orlando Arcia
Los Angeles (AL) Tony Watson Masahiro Tanaka Brett Gardner Nolan Arenado Blake Swihart
Miami Tyler Beede Sean Newcomb Jose De Leon Michael Wacha Nolan Arenado
Milwaukee Tyler Glasnow Wilson Contreras Alex Reyes Kris Bryant Anthony Rizzo
Minnesota Javier Baez Carlos Carrasco Steven Matz Jake McGee Ender Inciarte
New York (NL) Mookie Betts Patrick Corbin Addison Russell Bradley Zimmer Eduardo Rodriguez
New York (AL) Jorge Soler Drew Smyly Aaron Nola Robinson Cano Joey Gallo
Oakland Andrew Heaney Lance McCullers Taijuan Walker Roughned Odor Kole Calhoun
Philadelphia Giancarlo Stanton David Price Max Scherzer Zack Greinke Clayton Kershaw
Pittsburgh Greg Bird Rafael Devers Julio Urias Joe Ross Erasmo Ramirez
San Diego Joe Ross Jose Altuve Jackie Bradley Jr. Danny Salazar David Peralta
San Francisco George Springer Francisco Liriano Cody Allen AJ Reed Addison Russell
Seattle Mike Trout Gerrit Cole Corey Seager Matt Olson Elias Diaz
St. Louis Jason Heyward Anthony Rizzo Addison Russell Kyle Schwarber Kris Bryant
Tampa Bay Greg Bird Carson Smith David Ortiz Roberto Osuna Marcus Stroman
Texas Jake Lamb Carlos Martinez Jonathan Lucroy Starling Marte Mookie Betts
Toronto Stephen Strasburg Gio Gonzalez Danny Salazar Carlos Carrasco Cody Anderson
Washington Corey Dickerson Lucas Duda Kyle Seager Zack Wheeler Mike Trout

After sorting through all the picks, it was clear that people were afraid to shoot for the moon (with the exception of the Phillies, who ran the table). The reigning MVP's, Bryce Harper and Josh Donaldson, received a total of zero votes. The reigning Cy Young's, Jake Arrieta and Dallas Keuchel, received a total of zero votes. Madison Bumgarner, Buster Posey, Carlos Correa, Matt Harvey, Noah Syndergaard, Miguel Sano, Francisco Lindor, Manny Machado, Sonny Gray, Miguel Cabrera, Chris Sale, and a host of other elite players, received zero votes.

The same held true for prospects. While up and comers Lucas Giolito, Julio Urias, AJ Reed, and Tyler Glasnow were all stolen, Nomar Mazara, Yoan Moncada, Byron Buxton, Luis Severino, Dansby Swanson, Jose Berrios, JP Crawford, Aaron Judge, Jeff Hoffman, and Jon Gray all remained untouched.

With 92 players stolen, the average team had to deal with losing three players on their respective rosters.

Players lost Players Gained Net change
Arizona 6 4 -2
Atlanta 4 2 -2
Baltimore 1 2 +1
Boston 9 3 -6
Chicago (NL) 5 3 -2
Chicago (AL) 5 4 -1
Cincinnati 1 2 +1
Cleveland 4 2 -2
Colorado 3 3 0
Detroit 0 2 +2
Houston 4 5 +1
Kansas 2 2 0
Los Angeles (NL) 3 4 +1
Los Angeles (AL) 1 4 +3
Miami 4 4 +0
Milwaukee 3 3 0
Minnesota 2 3 +1
New York (NL) 3 3 0
New York (AL) 2 4 +2
Oakland 1 3 +2
Philadelphia 2 5 +3
Pittsburgh 6 3 -3
San Diego 0 3 +3
San Francisco 1 3 +2
Seattle 3 2 -1
St. Louis 3 1 -2
Tampa Bay 6 4 -2
Texas 2 3 +1
Toronto 3 2 -1
Washington 3 4 +1

Only two teams made it through this exercise without losing a player; the Tigers and the Padres. While the latter has a barren farm system, and few attractive options at the major league level, it was surprising to see Detroit hold onto every single player in their system. They have a considerable amount of talent on their 25-man roster, and Daniel Norris and Michael Fulmer are both highly rated pitching prospects, yet for various reasons, no Tigers player was selected.

The Red Sox had the worst luck (although Tampa was close with seven players stolen), as they lost a franchise crippling nine players. Xander Bogaerts, David Price, David Ortiz, Blake Swihart, Carson Smith, Jackie Bradley Jr., Craig Kimbrel, Rafael Devers, and Eduardo Rodriguez were all taken.

One of the most interesting aspects of this process was to see which players were selected most frequently. On the offensive side, Addison Russell was the most popular player with four votes. Rather than go for one of the top shortstops in baseball, these four teams seemingly all decided to target a less valuable player, and one who they thought would slip through the cracks. Unfortunately those four teams all settled on the same shortstop.

As for the pitchers, Gerrit Cole led the group, also with four votes. Like Russell, Cole isn't one of the top five players at his position, but he undoubtedly has value, which lead four teams to think that he was just far enough outside the elite group to fall into their hands.

The purpose of this exercise wasn't to name a winner, but rather to see how game theory would play out in a baseball environment. That being said, it's hard not to name the Phillies as the clear victor. By Steamer's projections, Philadelphia added a combined fWAR of 27.2 between their five players, and took advantage of the other 29 teams' unwillingness to cast a vote for the best power hitter in baseball, and four of the best pitchers available.

While they've inherited quite a bit of salary obligations ($129 million in 2016), the Phillies are no strangers to having a high payroll. From 2011 through 2014, Philadelphia spent at least $169 million, and peaked in 2014 with $183 million. Those five players would push their financial commitment in 2016 to over $200 million, but that's not out of the realm of possibility; especially given their principal owner's comments.

"Middleton said MacPhail will be given whatever resources he needs to succeed. There won't necessarily be a budget as far as spending goes, just a 'mandate to win.'"

There are few teams in baseball that could realistically take on that much money, but given Philadelphia's history, they're a part of that group.

This simulation proved to be as exciting as we'd hoped when we got our 30 GM's together. A variety of strategies were deployed and to varying degrees of success. The Cardinals tried to ruin the Cubs' franchise by taking Heyward, Rizzo, Russell, Schwarber, Bryant, which backfired due to the popularity of their core players. Houston addressed their need at first base with a controllable asset, and added pitching to help make up for the loss of Vince Velasquez, Mark Appel, Thomas Eshelman, and Brett Oberholtzer.

However without a doubt, the biggest theme throughout the simulation was that teams were unwilling to cast votes for the truly elite players. Between the three major award categories (MVP, Cy Young, ROY), only one winner received at least one vote (Bryant). Out of the top 20 pitchers in baseball last season (ranked by fWAR), 11 of them were selected; and out of the top 20 hitters, only six received votes.

If you have any questions about the process, or are curious about the reasoning for certain picks, many of the participants are going to post a paragraph in the comments section explaining how they came to select their five players.

. . .

Matt Goldman is a Featured Writer with Beyond the Box Score and a Contributing Editor at MLB Daily Dish. You can follow him on Twitter at @TheOriginalBull.