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Chess Players in Baseball

via thesun.co.uk

I ask a lot of stupid far-out hypothetical questions on Twitter with hopes of getting quantifiable answers.

On Tuesday, I asked my followers the following: “If every game that went into extra innings was decided by a chess match between one player from each team (that they choose), what kind of contracts would the world’s top chess players be getting from MLB teams?”

For example, after nine innings of a 2-2 game between the Mets and the Nationals, each squad gets to pick one of their active rostered players to play chess against the other. For this, let’s say that ties are not allowed. It could take a long time, but for our purposes we will say that if a chess match ends in a draw, they play again and again until someone wins. And the winner of that chess match wins the game for the team. Maybe it will count to their pitcher win-loss record or something. So, how much would the best chess players be worth?

More people answered in terms of wins than in terms of dollars, which is fine and probably better because we can still compare chess players and MLB players with no need to convert any stats.

Teams that just trot out their smartest baseball player would quickly realize it is not the best strategy. I’ll get to the math later, but for now, understand that it is essential for MLB teams to sign professional chess players to maximize their chances of winning. If everyone decided to put their “Kyle Hendricks” as the guy they trust to play chess and just one player signs a semi-decent pro player, that team would win every single time.

Under our new rule, chess players in the Majors are MLB players just like Mike Trout and Clayton Kershaw and there is no reason to treat them any differently. I guess you can think of it as a new role. There are currently position players and pitchers, but this rule would add “chess player” to the two existing options.

Chess players (who I may refer to as “CPs” for the rest of this article) would essentially just take up an active roster spot on a team’s 26-man and they only play chess, nothing else. Maybe in blowouts we could get CPs pitching but that’s beside the point.

The first question we need to answer when attempting to measure the value of a player is what a replacement level player is worth. That is how WAR, a metric that compares players of all positions to a replacement level player (think of them as a AAAA player), works. Luckily for us, unless there was a sabermetric revolution in chess baseball, win-loss record for CPs is a perfect way of quantifying their value to their team. A CP who goes 10-6 had a good year while one who goes 3-11 did not. Compared to pitchers, CPs have way more control over their record.

In WAR, a team of replacement level players would have a winning percentage of .294 (that is just how they set the replacement level), so we can set the replacement level chess player at .294 as well, since chess players are MLB players too. A CP that wins 29.4% of their extra inning matches would be a replacement level player in MLB.

This means that an MLB average CP (one that wins 50% of their matches versus other MLB level CPs) would contribute +0.206 WAR per extra inning game (.500 – .294). All I’m doing is taking the difference between their wins and the amount of wins of a replacement level player (aka wins above replacement). Average players always have an assumed winning percentage of 50%.

It also means that if a team did not sign an actual chess player to be their CP and just let one of their players do it, their team CP spot would contribute -.294 WAR per extra inning game (.000 – .294) because I don’t see any way even the best chess playing MLB player could beat a professional chess player. I don’t know all too much about chess but I see this the same way as if you put out a 30-year-old dude who was good at baseball in high school onto an MLB team. Yes, they’re good in comparison to others their age, but they would get embarrassed by people who actually play baseball for a living. Not signing a chess player to be their CP would be sort of similar to an AL team ignoring the DH rule and letting their pitchers bat instead. Their team would get negative value from their DH position as a result of not having a DH, the same way a team would see negative value from their CPs as a result of not having one.

So now we have established an average CP would be worth +.206 WAR per extra inning game and an MLB player trying to be a CP would be worth -.294 WAR per extra inning. However, those are not the only two options. Not every chess player is going to be average.

Chess uses a system called Elo ratings to measure how good its players are. Elo ratings are cool because you can easily plug in Elo ratings of two players and get estimated winning percentages of a hypothetical match between them. Elo ratings have been adapted into online video games, projections systems, and other sports like tennis, but I believe it started in chess.

Using the website 2700chess.com, we can find actual Elo ratings of chess players and plug them into this website to estimate win probabilities. I don’t know how accurate this is because I don’t know that much about chess but the math for the rest of this article will assume these ratings as fact. If I did something wrong, I’m sorry, but this is more of a ballpark than anything.

If all of the top 30 players were willing to sign with MLB teams, the top player would be Magnus Carlsen who is at 2,872, while the median player is at 2,758 and the worst player (who is still the 30th best chess player in the world!) is 2,717. (As an aside, I am using median and not mean for the average because players like Carlsen would skew the perception of a league average chess player.) Note how the difference between the best player and average player is significantly larger the difference between the average player and the worst CP in the league (if everyone signed one of the top 30). Even player number 100, who would be far worse than any player a team would need to sign, is at 2,649. How much would each of these players be worth in our MLB?

The website I mentioned earlier suggests that a player with Carlsen’s rating would beat an average MLB CP in roughly 80% of the matches that didn’t end in a draw. The #30 player, or the worst CP if everyone signed the best CP they could, wins about 37.5% of the time against an average player and the #100 player, a player that wouldn’t even be good enough to be in the league (maybe they’ll be a CP for a minor league team?) would win about 22.5% of the time against the median MLB CP.

Using the same process as we did to find the WAR of an average CP, Carlsen’s 80% win percentage gives him a WAR of +.506 per extra inning game (.800 – .294), while #30 is +.081 WAR per appearance and #100 is -.069 per appearance (.225 – .294). A player worth exactly 0 WAR in our league just so happens to be the #50 chess player in the world who is estimated to win 29.4% of their matches versus our league median player.

In 2019, there were 208 extra inning games, meaning each team played an average of 13.87 extra inning games (208 / 30 * 2 because each game featured two teams). We can multiply each CP’s WAR per game by 13.87 to estimate how much WAR they would be worth over a full season. We get the following:

  • Magnus Carlsen – 7.0 WAR
  • 15th best worldwide chess player – 2.9 WAR
  • 30th best worldwide chess player – 1.1 WAR
  • 50th best worldwide chess player – 0 WAR
  • 100th best worldwide chess player – negative 1.0 WAR
  • Not having a chess player on the team – negative 4.1 WAR

Their WARs would be dependent on the overall talent level of the CPs in MLB, but the list above is what each player would be worth if every top chess player agreed to play in MLB. If they didn’t, the differences between the best MLB CP and worst MLB CP would decrease assuming it was the elite players on Carlsen who didn’t want to play. There is much more variability among the top 10 players than there is among the next 50, which makes sense; that’s how it is among baseball players too. We wouldn’t see a CP worth 7.0 WAR if the top 10 players chose to just continue their normal chess careers because there would be way less dominance by the top players, but there would still be a huge dropoff between having a CP and not. Also note that even the worst CP in our hypothetical league is still a positive WAR player. This is due to the fact that after you get past the elite elite players, there isn’t a huge difference between each player. Everyone you would even consider signing would at least win you around a third of your extra inning games. But if you look past the top 50, they would not be of value compared to a replacement player, but still much more valuable than not having a CP.

Another condition I set was that each team plays the average amount of extra inning games. If a team signed Magnus Carlsen, it is likely that he would be the centerpiece of their team and they could try and make their team geared towards getting to extra innings more, allowing him to win them even more games. If I was a team with Carlsen as my CP, I would focus my roster more towards defense-first position players and good pitching and hope that with lower scoring games comes more extra inning games. In recent years, the #1 team each year in terms of getting to extras tends to play around 20-22 such games compared to the average of around 14. Just guessing, prioritizing your team towards getting to extras could get you from the average of 14 to around 18 or 19 with the rest being determined by randomness. You could still only play in 14, but also could play 22 just based on how things go. Let’s just say 18 is the average for a team trying to play low scoring games and get to extras (I have no idea if this is actually true). Playing 18 extra inning games with Carlsen as your CP would make his value 9.1 WAR, which would’ve led baseball in 2019. Your team would’ve had an extra innings record of approximately 14.4 – 3.6 just because of Carlsen and your effort to get to extras.

Likewise, a team that doesn’t have an elite CP would want to prioritize hitting over pitching in order to minimize the value they would lose in extras.

So if we are saying Magnus Carlsen is in the 7-9 WAR range (assuming his team would at least try a little to “get him the ball”), and chess players don’t face aging curves like pro athletes do, I could certainly see Carlsen signing something like a 20 year, $1 billion contract. That is $50 million per year and looking at recent huge contracts, I think $50 million is about what MLB teams would pay a player that would average 7-9 WAR per season. I know that WAR/$ suggests they would get paid more than that but I also personally believe that as a player’s WAR increases, their salary doesn’t increase linearly. Feel free to disagree with me on the salary, that doesn’t really matter and I am just throwing darts in order for me to get across how valuable this guy would be, but fact of the matter is we are looking at that much value per season for many, many seasons.

Average CPs would get about the same yearly pay as an average MLB player, maybe slightly more (2.9 WAR for the 15th best chess player is right in line with the notion that an MLB average player is worth around 2.3 WAR over a full season).

I would imagine that chess players would want to take this opportunity and that we can say that the top 30 would all do it, just based on the fact they’d see a major salary increase. Most sources I can find suggest that even the best chess players don’t make more than a couple million dollars per year, and I would think that with each team only needing one CP on their roster, all of the players would see pay increases.

Many people in the responses to my Tweet argued that an average CP would be worth about 7 WAR because they would win half of their games and go 7-7 and a scrub like me or you would go 0-14, but we are not the replacement level, just like pitchers hitting is not the replacement level for DHs. Refusing to have a DH is not its replacement level.

Anyways, I arrived to the conclusion that under these rules, the best chess player in the world would be about as valuable in MLB as the best baseball player in the world each year, but their longevity would make the best of the best more prized than any actual baseball player could ever be. Sorry for making this, it’s stupid, I know.

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