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Andrew Knizner, Carson Kelly, and Probabilistic Prospects

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What can probability distributions tell us about the future of Cardinals catching?

Minor League Baseball: Arizona Fall League-All Star Game Mark J. Rebilas-USA TODAY Sports

Let’s be honest with each other upfront- it’s the offseason. You’re about to get another article that relates, however tangentially, to the Paul Goldschmidt trade. I’d like to think, however, that this is more of an evergreen article. Others here have touched on trading Carson Kelly. Heck, people have even written about whether they prefer Kelly or Andrew Knizner, and boy is that ever a popular debate. Here’s the thing, though. Most people, when they evaluate prospects, tend to use things like ‘statistics’ and ‘watching baseball players play baseball’ to evaluate who they’d rather have. Then they say things like, ‘I’d rather have Knizner,’ or alternately ‘I’d rather have Kelly.’ What this article presupposes is, maybe that’s the wrong way to think about things.

See, what a baseball player has done in the past is a single thing. He’s gotten so many hits, framed so many pitches, saved so many runs with his defense. Those are facts, and they’re immutable. A player’s future, though, doesn’t work like that. I can say a thing like ‘Andrew Knizner projects to be worth about 2 WAR in a starting job in 2021.’ That doesn’t mean that he’s going to be worth 2 WAR in 2021, though. It’s just a point estimate, a single number trying to convey a distribution of possible outcomes. Andrew Knizner could be a 3 WAR player in 2021, or below replacement level. Carson Kelly could be NL MVP (okay, probably not) or non-tendered. When I see opinions about the two catchers, they’re trying to determine who’s a better prospect today. I’d argue, though, that that’s basically meaningless rounding. Both of them are within a margin of error of each other, and both of them are going to get better or worse (or, what the hell, maybe stay the same) over the next few years. Is it going to be at random? Well, no, probably not- at least not totally. It might as well be random to us, though. We can’t differentiate between skill and luck, between physical limitations and changes and things that hard work can improve.

My point here is that it’s not really useful to you for me to tell you which of the catching prospects I think is better. I think they’re both great! I did think it would be interesting, however, to look into what trading Carson Kelly does to the team’s projected catcher position in 2021, when Yadier Molina’s contract expires. See, it doesn’t really matter much who’s better right now. One of these guys will be better than the other in 2021, and it’s going to be random or near-random. They are both going to realize some point on the probabilistic distribution of their skill curves, and we can’t know how that will turn out. Instead of just saying they’re both two-WAR catchers, I’m going to simulate the potential outcomes and see how the team looks in a world with both catchers, as well as the world we live in now where Kelly has been traded.


Look, methodology is a fancy word that makes this look like an academic paper, but I’m going to keep this as simple as possible. First, I figured out how many WAR each of Molina, Knizner, and Kelly project to be worth per plate appearance in 2019 using Fangraphs’ Steamer projections. Using some historical ZiPS data, I estimated a standard deviation of year-over-year projection change (1.1 WAR per 550 PA, for those curious) and applied a .5-win-per-year aging penalty to Molina. Finally, I came up with three possible scenarios for how Molina plans to approach the 2021 season. The first one, Flexible Yadi, assumes Molina will play in 2021 if he can, regardless of his position. If he’s the best of the three catchers (or two catchers in the Kelly-traded world), he’ll start. If he’s the second-best, he’ll be the backup. If he’s the third-best, he’ll retire. The second, Starter Yadi, is more straightforward. If Yadi is the best catcher on the team, he remains on the team as the starter. If not, he retires. Finally, No Yadi (a hard scenario to imagine) assumes he retires at the conclusion of the 2020 season.

Okay, so we have our players and our scenarios. I then whipped up a Python script to iterate out these scenarios randomly a million times. As per usual, here’s the script in GitHub. Next, I worked out who started and who was second string in each scenario. I gave the starter 500 PA and the backup 150 PA. Those 650 PA are the team’s projected catcher production in 2021 in each of these scenarios. Lastly, if a catcher other than these 3 needed to play (if Molina and Kelly aren’t on the team), I assumed that catcher was replacement level. The grid of possible outcomes looks like this:

Cardinals Catcher Projections by WAR, 2021

Prospects Flexible Yadi Starter Yadi No Yadi
Prospects Flexible Yadi Starter Yadi No Yadi
Kelly & Knizner 3.68 3.55 3.16
Knizner Only 2.97 2.8 2

The benefit of having two catching prospects is most evident if Molina retires. Having two catchers who project as 2-WAR players is worth more than a win of expected value. This makes some intuitive sense- in the 50% of situations where Knizner gets worse, Kelly is more likely to be the starter, and vice versa for the 50% of situations where Kelly gets worse. With Molina projecting as the best catcher about a third of the time if he stays, the effect gets smaller, and if he’s willing to stay as the second-best catcher it gets smaller still. We don’t have to stop at 2021, though. Let’s add an extra year of random variation and look at 2022 in all three scenarios:

Cardinals Catcher Projections by WAR, 2022

Prospects Flexible Yadi Starter Yadi No Yadi
Prospects Flexible Yadi Starter Yadi No Yadi
Kelly & Knizner 3.77 3.64 3.28
Knizner Only 2.8 2.71 2

Interesting, but again reasonably intuitive. In the scenarios with Kelly gone, an aging Molina slowly drags down the expected wins, and a Knizner-only team still has a mean of 2 WAR. With Kelly still in the fold, this decline is a lot less pronounced- it’s offset by more time for one of Kelly or Knizner to improve randomly and seize the starting role. Indeed, in the event that Molina retires, a Knizner-Kelly tandem projects to be worth more in 2022 than 2021 just through uncorrelated random variation in their skill levels.

As a learning exercise, this is pretty neat. It kind of puts what the Cardinals traded away in Kelly into perspective. Carson Kelly projects to be a useful major leaguer, but obviously it’s not that simple. Andrew Knizner projects to be a useful major leaguer- potentially better than Kelly, and only one of them can start. The real thing the team loses is ‘depth,’ and that’s a very nebulous term. The grids above are an attempt to put a numerical value on depth. Taking two 2-WAR prospects and letting them develop for two years gives you an expected result of 3+ WAR worth of production. Think of it this way. The Cardinals didn’t trade Luke Weaver, Carson Kelly, Andy Young, and a draft pick for Paul Goldschmidt. They traded Luke Weaver, Andy Young, a draft pick, and a 3-WAR catcher for Paul Goldschmidt and a 2-WAR catcher. For me at least, that clears up how upset I should be about losing Kelly, probabilistically speaking.

Appendix- Infinite Prospects

I won’t lie to you. I had a pretty great time coding up the study in this article. So, why stop here? What if the Cardinals had 10 2-WAR prospects to develop for two years? What if they had 30? 50? 100? Okay, one assumption upfront. We’re going to assume these are 2-WAR per 600 PA players. That way, we don’t have to deal with backups. The script is here. Let’s get some answers, shall we? Okay, with 10 2-WAR prospects, the position projects to be worth 4.6 WAR two years out. That variance is useful! Just for comparison, with only two prospects, we’re looking at a 3 WAR position on average. Ten is already an absurd amount of prospects to have at one position, but let’s really kick it into overdrive. With thirty prospects, you can expect to have a 5.5 WAR player manning the position in two years. Thirty average major leaguers can build you a Bryce Harper just through a few years of variance! By 50 prospects, our gains are diminishing, because we’re so many standard deviations away from the mean that it gets increasingly hard to improve. Fifty prospects yields a 5.8 WAR expected value- better than 30, but not by much. A hundred prospects gives an expected value of 6.2 WAR. That seems to be about the limit of it. How many 2-WAR prospects would you need to create a Mike Trout by random chance? It sure looks like you couldn’t.

These calculations get a little silly, too. There probably needs to be a mean reversion term in there somewhere- if a player’s projection improves by 4 wins in a single year, I’m willing to bet that his next projection is more likely to decrease than increase. For the sake of this appendix, I’m ignoring it, but if I ever fancy up this model, this will be the first place I look.