Let's talk for a minute about defensive statistics. These tend to be pretty controversial among traditional baseball fans; people get ticked off when the numbers tell them something that conflicts with what their eyes tell them. The most famous example of this was Derek Jeter. Most people saw him as a good, possibly great, defensive shortstop, especially when he was young. The eyes saw all those awesome jump throws, the famous dive into the crowd, the famous flip play against Oakland and so on. Jeter won five Gold Gloves Awards.
Defensive numbers, though -- all of them -- suggested Jeter was a real liability at shortstop, a defensive couch potato who lacked range and cost his team a bunch of runs every year.
Those defensive numbers made a lot of people mad. I wouldn't say it sparked an interesting argument, though, because most people who saw Jeter as a good, possibly great, defensive shortstop simply wrote off the numbers. The numbers were stupid. The numbers were ridiculous. The numbers were hurting the game. And so on.

But here's the thing: With a few rare exceptions, advanced defensive numbers such as Fangraphs' defensive runs saved (DRS) or the now ubiquitous ultimate zone rating (UZR) actually match up very well to the eye test. We'll get to the exceptions in a minute. There is one huge exception -- I'll bet you can figure out who he is.
Here's what we did: Our own Tom Tango produces what he calls "The fans scouting report" every year, and you can find the leaderboard here. In it, he asks fans to rank players on seven fielding categories -- reaction, acceleration, sprint speed, hands, footwork, throwing strength and throwing accuracy. Then, based on the results, Tango creates a fans scouting report which he then puts on the same run scale as the above DRS and UZR.
So we compared them player for player from 2011-17. And in roughly 95 percent of the cases, the fans scouting report matches up stunningly well with DRS, UZR or both.
Let's repeat that: The eye test and the defensive numbers almost always are very close. Tango and I looked at the years 2011-17 to get a larger sample size, and the agreement between eyes and digits was pretty staggering. We've been led to believe because of a few examples that the numbers and the eyes see defense in entirely different ways, and it just isn't true.
Between 2011-17, Andrelton Simmons saved 96 runs according to you, the fans. UZR has him saving 99 runs.

The fans have the excellent third baseman and now shortstop Manny Machado saving 80 runs defensively over that time. DRS has it at 81.
This happened over and over. The fans and the numbers match on Yadier Molina, on Nolan Arenado, on Dustin Pedroia, on Starling Marte. It works in reverse, too. Fans see Daniel Murphy costing his team 61 defensive runs over the seven years; DRS sees him costing his team 65 runs.
The numbers are not always that close, but in almost every case, the advanced numbers basically match up to what fans are seeing on the field. The numbers say a player is very good defensively, the fans see it the same way. The fans say a player is average defensively, the numbers see it the same way. Both almost always agree about a defender being below average.
So what about those exceptions? What can we learn from those? (Have you figured out yet who is, by far, the big one?)
It seems like we as fans generally underrate Mitch Moreland and Mike Napoli as first basemen. Fans rated Moreland as seven runs above average, while his DRS and UZR average out to 20 runs above average. Fans had Napoli as an average first baseman, while the defensive numbers say he saved about 15 runs with his defense. Moreland and Napoli are not particularly graceful athletes; it is quite possible that we underrate them because of that.

Meanwhile, we generally overrate second basemen Brandon Phillips and Robinson Canó. Oh, both are good defenders by the advanced numbers -- 24 runs saved for Phillips, 25 for Cano -- but we see them as crazy good (72 for Phillips; 52 for Cano). Again, this makes perfect sense. Phillips and Cano are both so fluid and fun to watch defensively. They both make dazzling plays.
There are two center fielders who, compared to the defensive numbers, we pretty seriously overrate. One is, yes, Mike Trout. We as fans have him as a ridiculously awesome defensive center fielder, the best defender in the game, saving 42 runs over the seven years. The numbers have Trout much, much closer to average (4 DRS, -2.2 UZR).
This one makes perfect sense to me. We as baseball fans want Trout to be better than he is as an outfielder, just like we as baseball fans wanted Jeter to be better than he was as a shortstop. It fits our narrative so much better. Trout is the best player in baseball, he's already one of the five best players I've ever seen, and so I want to believe he is superior in every possible way. Fans rated Trout above Lorenzo Cain. There is no possible way, looking at any numbers that you want, that Trout is as good a defender as Cain. But we want to believe.

The other center fielder who is widely viewed as way better than his defensive numbers is Baltimore's Adam Jones. The numbers say that Jones is a burden in center field. The fans consistently rate him as about average, perhaps a touch better than average. Again, this makes sense. Jones makes some great plays. He's a wonderful player. Jones is the face of Baltimore baseball. Fans aren't saying that he's a superior outfielder; they're saying, "Eh, he's not that bad." The numbers are a bit colder.
All of which leads us to the player who has the biggest gap between what the eyes tell us and what the numbers say. I assume you guessed him:
Yep, it's new San Diego Padres first baseman Eric Hosmer.
The fans have Hosmer as a great first baseman. They have him saving 28 runs over the seven-year period, which puts him in the realm of the best first basemen: Paul Goldschmidt; Anthony Rizzo; Brandon Belt and Adrián González. The fans see Hosmer as a defensive star, and he has four American League Gold Glove Awards to match the reputation.
But the numbers show Hosmer to be a real problem as a first basemen, one of the worst in the game, minus-21 runs by DRS (only Prince Fielder and Ryan Howard were worse) and minus-29 by UZR (nobody was worse).
Hosmer is the only player in baseball who has such a vast gap between perception and what the numbers say. No other player has the fans seeing superstar while the defensive numbers calculate major trouble. What is it about Hosmer?
Well, it could be the numbers are wrong. Hosmer's greatest skill, by nearly unanimous opinion, is his hands. One theory is that he's as good as anybody in baseball at saving infield errors by scooping bad throws out of the dirt -- again and again people say that he saves 20 to 50 errors a year with the slickness of his glove -- and the numbers don't pick that up.
But is this true? Probably not. If Hosmer was really saving so many errors, wouldn't this show up in his teammates' defensive numbers? Wouldn't we be able to see this in, say, a substantially lower error total for third baseman Mike Moustakas and shortstop Alcides Escobar? But it doesn't seem like that's true. Escobar finished tied for the most in errors in the AL in 2012, when Hosmer was 22, and you would think at the top of his defensive powers, and he's been in the top five in errors two other times. Moustakas has been top five in errors as well.
And Hosmer has been top five in errors among first basemen five times. I don't like errors as a statistic and feel lousy for using it, but errors are useful here because they are part of the eye test. People who want to say that Hosmer's advanced numbers miss something have a harder time explaining why he makes quite a few errors.

There are probably other ways to pick at the numbers, but realistically I think it's much more likely that the problem is that people simply (and wildly) overrate Hosmer's defense. That just makes much more sense. For one thing, Royals fans tend to see the group of young players that finally brought a World Series to Kansas City dreamily. As mentioned above, they probably overrate Escobar defensively. They also have catcher Salvador Perez (69 runs saved) well above his advanced defensive number (27). Hosmer was the most beloved player on one of the most beloved teams in baseball this decade, so that surely plays a part in the high rating.
And then there is Hosmer's style. He's just looks like a first baseman -- he's big, rangy, throws left-handed. When you picture a first baseman, you picture Hosmer.
The interesting question is: Will Padres fans, who will only now get to know Hosmer, see him that same way? Or will they judge his defense more the way the numbers do?