What makes a player the worst ever?

It's a conceptually difficult question. A major league baseball player, virtually by definition, is in some small fragment of the top 1% of the greatest baseball players in the world at that time. Whoever the worst player in the majors is, he's many, many times better than you or me, and considerably better than thousands of people around the world who are currently making a living (or trying to) playing baseball. By extension, I'm sure there are a lot of players who made it up for a day, or a week, or a month, who just weren't nearly good enough to make it on anything like a full-time basis. I don't think they can count, either. So the real question is: who's the worst player who ever made it to the major leagues and managed to stick for a while?

I'm only looking at hitters here, no pitchers. I'm setting a minimum of 1,000 PA. If you came up a thousand times in the majors, you either (a) were a regular for two seasons or more, (b) hung around as a bench player for a really long time, or (c) something in between. Credit will be given, however, to guys who stayed around for longer than that (that is, if player A was awful for 1,001 PA and player B was equally awful for 3,000, player B is "worse").I'm starting with a certain maximum threshold for OPS+ per Baseball Reference (the threshold will vary a bit by position), and then looking at WAR from Sean Smith's database.

Your contenders:

Bill Bergen, C, 1901-1911: 3228 PA, .170/.194/.201, 21 OPS+, -17.7 WAR; -3.62 WAR/660PA
Frankly, this whole thing is a test of my assumptions. I've always taken it as a given that Bergen was the worst player of all time, but some friends of mine have recently challenged my convictions. Understand this: not counting pitchers, Bergen is the worst hitter of all time. There's no contest. He's not only the worst at 1,000 PA; he's the worst at 900, and 800, and 700. You have to go all the way to John Vukovich, with just 607 career PA, to find someone with a worse OPS+ than Bergen (and Vukovich "beats" him only 20 to 21). And Bergen, with more than five times as many PA as Vukovich, was at least a half-time player (generally closer to a full-timer). Setting the limit back at 1000 PA, Bergen has barely half the career OPS+ of the number 2 man on the list (21 to 40). You have to go to spot #9 to find the next guy with 2500 PA (Rafael Belliard, at 46) and to #23 to find someone with more than 3000 (Hal Lanier, 49). It's especially amazing when you consider that Bergen was "hitting" during the dead ball era; it seems almost impossible to put up numbers that are that far below a league average that's already very, very low (adjusting for park, the league put up just a .655 OPS during Bergen's career; compare to the 2009 NL's .739 OPS). Simply put, it's utterly impossible to overstate how inept Bergen was as a hitter.

On the other hand, Bergen's Wikipedia page calls him "a first-rate defensive catcher," and cites a number of contemporaries and historians ranking him as among the best ever at the position. Fair enough. That's not reflected in his WAR, but we're having enough trouble measuring current catcher's defense; let's not pretend that the numbers from 99-109 years ago are worth the intangible pieces of cyberspace they're printed on. Instead, let's pretend that he was every bit as good as Johnny Bench, who under Smith's system (adjusting for Bergen's many fewer PA) would make his defense worth +36 runs over his career. That's about a 2.1 win positive adjustment, giving him a career WAR of -15.6, -3.9 per 660 PA (that is, per approximate full season, at least for non-catchers). He was a truly terrible player any way you slice it. There are tons of awesome defensive catchers in the minors who can't hit a lick (see e.g. Drew Butera). If they hit like pitchers, you can't afford to put them in your lineup.

John Gochnaur, SS, 1901-1903: 1030 PA, .187/.258/.240, 46 OPS+, -0.8 WAR, -0.5 WAR/660PA
This was the player with whom my friends challenged my assumptions, and one who has, in fact, been cited as the worst player of all time. Make no mistake, Gochnaur (sometimes also spelled Gochnauer) was a terrible, terrible major league ballplayer. If he were born 100 years later, it's hard to imagine he'd get out of high-A (assuming he made varsity in high school). But think about this: as bad as he was, he was nearly twice the hitter Bergen was. Gochnaur posted identical .185 BAs in his two more or less full years as Nap Lajoie's double-play partner, and in the second, his 59 OPS+ would've shattered career records for Bergen.

What puts Gochnaur on these lists is his defense; he committed 48 errors in 1902, which sounds like a lot in and of itself, but then committed 98 in 1903. But you have to put it in the context of a time in which the fielder's glove was basically a very slightly larger, clumsier human hand. With the 48 errors in 1902, yielding an unsightly .933 fielding percentage, Gochnauer was actually more sure-handed than the average shortstop, who came in at .928. And his range factor is well below average, but Smith's system still likes him, actually crediting him with +10 runs for the year. Now, a 98 error season is never going to be normal, and Gochnaur came in well below average in both FP and RF in 1903, and Smith's system gives him -7 runs. That's hardly terrible, though (Yuniesky Betancourt has been worse than that in the field in each of the last two years, though using more reliable numbers).

Peter Bergeron, CF, 1999-2004: 1256 PA, .226/.303/.308, 56 OPS+, -4.0 WAR, -2.0 WAR/660PA
There have to be some modern players in here. And I feel terrible saying something like this about someone who's still around to potentially catch wind of it (and is about my age, actually), and let me say this: it's a great feat to be selected in the fourth round of the MLB draft, and to hit .320/.396/.480 in a season between AA and AAA, and to make two consecutive Baseball America Top 100 Prospects lists, and to make the major leagues at all. But for whatever reason, Bergeron's time in the major leagues -- spent mostly as the Expos' full-time centerfielder in 2000 and 2001 -- was not pleasant. Not only was his hitting very poor (he has the fifth-worst career OPS+ of anyone with over 1000 PA whose primary position was 1B, 3B or OF, and the four in front of him all retired prior to 1930), but Smith's Total Zone rating thinks he was a nightmare in center, too, racking up -20 runs in his two mostly-full years out there. Given his minor league track record, I think it's safe to assume he just got unlucky or hurt, and remove him from consideration for the #1 spot. But given his numbers and the parameters here, he certainly has to be in the conversation.

Goldie Rapp, 3B, 1921-1923: 1170 PA, .253/.303/.312, 57 OPS+, -4.3 WAR, -2.4 WAR/660PA
That batting average doesn't look so bad, but consider that during Goldie's three-year career, four guys hit .400 or better over a full season, and the entire National League hit over .300. In 1921, Rapp was a 27 year old rookie hitting .215/.276/.276 for the Giants (40 OPS+), and the Phillies liked that so much that they traded Casey Stengel and another guy to get him (and two other guys who weren't much more impressive). Now, it's not what he's known for, but Stengel was a fine player, and put up great stat lines as a part-timer for the Giants in 1922-23. Goldie, meanwhile, did exactly what the Phils should've expected him to do, and was out of the majors forever before his 30th birthday.

Craig Paquette, 3B/LF/1B, 1993-2003: 2766 PA, .239/.274/.411, 77 OPS+, -2.9 WAR, -.7 WAR/660PA
Sorry, Mr. Paquette. He's not nearly as poor on a per-PA basis as a lot of these guys, but he gets some extra points for staying power. And for the fact that there just wasn't any reason to keep him around, really; he could only play the power positions, and didn't play them well, and while he had some power, it wasn't nearly enough for a "power position" in the 1990s. And yet, five different teams gave him a look, and four of them made him more or less a full-time starter at one point or another. It's a pretty impressive feat, really.

Mario Mendoza, SS, 1974-1982: 1456 PA, .215/.245/.262, 41 OPS+, -4.6 WAR, -2.1 WAR/660PA
Famous for his inability to clear a .200 BA, Mendoza has nowhere near the worst BA on our list. He was an abysmal player, though, who managed to hang around for nine seasons as a part-timer with three different teams. Only an anomolous-looking +10 fielding runs in his penultimate season saves his per-season WAR from approaching Bergen territory.

Luis Gomez, SS, 1974-1981: 1391 PA, .210/.261/.239, 40 OPS+, -5.1 WAR, -2.5 WAR/660PA
Unsurprisingly, Mendoza tops Gomez's most similar player list per Baseball Reference, and Gomez is #2 on Mendoza's. They were basically the same, sub-sub-replacement player, over the same stretch of years. Odd.

Fritz Mollwitz, 1B, 1904-1913: 1904 PA, .241/.278/.294, 72 OPS+, -4.1 WAR, -1.5 WAR/660PA
Had to find a 1B to put on here. But the thing is, if a 1B can't hit, there's no reason to keep him around (such as the illusion that he's a good defensive SS or 2B, a la Mendoza and Gomez). Unless you've got family connections, that is; the only other one in serious consideration was Hank Aaron's little bro Tommie.

Jim Lillie, RF, 1883-1886: 1541 PA, .219/.230/.272, 54 OPS+, -8.1 WAR, -3.5 WAR/660
Even in the 1880s, right field was more or less a hitter's position, manned by stars like King Kelly, Sam Thompson, and Billy Hamilton. Lillie was not one of those guys. Yet the Buffalo Bisons, and when they folded, the Kansas City Cowboys, kept plugging him into the lineup almost every day. Lillie wasn't historically awful until his last year, 1886, in which he played 114 games and "hit" .175/.197/.197, coming up with 73 hits (9 doubles, no triples or homers) in 415 at bats, good for an OPS+ of 17. Maybe he gave Bergen some pointers.

Moe Berg, C, 1923-1939: 1961 PA, .243/.278/.299, 49 OPS+, -5.9 WAR, -2.0 WAR/660
One of the most interesting stories in baseball history (seriously, read this book), he was also, not at all coincidentally, one of its worst players. Hindsight and all that, but if you've got a team of traveling all-stars, and one of the roster spots is taken up by Moe Berg, how does that not set off alarm bells someplace? Anyway, amazing guy, but he couldn't play big-league baseball. Clearly not as bad as Bergen, though, at the same position. I just needed a tenth, and wanted to talk about Berg.

Your Winner Is...
That's ten, and I'm sure it's not actually the ten worst players of all time, even under these parameters, but it's as close as I can get. It's harder than you'd think to come up with ten very, very poor players. Think of some awful recent players. Neifi Perez? Had enough not-awful years in there that he comes out as exactly a replacement player. Willie Taveras? Good defender in center, a bit better than a replacement player. Phil Plantier? That one decent year he had early in his career kept him well clear of this list. It's a hard thing to do to be sub-replacement for more than one year in the major leagues, and I think it's been progressively getting tougher.

So who wins? I'm coming away from this as convinced as ever that it's Bill Bergen. Let's think about it. Per 660 PA, under the batting runs system, Bergen's bat was "worth" approximately -62 runs. Mendoza was about -54, Gomez -47, Lillie -46, Gochnaur and Rapp -40. Just to be as poor as Bergen on an annual basis, Mendoza would need to be eight runs worse on defense (including position adjustment) in order to "catch up" to Bergen, the others all between -15 and -22.

Mendoza can do it. Bergen gets +5 runs per season for being a catcher rather than a shortstop (using current position adjustments, which are at least a little different than the ones actually used in the WAR calculation), and we can certainly believe that a reputedly great catcher is more than three runs/year better than a middling shortstop. By the same token, it's not a huge stretch that Gomez might be worse, on a per-year basis.  Lillie takes a huge position adjustment penalty for being a RF (20 runs by the current figures), so he's almost certainly worse. It's harder to see with Gochnaur and Rapp, but if their defense was bad enough and/or Bergen's was good enough, it could happen.

But then I keep coming back to those 3,228 PA. What we're talking about here is that if we make some assumptions about defense, maybe some of these short-career, part-time players were arguably as bad as Bergen was. But none of those guys managed to do it in the big leagues for even half as long as Bergen did. Bergen played more than half his team's games for eleven years, and every time he was out there, it was like his team was putting two pitchers in its batting order.

If there were a player who was just unbelievably atrocious for 1000 or 1500 PA -- say, a lead-gloved first baseman who hit like Bergen himself -- then you'd have to consider it. But that guy isn't out there. Given the career length and consistency, I'm entirely comfortable saying Bergen was the worst ever.