One of the best features of the wins above replacement (WAR) statistic is that it allows us to compare the greatest single-season performances across different eras in baseball history.  Anyone who has browsed the FanGraphs Leaders page should know that Babe Ruth had the top-five WAR seasons in history, all in the 1920s.  In terms of offensive runs added (batting and base running), Ruth’s 1921 season ranks as the best ever, followed by Barry Bonds’ 73 home run “asterisk” season of 2001.  But what about fantasy baseball?  Were these also the greatest (read most valuable) rotisserie seasons ever recorded?  That’s the question I set out to answer.

Using a slightly modified version of Zach Sander’s fantasy value above replacement (FVAR) system for valuing fantasy players, I estimated the auction value for every hitting season from 1920-2013.  First, I determined every player’s position eligibility based on some simple assumptions (meant to reflect Yahoo’s approach) whereby a player is eligible for a position if they meet any of the following criteria:

• Played at least 20 games at the position in the previous season.
• Started at least 5 games at the position during the current season.
• Played at least 10 games at the position in the current season.

With that established, I proceeded to calculate the z-scores, FVAR and  auction values (FVAR$) for roto leagues.  Based on a 5×5 12-team mixed league with $260 budget per team (and quite a few other assumptions) here are the ten most valuable fantasy seasons for hitters since 1920 (5×5, 12-team mixed):

At this point you’re probably asking: “What, A-Rod?!?!”  I know, as a Red Sox fan and sentient being I was not happy to see A-Rod at the top of the heap.  As much as you may like or dislike A-Rod in real life, if you drafted him first overall in your 2007 fantasy league you were not disappointed with his across-the-board production.  But, you might also be asking, as I did, how was A-Rod’s 2007 season worth $5 more than Babe Ruth’s 1921 season?   Ruth’s hitting and base running in 1921 added 119 runs compared to 75 runs added for A-Rod in 2007, so what gives?  As best I can tell, here are some reasons why A-Rod-2007 had a higher FVAR$ than Ruth-1921:

• Ruth’s replacement in 1921, Ralph Miller, was much worse than A-Rod’s replacement in 2007, Melky Cabrera.
• As a result Ruth-1921 had a much higher FVARz score than A-Rod-2007, but the average above-replacement player in 1921 also had a higher FVARz than the average above-replacement player in 2007.
• As shown in Zach Sanders’ third post on FVAR, the auction values are a function of FVARz divided by the average FVARz for above-replacement players.  Hence, Ruth’s FVARz was divided by a larger number to calculate FVAR$.

Does this make sense?  Yes actually, I think it does.  What it means is that in 2007 A-Rod and Melky Cabrera together were worth more than Babe Ruth and Ralph Miller together in 1921.  In a fantasy auction in 1921 it would have been unwise to spend too many fake dollars on the best players like Ruth and Hornsby (or drink in public because of that Prohibition thing) because you would have been stuck with the bottom players, like Ralph Miller, who were really, really bad (there were only 16 teams back then and no DH).

For fun, below is a dream fantasy lineup with the best hitters since 1920 at each position (5×5, 12-team mixed).  Enjoy.

I’m hoping to write more posts like this using historical FVAR, especially if readers/commenters think it worthwhile.

Twitter: @FVARBaseball

Website: fvarbaseball.wordpress.com

Jeff Sullivan, esteemed overlord of the Community blog, wrote a fun article this past week looking at how the average schlub like you or me would produce if given an opportunity to bat and chose to literally never swing. Pitchers, as it turns out, are surprisingly fallible when it comes to striking out realistic simulacrums of hitters, and the expected production would be nonzero by a hair. What a couple people claimed in the comments was that they could be better than Jeff’s predicted .000/.073/.000, that they could swing blindly a couple times and occasionally get on base, somehow. Maybe that was you! I call shenanigans. Swinging obviously leads to negative outcomes as well, and I think the decreased chance of a walk would outweigh the nonzero chance of a hit. I took Jeff’s frequently given advice (if you want to know more, do the research yourself) and decided to see what would happen if you did decide to swing sometimes.

Throughout this, I’m going to follow a fairly similar methodology to Jeff and use a lot of his numbers whenever possible, so we’ll assume pitchers have the same abilities to throw strikes he gave. It’s true that it might change a bit if they knew what you were planning, but Jeff assumed the pitchers thought you were at least thinking about swinging, so it’s not too big a stretch. To extend the conclusions, we have to decide a few things — when you swing, how likely you are to make contact, and what happens when you do.

In making these assumptions, I’m trying to channel what you or I, a reader of FanGraphs, would do in the batter’s box. If I decided to swing ever, it would be just that, a conscious decision, one I would probably have to make before the ball ever left the pitcher’s hand. There is no way I have the ability to determine if a pitch is a ball or a strike or at all hittable while it’s approaching me rapidly. Therefore, in our scenario, you have a predetermined chance of swinging at any pitch, ball or strike. We’ll call that swing rate, and it depends entirely on how aggressive you’re feeling.

Now we need contact percentages, and for the next few sections, I’m again going to follow Jeff’s lead by looking for some of the historically worst contact percentages ever, and adjust those down somewhat. Looking over the last six years for players with at least 20 plate appearances, there are some pretty terrible numbers for both in-zone and out-of-zone contact rates. Sean West of the Marlins and Alex Wood of the Braves both have O-Contact rates of 0.00%. The lowest non-zero rate belongs to Sean Gallagher, at 14.3%. The lowest from a position player is that of Reid Gorecki, outfielder for the Braves, at 18.8%. It seems fairly reasonable to set your O-Contact% at 10%. Z-Contact% is better, but we see some of the same names. The lowest is Rick VandenHurk, 36.8%. Sean Gallagher ranks third-worst here as well, at 55.6%. Mike Costanzo is the worst position player at 59.3%, though good ol’ Reid Gorecki isn’t far behind, the fifth-worst position player at 68.6%. 50% seems like a good round number to choose for Z-Contact%.

So now we know when you swing, and whether or not you make contact. What happens then? There are 10 players with at least 20 PAs who have a BABIP of .000, so it’s presumably possible (maybe even likely) to ground out every time we even manage to make contact. Brandon McCarthy is the lowest-nonzero rate, at .037, or one hit in the 27 times he’s put the ball in play. The lowest position player is Oswaldo Navarro, shortstop, at .063. We’ll be generous, and assume some of these awful numbers are bad luck and need to be duly regressed, and put your true-talent BABIP at .050.

The floor for your hypothetical power abilities is even lower. Lots of position players have .000 ISO, with all of Luis Durango’s 19 career hits in 74 PAs (the largest sample size among players at .000) being singles. That’s boring, however. We want at least some chance for extra bases. ISO, however, measures extra bases per at-bat, when really what we want is extra bases conditional on the ball being a hit. We can safely set that pretty low as well. Johnny Cueto has a surprising number of PAs, at 340, and the lowest nonzero ISO at .004. Of his 26 hits, 25 were singles, with one double. There are lots of similarly bad numbers, so we’ll put your chance at extra bases at .02, or once per every fifty hits. Sounds about right. They’ll all be doubles — no way you’re hitting the ball hard enough for a triple or dinger, inside-the-park or otherwise.

Now it’s time to plug and chug. (Before continuing, an aside: we’re obviously assuming unrealistic things here, like that our BABIP will be the same on pitches in the zone and on those not, and that the probabilities will be the same regardless of the count, but we’re also assuming that you’re in a major-league game, so let’s not quibble over realism.) Continuing to shamelessly appropriate Jeff’s numbers and methodology, when we step up to the plate, there’s about a .24% chance we’ll be hit in the at-bat and automatically reach base. Nice! Jeff set an expected strike-rate of 70%, and we’ll use that as well. If we didn’t swing, we walked or were hit enough for an OBP of .073. How does swinging sometimes change your production?

Oof. Not well, is the answer. You can see that while BA and SLG increase when you swing more, it’s not nearly enough to cover the increased strikes and in-play outs, and reasonable swing rates in the 25-60 percent range cause lead to some even worse wOBAs in the .020s and .030s. Interestingly, the minimum wOBA comes right around a swing rate of 45%, after which it is better to swing more no matter what your rate is, until you’re deciding to swing before literally every single pitch. They should probably learn your strategy fairly quickly, but until they do, your OBP is about .040 (you get on base once every 25 at-bats!) and your wOBA is about .036. For comparison, Jon Lester (my go-to terribly-hitting pitcher) has a lifetime OBP of .030 and a wOBA of .021.

How good would you have to be for swinging sometimes to be better than doing nothing? It doesn’t take a lot. If you can make slightly more solid contact, and we up your BABIP to .150 and the chance of a double given a hit to 15%, swinging more is a very good thing, with your wOBA topping out at .110 (!!!) when you swing 100% of the time. To be fair, though, while this is a small increase in magnitude, it’s better contact than a lot of pitchers make, so I think the original assumptions are probably closer to the truth.

So now you know. If you’re ever dropped into a baseball game somehow, remember Eddie Gaedel, and keep the bat firmly fixed on your shoulder. Because while you would be terrible, really really terrible, it would be even worse if you for some second you forgot how terrible you were and tried swinging.

PS — I put together a whole spreadsheet where you can mess with all these numbers and see how it changes the results, and if that’s something people would be interested in I could provide a link so you can make assumptions of your own.

There were two outs. Many baseball stories, whether real or fantasy, begin with this situation. It’s when the stakes are highest for both the offense and the defense. An out means reprieve and perhaps a win for the team on the field, while reaching base means an extended opportunity for the hitters and possibly a win as well. Such stories tell moments of baseball history. They freeze the instance in time that might otherwise get lost in the accumulation of statistics, games played, and sometimes even wins and losses. Baseball moments can encapsulate a player’s entire career, or the essence of baseball at a particular time. Moments are what we remember. They are not always heroic—sometimes a great baseball moment does not capture the essence of a player as much as a quotidian aspect of the game—but they can nonetheless be what I would consider a Hall of Fame moment. While these stories will not, and should not, be part of the calculations when determining a Hall of Fame player, they have a way of remaining with the observer.

In one of my own early baseball memories, there were two outs. It was, in my estimation, a Hall of Fame moment. What makes it notable is that there were only two outs. In an April 24^th game of the strike-shortened 1994 season, the Montreal Expos played a nationally-televised away game against the Los Angeles Dodgers at Chavez Ravine. In the bottom of the first inning, with a runner on first base and one out, there was a pop-up to Expos right fielder Larry Walker. Being the quality defender that he was and given the relative ease of the pop-up from a right-hander, Walker tracked down the ball for the second out. So far unremarkable, but what he did next stood out.

Walker handed the ball to a receptive young baseball fan in the front row and started trotting back to the dugout. The runner on first, Jose Offerman, tagged first and took off running. Noticing that he just turned a live ball into a souvenir, Walker ran back to the fan, took the ball, and threw it to the infield. It turns out he didn’t need to retrieve the ball. According to the rules, once the ball left the field of play the runner was awarded two bases. In the moment, though, neither Offerman nor Walker mentally flipped through the rulebook. Offerman tried to score before Walker could get the ball back in play, all while Larry Walker pilfered a material object from a fan and in the process made a memorable moment for one fan unforgettable for everyone watching.

In 1994 Larry Walker was in his fifth full major-league season. His career was off to a fantastic start. Through the 1994 season, Walker slashed .281/.357/.483. He had hit 99 home runs, stolen 98 bases, had a wRC+ of 128, and accumulated a WAR of 20.9—about seven wins more than Jose Offerman produced in his 15-year career. Not only that, but in the strike-shortened 1994 season, Walker put up numbers that would be All-Star worthy over the course of 162 games. In 452 plate appearances, he hit .322/.394/.587 with 19 home runs, 15 stolen bases, a wRC+ of 149, and put up 4.4 WAR. While WAR is the only statistic cited that includes defensive value, it should be noted that over this time he played above-average defense, had a cannon for an arm, and had already won two Gold Gloves—something a cheeky producer reminded the audience of after Walker forgot how many outs there were.

That particular play is so memorable because it showed a famous athlete, a group so often abstracted as herculean, as eminently human. Incidentally, in the time-span from 1989-1994, admittedly chosen only because of my focus on Larry Walker’s early career, the major-league leader in WAR was well ahead of not only Walker, but everyone else in Major League Baseball. At 50.8 WAR and 15 wins ahead of Hall of Famer Ricky Henderson, it would only be later that Barry Bonds’ all too human actions, including mistakes, would be cause for the indictment of a generation and withholding him and others from the Baseball Hall of Fame.

But back to the play at Chavez Ravine in 1994. It was not just a Hall of Fame moment because a right fielder who in my opinion should be in the Hall of Fame fielded a routine pop fly and brain farted it into the stands. The other part of the story is the hitter, who happens to be someone else who I believe belongs in Cooperstown: Mike Piazza. In 1994, Piazza was a year removed from a Rookie of the Year award. Earning this award is anything but a guarantee of a Hall of Fame worthy career or even years of average play. For instance, Piazza was second in a string of five consecutive National League Rookies of the Year for the Los Angeles Dodgers from 1992 until 1996. Eric Karros, Raul Mondesi, Hideo Nomo, and Todd Hollandsworth have garnered little attention and even fewer votes for the Hall of Fame, despite solid to above-average careers. Piazza, like Walker, had a shortened 1994 season that would be valuable for an entire 162-game season. In 441 plate appearances, he slashed .319/.370/.541, hit 24 home runs, had a wRC+ of 139, and accumulated 3.8 WAR.

Like Walker’s case, only the most aspirational observer would have been thinking about the Hall of Fame and Mike Piazza in April of 1994 when he popped out to right field. Also like Walker, it’s the rest of his career that makes him a Hall of Famer. Piazza accrued 7745 plate appearances and hit 427 home runs over the course of the rest of his career, which ended after the 2007 season; his triple slash was .308/.377/.545; he had a wRC+ of 140; he ended his career with 63.7 WAR. He was the best-hitting catcher of all time, and the only real debate left, as Eno Sarris compellingly demonstrates, is whether he or Johnny Bench was the best catcher of all time. Larry Walker concluded his career after the 2005 season with more plate appearances than Piazza, 8030—his final tallies were a line of .313/.400/.565, a wRC+ of 140 (the same as Piazza’s), and 69 WAR. That Walker was able to do all of this despite missing quite a bit of time due to injury should buoy his Hall of Fame chances rather than diminish them, contrary to what Denver Post writer Troy Renck suggests. Additionally, that wRC+ and WAR are park-adjusted stats should mitigate the stigma of Coors Field.

Finally, somebody had to pitch the ball to Mike Piazza for Larry Walker to run it down, catch it, and give it away—that somebody was, in fact, future Hall of Famer Pedro Martinez. It was Martinez’s second full season as a major-league pitcher, and it was his first with the Montreal Expos. Prior to the beginning of the 1994 season, the Expos traded second basemen Delino Deshields to the very same Los Angeles Dodgers for Martinez. 1994 was also Martinez’s first great season as a starting pitcher. He tossed 144.2 innings in the short season, had an ERA of 3.42, which was slightly worse than his FIP of 3.32, and he struck out 8.83 batters per nine innings, all contributing to a 3.4 WAR mark. Martinez’s 1994 season in the context of the rest of his career was a blip akin to a pop out. He ended his career after the 2009 season with a 2.93 ERA, a 2.91 FIP, 10 K/9, 87.1 WAR, and a near guaranteed first-ballot selection to the Baseball Hall of Fame when he becomes eligible next year.

That play at Chavez Ravine in April of 1994 was as extraordinary as it was banal. Pedro Martinez got Mike Piazza to pop out to Larry Walker in right field in the first inning of an April game and within a shortened season when there wouldn’t even be a World Series. At the time, they were just baseball players. They are now potential and future Hall of Famers. One will be a first-ballot selection, another will likely be elected in the next two years, and I can reasonably see the third as either being the victim of an overcrowded ballot and losing candidacy—or sneaking in somewhere around his 13^th-15^th year of eligibility. The pop out that resulted in the second out of an inning was a Hall of Fame moment not just due to the players involved, but because it was a story that lodged itself into the collective memory of baseball fans. Stories and moments accumulate to create baseball legacies just as much as statistics do. Viewed in context, they are counter-narratives that illustrate that great baseball moments, and the greatness of players, are told through the stories of exceptional athletes and flawed human beings. Take a look.

As the second half of the brain trust known as “The ‘I’ in Team is in the A-Hole,” I am tasked with the responsibility of handling the analytic side of our fantasy baseball team. In my continuing preparation for the March draft, I stumbled across an interesting question: What is the best way to prepare for a fantasy draft in a keeper-style league?

From the outside, it is a very easy question to answer. The convenient availability of projections, rankings, and draft cheat-sheets provide a nice guide to determine which players to select. How would you prepare for the draft if the top 150 players were removed from the pool of players before the draft began? This is a challenge that team owners in keeper leagues face. In my league, assuming every owner keeps the maximum of 10 players, the top 100 players will be removed from the talent pool. Drafting in order and ranked by WAR, Starlin Castro would be the first overall pick in the draft. Although this is an exaggeration, it still proves the point I am trying to make. Keeper-league owners need to prepare for the draft differently than traditional redraft-league owners.

I like the umbrella approach WAR has to describing player value. I understand that rotisserie points are dependent on production. WAR provides a measure of general offensive production (wRAA), their ability to advance when on base (UBR and wSB), and their positional value on the field which, theoretically, translates to more playing time (UZR). To test the fantasy relevancy of WAR, I compared 2014 Steamer WAR projections to ESPN’s 2013 end of the year Player Rater. Although not significant, there was a 0.631 correlation. For the most part, the Player Rater aligned fairly well with the player’s projected WAR.

I then took the top 40 players ranked by WAR for positions 2, 3, 4, 5, 6, and DH and selected the top 100 players for the outfield. The total sample was 283 players. On average, Third Base (3B) is the most productive position (2.587) followed by Catcher (C) (2.487) and Outfield (OF) (2.376). To eliminate Mike Trout’s 9 WAR, I broke the position samples into four tiers. Tier 1 included the elite players (Top 25%) with subsequent tiers composed of lesser ranked players. Tier 1 players averaged a 3.88 WAR across the seven measured positions. When breaking the players into performance tiers, we see a significant decline from Tier 1 to Tier 2 (3.887 to 2.422). This is relevant because the majority of kept players will be from the Tier 1 group and will be ineligible for the draft. This decline continues through the four tiers. Third base represents the largest decline in projected WAR at -3.93.

With the elite players gone, how do you decide which players to select? More importantly, how do you determine depth scarcity without the presence of those elite players? First Base (1B) and C represented the highest average WAR across the remaining three tiers (1.947 and 1.867 respectively). You could argue here that reaching for a 1B in the early rounds is unnecessary because there is potential performance deeper in the draft. Surprisingly, 3B also presents an opportunity for those owners without Miguel Cabrera. As a position, Tier 2 and Tier 3 average 2.88 and 1.9 WAR respectively and represent the highest average WAR for each of the collective tiers.

Where is the position scarcity? If you are looking to draft OF, the data indicates you should plan on taking them early. After eliminating the elite players from the sample, OF averages the second-lowest WAR among the remaining tiers (1.287).

Interestingly enough, the data presents some obvious draft windows. For example, Second Base (2B) has one of the lowest average WAR (1.897); but teams need to select either a Tier 1 or a Tier 2 2B as the performance drop is significant (-3.17). Not only does this represent a decline in performance, but it also indicates an obvious area of position scarcity. Injuries here could be difficult to overcome during the season. The data also shows that there is no need to reach on a C or 1B as there will be decent depth throughout the draft. Tier 4 C averaged 1.23 WAR representing the highest value in Tier 4.

It is critical to consider the value of your available roster spots. In the same way that MLB teams are looking to maximize their available 27 outs, fantasy owners should consider the value of their 25 available roster spots. An owner would need to roster a Tier 2 and a Tier 3 3B to produce comparable value to a Tier 1 3B. Maximization of available roster spots will provide the owner with the flexibility needed to adapt to the 26-week season.

Pitching statistics are mostly based on rates. Sure, we have innings pitched, and if you want to annoy me, you can talk about wins and losses, and of course there are the “three true outcomes” of strikeouts, walks, and home runs, plus WAR. But nobody ever looks at how many runs a pitcher was above or below average. Runs allowed isn’t all that common of a statistic; you’re more likely to see ERA or RA9. Even strikeouts and walks are often expressed as a percentage of all plate appearances, or as an amount per nine innings. The defense-independent ERA estimators like FIP and its spinoffs are rates, just like ERA. Where batters have regressed plus-minus or counting stats like wRAA and wRC, pitchers have nothing.

However, there has got to be some value in counting stats for pitchers. If we want to know how many more or fewer runs a team would allow by putting in an average pitcher instead of any given pitcher, that statistic would be able to tell us. So I’m going to present here three basic different numbers, one based off of FIP, one based off of straight runs allowed, and the third based off of linear weights. Each will be in two forms – raw runs allowed and runs allowed above or below average. I’ll call them FIP-Runs and FIP-Runs Above Average (FIPRAA), wRC-Runs and wRC-Runs Above Average (wRCRAA), and, obviously Runs and Runs Above Average (RAA). Kind of long, yeah, but I didn’t want to call the FIP one FRAA because that already exists.

All data was obtained from FanGraphs except for the singles, doubles, triples, home runs, walks, and HBP against used to calculate wRC; FanGraphs does not have some of those so I used Baseball-Reference.

FIP-Runs

This should be pretty simple. Take a pitcher’s FIP. FIP is scaled like ERA, but we want to scale it to RA9 because we want to scale it to all the runs a pitcher allows, not just the earned runs. To do this, multiply it by a constant that changes yearly – for 2013, it was 1.08. This is the league RA9 divided by the league ERA.

Take that figure, multiply it by the number of innings they pitched, and divide by nine to get the number of runs that FIP says a pitcher should have allowed. That’s their FIP-Runs. Great. But now how do we get that to express how many runs above average they were worth?

Well, we already have FIP-, which tells us how much better a pitcher’s FIP was than league average – and it’s already park- and league-adjusted, to boot. So what I did was subtract each pitcher’s FIP- from 200 to get the inverse of their FIP- (so if a pitcher had a 90 FIP-, the inverse would be 110) and multiplied that by their FIP-Runs. That gave me the number of runs (adjusted to the park and league) that an average pitcher would give up in the same number of innings. Just subtract the pitcher’s FIP-Runs, and you have your FIPRAA. And while I was at it, I did the same thing for xFIP. You can find the numbers at the end of the article. But first, the next part:

Runs

I didn’t have to calculate these like I did with FIP-Runs because the numbers are already there – it’s just the total number of runs a pitcher allowed. I did, however, have to calculate RAA, for which I used the same method as I did with FIP-Runs: find the RA9- (this was not park- or league-adjusted because I calculated it myself), take the inverse, multiply it by the runs, and subtract the runs from that. Piece of cake. Now for the last, and hardest, part of this:

wRC-Runs

These were tricky. I had to calculate each pitcher’s wRC against by first finding their wOBA against with the raw number of singles, doubles, triples, etc. they gave up and converting that into wRC. (I’ve actually already put this in a community post in a different form). But from there, I could follow the same instructions as before: use the wRC against as runs allowed, find the wRC/9- (if you didn’t read the article I linked to earlier, wRC/9 is just wRC against scaled like RA/9), and from those two find the wRCRAA (quite a mouthful, I know).

So, without further ado, here are the numbers (sorted by FIPRAA):