Brilliant Reader Replacement Level

So, Tom Tango did the coolest thing. Using your rankings of four pitchers -- Nolan Ryan, Bob Gibson, Pedro Martinez and Roy Halladay -- he came up with what we can call “Brilliant Reader Replacement Level.” I’ll try to explain here what he did, how it’s an interesting way to look at WAR and replacement level, and I’ll offer a few rankings for fun.

I will also include his email explanation on the bottom if you would like to understand the math.

The idea here, essentially, is that every baseball fan has an implicit “replacement value” in their mind. Baseball fans mostly don’t think about it that way -- I never did -- but consider the MVP arguments you hear at the end of every season. The arguments often do not revolve on how good the player is, but rather how bad the team would be without him. Think about how many times you’ve heard a commentator say something like, “They would not even be a playoff team without him.” Or: “Losing Player A would hurt the team more than losing Player B.”

True, this kind of circular thinking often leads to bizarre statements -- I guess the other day on the MLB Network Billy Ripken was nominating PIttsburgh closer Jason Grilli for first half MVP. That’s all about replacement level. Ripken obviously believes that if the Pirates did not have Grilli, who is pitching great, they would be much worse than they are now. I think that’s probably ridiculous, and that Grillii -- as well as he is pitching -- is probably the eighth or ninth most valuable player on the Pirates. It’s a different view of replacement value. I think, just as a starting point, that Andrew McCutchen’s combination of defense and defense, power and speed or Jeff Locke’s seven starts without allowing a run are MUCH more difficult to replace than Grilli’s fine ninth inning work. But, hey, it’s all opinion.

And I think we all have different opinions about replacement value. Baseball Reference and Fangraphs and Tango and Baseball Prospectus and others have done a lot of hard work to calculate what is realistic replacement value, and I think they’ve done an amazing job. For proof: Think about Derek Jeter. He got hurt, and the Yankees -- the rich, powerful, historic Yankees -- had to replace him for a chunk of this season. They found Jayson Nix.

At the moment, Jayson Nix’s WAR according to Baseball Reference is 0.1. Almost precisely replacement value.

Meaning even the Yankees, with all their money and history, are still bound by the pain of replacement value.

But just because these baseball wizards have come up with something that’s realistic doesn’t mean that is speaks to baseball fans Last year, WAR showed that Mike Trout was a much more valuable player than Miguel Cabrera, but Cabrera easily won the MVP and, if there had been a fan vote, he probably would have won it in an even more crushing landslide. In many, many people’s minds Cabrera’s home runs and RBIs and batting average were more irreplaceable than Trout’s on-base percentage, power-speed combination and defense.

Is that correct? I don’t think so. But baseball is meant to be enjoyed. There are no exams at the end of the semester.

So, what is the Brilliant Readers’ unexpressed replacement value when it comes to pitching? Well, Tango came up with a very simple formula simply using ERA- (Fangraphs’ excellent version of ERA+, where each point BELOW 100 is a percentage point better than league average) and innings pitched.

Take the four pitchers: Gibson (78 ERA-); Halladay (76 ERA-); Martinez (67 ERA-) and Ryan (90 ERA-). Rank them. According to Baseball Reference WAR, they come out like so:

-- Pedro Martinez, 85.9 WAR (14th since 1901)-- Nolan Ryan, 83.7 WAR (16th since 1901)-- Bob Gibson, 81.9 WAR (20th since 1901)-- Roy Halladay, 65.4 WAR (33rd since 1901)

OK, but in gathering your rankings here and on Twitter, the rankings looked more like this:

Bob Gibson or Pedro MartinezPedro Martinez or Bob GibsonNolan RyanRoy Halladay

Hmm. Brilliant Readers clearly and unequivocally had Gibson and Martinez ahead of Ryan. Why? It’s because Brilliant Readers mostly value quality over quantity. This makes some sense -- as Tango points out, higher peaks will lead to more championships. Ryan pitched twice as many innings as Martinez, 1,500 more than Gibson, but as unhittable as he was, he did not pitch as well as either (probably because he walked 1,000 more batters than any pitcher ever). Brilliant Readers made it clear that they want Gibson and Martinez’s extreme brilliance more than they want Ryan’s durable excellence.

So, Tango went to work to come up with a formula. Most people have replacement value at about 125% of league performance -- in this case, this would mean, roughly, that the ERA of a replacement pitcher will be 25% higher than the league average. If the average ERA is 3.93 like it is so far this year, that means a replacement level pitcher will give you a 4.91 or so ERA.That sounds logical enough.

But if you put replacement level there, Ryan is the most valuable pitcher of the bunch:

Nolan Ryan, 94.3 WARBob Gibson, 91.3 WARPedro Martinez, 82.0 WARRoy Halladay, 66,.7 WAR

This does make sense. The worse you make a replacement pitcher, the more value you are giving to Nolan Ryan’s many innings. Trouble is, at this level of replacement, lots of very good pitchers with long careers -- like Tommy John and Eppa Rixey, Bert Blyleven and Don Sutton -- also rank higher higher than Pedro Martinez. And that probably feels wrong to you.

So, one way to highlight quality is to adjust replacement level. By doing so, you are tilting the scale toward excellence and away from the consistently good. Sometimes people ask, “Why do you rate players against replacement value instead of against the average player?” Well, you could do that, but if you do then the value of durability almost entirely disappears. Here are the same four pitchers when judged against average pitchers:

WAR at 100% replacement value:

Pedro Martinez, 56.5 WARBob Gibson, 56.3 WARRoy Halladay, 42.2 WARNolan Ryan, 26.9 WAR

Fascinating isn’t it? Ryan is one of the most valuable pitchers of all time when compared to our earlier replacement level. But against average pitchers, he drops way down into Eppa Rixey and Billy Pierce territory. That’s because, as mentioned, he was not as good at run prevention as the other three on the list. Pedro’s amazing pitching is still amazing no matter who you compare him against. The better you make replacement value, the better he will look.

Maybe the easiest way to explain it is this way: Nolan Ryan’s career ERA- was 90, meaning his ERA was 10% better than league average. OK, let’s say you could somehow guarantee that you could find a pitcher who would have an ERA- of 90, same as Ryan. Bartolo Colon would be a good example this year. Let’s say you had a crystal ball and every year you could find the Bartolo Colon, the surprising pitcher who would have an ERA 10% better than the league.

What would that make Nolan Ryan worth against replacement value?

Answer: 0.0 WAR. That’s because you could guarantee that his run prevention could be replaced. Meanwhile, Pedro Martinez would still be extremely valuable.

WAR at 90% replacement value:

Pedro Martinez, 32.5 WARBob Gibson, 23.3 WARRoy Halladay, 19.0 WARNolan Ryan, 0.0 WAR

It’s fun to play with the numbers. OK, finally, we are led to the Brilliant Reader Replacement Level. What is it? Well, Tango looked at the few results and comments and estimated a Brilliant Reader Replacement Level of about 107.4% (he actually suggested 110%, but I preferred 107.4% because it makes Bob Gibson and Pedro Martinez of exactly equal value -- and puts them both ahead of Bert Blyleven). That means that replacement pitchers are not league average, but they’re much better than the replacement level you see on all the sites:

Here, then, are the 30 best pitchers since 1901 based on Brilliant Readers WAR:

Walter Johnson, 119.5 WARRoger Clements, 91.9 WARPete Alexander, 89.3 WARChristy Mathewson, 79.4 WARGreg Maddux, 78.6 WARLefty Grove, 75.7 WARTom Seaver, 67.9 WARRandy Johnson, 64.9 WARWarren Spahn, 61.3 WAR

Gaylord Perry, 59.9 WAR

Three Finger Brown, 59.3 WAR

Ed Walsh, 58.4 WARBob Gibson, 57.1 WAR(tie) Pedro Martinez, 57.1 WAR(tie) Eddie Plank, 57.1 WARBert Blyleven, 55.7 WARCy Young (since 1901), 55.3Phil Niekro, 55.1 WARCarl Hubbell, 54.6 WAR

Jim Palmer, 54.1 WAR

Steve Carlton, 53.2 WAR

Whitey Ford, 51.4 WARBob Feller, 48.6 WARKevin Brown, 47.9 WARTom Glavine, 47.2 WARHal Newhouser, 47.0 WARNolan Ryan, 46.9 WARJuan Marichal, 46.3 WARFergie Jenkins, 45.9 WARJohn Smoltz, 45.8 WAR

That list makes some sense to me. If you want, you can add value to pitchers who pitched after Deadball ended in 1920, and after Jackie Robinson crossed the color line in 1947. I would do that. But we’ll stop here.

Well, let’s include one more list: Here are the 10 best pitchers in baseball for the first half against Brilliant Reader WAR:

Matt Harvey, Mets, 3.1 WARClayton Kershaw, Dodgers, 3.1 WARAdam Wainwright, Cardinals, 3.0 WARPatrick Corbin, Diamondbacks, 2.9 WARClay Bucholz, Red Sox, 2.8 WARHiashi Iwakuma, Mariners, 2.6 WARJordan Zimmerman Nationals, 2.6 WARJeff Locke, Pirates, 2.5 WARCliff Lee, Phillies, 2.5 WARYu Darvish, Rangers, 2.5 WAR

Here is Tom Tango’s mathematical explanation of all this:

I compiled the list of your Brilliant Readers. There were ten of them that gave an ordered list. They had Pedro and Gibson tied, followed easily by Nolan Ryan, and then followed easily by Doc.

Focusing only on Pedro v. Gibson, five readers preferred Pedro and five preferred Gibson. In all ten instances, they were separated by one slot (meaning they went 1-2 or 2-1 or 3-2).

It's clear therefore that to Brilliant Readers, the extra quantity from Gibson is perfectly balanced by the extra quality by Pedro. All that's left to do is figure out how to use ERA+ and IP to get these two guys equal.

WAR is a simple construction, which basically boils down to:

Production = (Quality over baseline) x Quantity

That's all it is.

Quality is captured with ERA-, and you can get that from Baseball Reference by doing 10000/ERA+. For Pedro's ERA+ of 154, that gives us an ERA- of 65. For Gibson's ERA+ of 127, that gives us an ERA- of 79.

Quantity is simply IP.

So we have: PedroProduction = (Baseline - 65) x 2827 GibbyProduction = (Baseline - 79) x 3884

To make Pedro = Gibby means that Baseline = 116

That is, the baseline level that Brilliant Readers use is 116% of the league average runs allowed. (Unrounded, it's 115.667)

Pedro_Production = (115.667 - 64.94) x 2827 ~= 143400

GibbyProduction = (115.667 - 78.74) x 3884 ~= 143400

To convert "Production" into "Wins", you divide the above number by 2000. (I can explain more if interested.) So, we have:

Pedro_Wins = 72

Gibby_Wins = 72

Now, all we have to do is apply that to Ryan and Doc and we get:

RyanWins = 71 DocWins = 54

And that's where the problem lies. Ryan should be nowhere close to the other two, according to Brilliant Readers.

If we instead use Fangraphs' version of ERA- instead of Baseball Reference, we end up with a baseline level of only 107% of league average, and these win numbers: PedroWins = 57 GibbyWins = 57 RyanWins = 47 DocWins = 43

It makes a bit more sense, but Ryan and Doc are too close together.

The answer therefore is somewhere in between. And that answer is around 110% of league average. That is the replacement level that Brilliant Readers have implicitly recognized. This is in stark contrast to what Baseball Reference uses (around 120-125% or so) and what I use (around 125-130%). Brilliant Readers prefer quality to quantity. But, they are also recognizing that higher peaks leads to more team championships, so, we can see why they gravitate toward the level they do.

So, that's how you figure the Brilliant Readers WAR level (which we can label as pWAR for Posnanski):

Wins = (110 minus ERA-) times IP divided 2000

All that's left to do is apply that construction historically for all pitchers to get the Brilliant Readers preferred pitchers list.

Source:http://joeposnanski.blogspot.com/2013/07/brilliant-reader-replacement-level.html

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