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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:

  1. Bob Gibson or Pedro Martinez
  2. Pedro Martinez or Bob Gibson
  3. Nolan Ryan
  4. Roy 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 WAR
Bob Gibson, 91.3 WAR
Pedro Martinez, 82.0 WAR
Roy 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 WAR
Bob Gibson, 56.3 WAR
Roy Halladay, 42.2 WAR
Nolan 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 WAR
Bob Gibson, 23.3 WAR
Roy Halladay, 19.0 WAR
Nolan 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:

  1. Walter Johnson, 119.5 WAR
  2. Roger Clements, 91.9 WAR
  3. Pete Alexander, 89.3 WAR
  4. Christy Mathewson, 79.4 WAR
  5. Greg Maddux, 78.6 WAR
  6. Lefty Grove, 75.7 WAR
  7. Tom Seaver, 67.9 WAR
  8. Randy Johnson, 64.9 WAR
  9. Warren Spahn, 61.3 WAR
  10. Gaylord Perry, 59.9 WAR

  11. Three Finger Brown, 59.3 WAR

  12. Ed Walsh, 58.4 WAR
  13. Bob Gibson, 57.1 WAR
    (tie) Pedro Martinez, 57.1 WAR
    (tie) Eddie Plank, 57.1 WAR
  14. Bert Blyleven, 55.7 WAR
  15. Cy Young (since 1901), 55.3
  16. Phil Niekro, 55.1 WAR
  17. Carl Hubbell, 54.6 WAR
  18. Jim Palmer, 54.1 WAR

  19. Steve Carlton, 53.2 WAR

  20. Whitey Ford, 51.4 WAR
  21. Bob Feller, 48.6 WAR
  22. Kevin Brown, 47.9 WAR
  23. Tom Glavine, 47.2 WAR
  24. Hal Newhouser, 47.0 WAR
  25. Nolan Ryan, 46.9 WAR
  26. Juan Marichal, 46.3 WAR
  27. Fergie Jenkins, 45.9 WAR
  28. John 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:

  1. Matt Harvey, Mets, 3.1 WAR
  2. Clayton Kershaw, Dodgers, 3.1 WAR
  3. Adam Wainwright, Cardinals, 3.0 WAR
  4. Patrick Corbin, Diamondbacks, 2.9 WAR
  5. Clay Bucholz, Red Sox, 2.8 WAR
  6. Hiashi Iwakuma, Mariners, 2.6 WAR
  7. Jordan Zimmerman Nationals, 2.6 WAR
  8. Jeff Locke, Pirates, 2.5 WAR
  9. Cliff Lee, Phillies, 2.5 WAR
  10. Yu 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.

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34 Responses to Brilliant Reader Replacement Level

  1. I think the disconnect comes when you are talking about career value vs. season value. I think everyone recognizes that if a player is lost during the season to injury that his replacement will not be nearly as good. But if a team loses a player because his contract is up, then the theory is that team should be able to replace him with a better player because they now have available salary to use.

    So when you compare the entire career, Gibson/Pedro are thought to be better than Ryan because if you were a team owner you could pay Pedro for a period of years, and then when he retires you can use the salary you were paying Pedro to get a pitcher who is better than the typical “replacement level” player. I think that is why so many of the brilliant readers preferred Pedro/Gibson over Ryan.

    If you are looking at an individual season, I think the extra playing time is a much bigger factor.

    • Rob Smith says:

      I agree with your point…. but you have to add in the reality of Ryan’s career too. As Joe pointed out, he walked more than a thousand more than anyone else ever. He imploded early in games. He walked the bases full. He showed up to games with no idea of the strike zone. As a result, his wins and his WHIP were not spectacular. So, while he was a HOFer for his sheer dominance, 7 no hitters and the 100+ fastball, which he sustained late in his career. Well, he never performed to the level of dominance of Gibson or Martinez as a complete pitcher…. which means all the baserunners he put on base even in good years.

    • zeke bob says:

      There are several statistical categories where Ryan is simply an outlier, and I think it just relates to the nature of how he pitched and sometimes makes him difficult to quantify. (For the record, I would take Pedro in the intellectual exercise Joe proposed, I’ve just always thought Ryan is a force of nature.)

      We all know he leads the record books in strikeouts, walks and no hitters, but the degree to which he does so is still startling.

      His 5,714 strikeouts (almost 900 more than 2nd place Randy Johnson) exceeds the combined amount of the guys 17th & 18th on the career list (Jim Bunning 2,855 & Mickey Lolich 2,832) and his 2,795 walks (almost 1,000 more than Carlton) surpass the combined total for the guys ranked 18th & 19th (Sam Jones 1,396 & Joe’s HoF whipping boy Morris 1,390). After his 7 no hitters, the next most was 4 from Koufax and then 3 apiece for Cy Young, Bob Feller and Larry Corcoran.

      Just an interesting pitcher.

  2. Josh says:

    Next post: the Replacement-Level Reader. I think it’s the football people who post on Calcaterra’s blog whenever PEDs come up.

  3. Corey says:

    I think it’s more than just career vs. season value, it’s that player value is not really linear. An 8-win player is more valuable than two 4-win players, because of lineup and roster constraints.

    • James says:

      Let’s say two 4-win players are only as valuable as a 7-win player. Look what happens if we raise the replacement level by one win: the 4-win players become 3-win players and the 7-win player becomes a 6-win player. Suddenly we get 3+3=6! So you just need to adjust replacement level and the equation works out. The key is that replacement level is *already* set specifically so 4+4=8, 3+3=6, 1+5=2+4, and so on and so forth.

      Basically, someone already came along and said “You know what, 5+5=9, so let’s increase replacement level by a win, so now 4+4=8” but now you’re coming along and saying 4+4 does NOT equal 8. It’s already been fixed!

    • Tangotiger says:

      Another perfect post. I really hope people re-read this.

  4. NMark W says:

    With regard to Jason Grilli’s importance to the Pirates in the first half of this season… I think Joe is way off base saying there are probably 8 or 9 more valuable players on the Pirates roster at this point of the season. Despite his 10+ year pitching career, Grilli had never before been asked to be a regular closer out of any bullpen before this season so his ability to be a consistent performer was somewhat in question. The club traded Joel Hanrahan to the BoSox in the offseason primarily for monetary reasons. Grilli is making less than half what Hanrahan would have made in 2013 so Jason is valuable for the Pirates simply because he’s working cheap and doing as well or better than Hanrahan closed the previous two years when he was considered one of the best closers in MLB. For a fragile team like the Pirates coming out of ’13 spring training, having a shut-down closer like Grilli has meant a great deal to the team’s success. Jason has closed 27 out of 28 chances and with such infectious gusto that has inspired the rest of the Bucco bullpen, now one of, if not, the very of best in MLB so far in 2013. Sure, everyday players like McCutchen and Russell Martin have been vital to their team’s success up to now and the standout starting pitching of no-name Jeff Locke has been a wonderful surprise but no one on the Pirates roster has been as much of an inspirational leader as Jason Grilli. Stats don’t measure all of this but just like Kurt Gibson changed the chemistry of the 1988 Dodgers I’d say Jason Grilli has done similar things for the 2013 “Shark Tank” Pirates. It may all come crashing down for the Pirates this 2nd half and if it does I’ll bet much of it will be because Jason could not sustain the near perfection that he has brought to the table the first half of this season. Go Buccos!!!

  5. Frank says:

    Joe begs us to believe that WAR is simple. I guess it’s just me – I read this story and am left dizzy. I am left with the sense that WAR can be manipulated to make it come out to your desired result.

    Maybe it’s the terminology “replacement player.” For one thing, a player off the bench or out of the minors is unlikely to have a 0.0 WAR (Jayson Nix notwithstanding). A true replacement player is a wild-card – you don’t know what you are getting. You may get the first six weeks of Jeff Francouer’s career, or you may get the last six years of his career – all in the same player.

    The concept should be quantifying an “average” player as a constant against whom we can compare. What I see happening in this article is that we can redefine “average” depending on the weight we give certain factors. Because we can adjust that in so many different ways, the whole concept is not nearly as useful as its adherents make it out.

    • Ian R. says:

      Sure, a true replacement player may actually play much better or much worse than 0.0 WAR. On average, though, the players most teams call up as replacement are at or slightly above replacement level – and the slightly above, in most places, has to do with distributing playing time to the guys who are playing better.

      If the question is ‘how well would the team do without this guy?’ then it makes sense to use an average replacement level. Yes, the team COULD call up a replacement player who plays like an MVP (see Vernon Wells the first month of this season) or someone who crashes and burns, but we may as well use the typical performance as a baseline.

    • Jesse says:

      “I am left with the sense that WAR can be manipulated to make it come out to your desired result.”

      Of course, why anyone would do that and expect to get away with it is baffling. Besides, the people who try to manipulate stats like that, to make Player A look better than Player B, usually don’t resort to WAR. They stick to baseball card stats.

      “The concept should be quantifying an “average” player as a constant against whom we can compare.”

      In a framework like that, no player who is below average has value. Since real baseball teams treat even below-average players as valuable to an extent, it doesn’t hold up logically.

  6. Mike Beyer says:

    I was completely lost about a third of the way into this article. Math was never my strong suit. I realize that WAR can provide valuable insight into a player’s value, and I agree with many of the conclusions drawn here, but the nuts and bolts of wins above replacement level completely elude me.

  7. Steve O says:

    Billy Ripken says a lot of silly things. He said that Brian Roberts, when healthy, is as good offensively as any other player in baseball. Wha???

  8. That’s a damn good list of top 30 pitchers in history. Using only one statistic, other than some minor quibbles it’s pretty close to what I would come up with using a mostly subjective view.

    “Replacement” is elusive. If a star pitcher gets injured in August, the team is looking at whatever they can find on their AAA team or maybe find a 40 year old Derek Lowe. If a star pitcher is lost in November (surgery, retirement, free-agency et ceter.), you have the opportunity of replacing him with the best pitcher on the market, Felix Hernandez or Cliff Lee if available. But that requires a $125 million investment which would cut significantly into what can be spent on other roster spots. There will always be pitchers like Bartolo Colon and Jason Marquis who have an annual salary below average. That’s why most of us would much prefer Gibson and Martinez to Ryan. When Martinez goes seven straight years with a .766 winning percentage ans a 213 ERA+, it is impossible to replace those years with anything close to that level. For nearly half his career, Ryan pitched at a level that was easily “replaceable”

  9. Ian says:

    I’m not sure I’m ok with fiddling with the numbers until you get the desired result you wan.

    Anyhow, I’ve always felt that WAR underrates durability in starting pitchers. As good as Pedro was, he didn’t throw a lot of innings even for his time. He missed lots of starts so his rate stats probably look better than they should. I’ve always felt he was one of the more over-rated players of this generation. (Which does not mean I don’t think he’s a HOFer).

  10. eightyraw says:

    There is no fiddling with numbers. Tango is simply using the rankings of the sample of four players to create a framework to apply to the measurement of all players. The math behind WAR is not changing, just the baseline. The examples show how the rankings were changed according to a different valuation of replacement level. The survey captures the feelings of the BR, which can then be used to show how the readers would rank the entire population if held to consistent standards.

    As for your second poitn, WAR does not under or over value anything. WAR is just a framework. If you think rWAR or fWAR or pWAR fails to accurately capture your valuations, then change the replacement level. You prefer longevity over peak? Change the baseline. Just be sure to explain your reasoning and be consistent in application.

  11. Rob Smith says:

    I was with you until right after you wrote “So, Tom Tango did the coolest thing”. After that, you lost me.

  12. kehnn13 says:

    There has to be a problem with this ranking. I mean, Bert Blyleven is on this list and Jack Morris isn’t!

  13. Alejo says:

    I would gladly pay a ticket to watch Pedro’s 57.1 WAR but I would think twice before turning the radio on to listent to Bert Blyleven’s 55.7 WAR.

    that’s the difference between unexciting, long-term quality and short-termed artistic brilliance, I guess.

    • Rob Smith says:

      Did you ever see Blyleven? He was almost always on terrible teams, so generally the one game you had to worry about when his team came into town was the one Blyleven pitched. He had 14 seasons where his ERA+ was 120 or better, 7 seasons where it was 130 or better and 6 seasons where it was 140 or better. No, he was never Pedro in his prime. Pedro’s prime was otherworldly, if that’s the point you’re making. But, Blyleven was awfully good. I enjoyed watching him pitch. His curveball was amazing. I think any real baseball fan would go see him pitch. Granted, I was a season ticket holder in the 70s and 80s and loved to watch good pitchers, so I may be different than the average fan.

  14. Frankie B says:

    The reason I think this post is so cool is central to the argument about WAR. BA, HR, RBI and the like don’t change because of fan perception. WAR does, and that’s why there are so many arguments about it. What Tom Tango did, which appeals to me as a long-time fan, is to attempt to take perceptions of knowledgeable, long-time fans (Brilliant Readers), and build WAR around that. The focal point happens to be Bob Gibson and Pedro Martinez – two pretty good examples, if you think about it, out of all the pitchers of varying quantity and quality in MLB history. Two pitchers whom devoted long-time fans will love for various valid reasons. Then, figure out a way to make ’em equal in WAR, and put everyone else in around it.

    There will always be arguments about the greatest pitcher, or top ten pitchers – that’s just one of the many reasons I love baseball, and why so many of Joe’s readers do, too. But that list of 30 is pretty good.

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  16. Zubin says:

    Joe, what might be useful would be to quantify the number of games a replacement level team (full of such players) would win.

    If R = 30% less than league average, such a team wins 57 games (81 * [1.0-0.3]).

    For brilliant reader R, that number is 61 games (81 * [1.0 – 0.3] * 1.074).

    Intuitively this makes a lot of sense, since I think people often think of replacement level being a ~60-win team instead of something less.

  17. Tangotiger says:

    When you set the replacement as Fangraphs and do, it implies a team win% around .300. If you set it at 110% of league average for runs allowed (and 90% for runs scored presumably), that makes it a team win% of .400.

    • Zubin says:

      Thanks Tango… I should have thought before I wrote that. I imagine you are using RS^2/(RS^2+ RA^2) = win% to get to .400.

      So a BR or Fangraphs replacement level team is ~49 wins?
      Your (Tango’s) brilliant reader replacement level is ~65 wins?
      And Ponanski’s brilliant reader replacement level is ~69 wins?

  18. Chemo says:

    I’m surprised nobody has mentioned the way that WAR is spread out. Ryan accumulates a ton of wins over replacement, but it’s over a 26 year stretch. Gibson rolled up his over 16 years, and Pedro got them in about 14 years. So if you look at WAR per season, it looks like this:

    Pedro: 6.13
    Gibson: 5.1
    Ryan: 3.22

    So while I think most BR’s wouldn’t quibble with the standard replacement level, you also have to take into account when those wins are accumulated. Ryan was great over a long period, but I think if your goal is to win a World Series, you want the shorter bursts of pure domination (especially when the pitchers are also relatively close over time, as these three are). That’s why the Brilliant Readers chose Pedro and Gibson well ahead of Ryan.

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