Well, I was just poking around in baseball-reference's bWAR documentation area, and they've set up a side-by-side comparison for fWAR, bWAR, and BP WARP! (it also includes the original rWAR that is the ancestor of bWAR).

WAR Comparison Chart

It may not be entirely accurate about WAR versions other than bWAR, but it's a very handy source.

Sadly, it does not seem to include any information on the fWAR "league" element.

That being said, it looks completely borked for the 19th century.

This is a casual observation, not a rigorous one, but I feel like Fangraphs as an organization is more about evaluating modern-day players than older ones, so it wouldn't surprise me if some of their numbers are less reliable for 19th-century or pre-integration players. (You can kind of tell this because the descriptions of WAR in the Fangraphs glossary don't actually talk about older players; obviously they can't evaluate Tris Speaker's fielding with UZR, but they don't really say what they use instead.) They also don't give any info about how their positional adjustment changes over time (although if you look at the numbers, it does change; Johnny Evers is at 0 positional runs for most of his seasons, which correctly reflects second base being a less-important position 110 years ago than it is now).

Brent 91, I would suggest familiarizing with Kiko Sakatas Win-Loss records, of which he can explain here. Utilization of Retrosheet and a metric tied to team wins gives us some alternative insights.

Thanks for the mention, Bleed. If you're not familiar with my Player won-lost records, my website is here, an article describing the basics is here. Since the subject of positional adjustments came up, I delve into that here (warning: that's a 53-page PDF). And you can construct a custom-weighted HOM ballot from my Player won-lost records here.

One-paragraph explanation of my Player won-lost records. They're calculated at the game level using Retrosheet play-by-play data. pWins are tied to team wins - the guts of the calculation of pWins is Win Probability, with an adjustment at the end of the game so that total pWins and pLosses are the same in all games, regardless of how close they were - the players on the winning team get 2 pWins, 1 pLoss; players on the losing team get the reverse (1 pWin, 2 pLosses). After calculating pWins, I then also calculate eWins (expected wins) which control for context and the quality of a player's teammates. I also calculate wins over positional average (WOPA) and replacement level (WORL). The latter is one standard deviation below average (same basic concept as Dan Rosenheck's numbers, as I understood them).

My system is a big fan (relative to other systems) of above-average "inning eater" pitchers - Tommy John frequently gets "elect-me" votes from me; Tim Hudson debuted very strongly; my system is a fan of Andy Pettitte. In terms of position players, I've found that power tends to show up as more valuable than most run-based estimators show it - so, for example, I'm a big fan of, say, Jason Giambi, or, debuting in 2022, David Ortiz, whereas my system is less enamored of, say, Tony Gwynn or Ichiro Suzuki, who lacked the power one typically expects of a corner outfielder. Fielding credit is shared with pitchers, so the spreads of fielding value in my system tend to be a bit narrower - I didn't vote for Kenny Lofton, my system thinks Buddy Bell is a non-candidate (in both cases, their lack of power also hurts them). Conversely, my system really likes power hitters at premium defensive positions - the recently-elected Jeff Kent, Vern Stephens; Jorge Posada looks very good in my system if you make no further adjustments for his defense. Which segues into - for catchers, their fielding numbers are based purely on SB/CS, WP/PB, and balls in play. They share credit with pitchers for the first two and catchers handle very few balls in play, so my fielding numbers for catchers tend to be very small. That's probably the biggest weakness of my system, in my opinion.

Final caveat: because my system is built from Retrosheet play-by-play data, I have only calculated Player won-lost records for seasons for which Retrosheet has released play-by-play data, which, as of right now is 1916 - 2020 (and actually, I haven't updated my Player won-lost records for 2020, because I haven't taken the time to figure out how to incorporate the stupid zombie runner in extra innings atrocity into a win-probability framework; I promise to get around to that before 2020 players start showing up on HOM ballots (I believe that gives me five years, right?)). My system also doesn't do anything with Negro Leaguers. Retrosheet did just release some pre-integration Negro games (see my comment #85) and I'm hoping to do something with them in the next few months, but there aren't enough games there (yet) to really be terribly useful for something like the HOM.

This is the fangraphs WAR explainer for position players, although it is somewhat outdated - it doesn't talk about their framing metrics, which were introduced in 2019, but it does account for the unified replacement level which was 2013.

Here's the relevant section on the league adjustment:

The league adjustment is a small correction to make it so that each league’s runs above average balances out to zero. Each league’s Batting Runs + Base Running Runs + Fielding Runs + Positional Adjustment often total to something slightly different from zero. The league adjustment fixes this and has a very tiny impact on player value.

To find the league adjustment find the league specific values (AL or NL) and do the following:

League Adjustment = ((-1)*(lgBatting Runs + lgBase Running Runs + lgFielding Runs + lgPositional Adjustment) / lgPA)*PA

This will tell you how many extra runs you need to add to the entire league per PA and then you multiply that by the specific player’s PA. This will add between 0 and 5 runs to a player’s value per season based on their league and PA.

Looking at BBRef's WAR explainer

They have a nice chart detailing their league adjustments as part of Rrep, which also includes a debit for 1942-1946. No explanation of where those numbers come from though.

Brent, I think the most important thing you said in your post is that YOU’RE BACK!!!!

Yay, we’ve missed you and the many contributions you’ve made over the years. WELCOME BACK!!!

Bleed (#94)

Tommy Bridges has WWII and PCL.
Urban Shocker has WWII.
Babe Adams has WL/AA.

You must be confused about Shocker. His career spanned 1916-1928, well before WWII even started, and he was in MLB and the minor leagues during the tail end of WWI, not missing any MLB time or development time for war service (as far as I can see he had none).

You are right that Bridges missed 1944 for WWII. For Babe Adams, it is odd that he was demoted in 1917, I guess the Pirates must have thought he was done having posted a 5.72 ERA in 1916, but I guess I can see giving him some WL/AA credit for 1917. So, fair enough, my bad.

You must be confused about Shocker. His career spanned 1916-1928, well before WWII even started, and he was in MLB and the minor leagues during the tail end of WWI, not missing any MLB time or development time for war service (as far as I can see he had none).

Pretty sure this should have said WWI for Shocker. Per Shocker's SABR player biography, he was drafted in June of 1918, and didn't return from service until the May of '19. That's most of a year missed.

Similarly, Bridges didn't just miss '44 to WW2; he wasn't discharged until August of '45.

Thanks, everyone, for answering my questions and giving me helpful comments.

Chris Cobb, 91. "1) For bWAR's cross-league quality adjustments, their notes say that they are based on players who moved between leagues and on interleague play."

When I was looking through the old thread on DanR's WARP from 2007 I ran across the following comment from Rally:

Dan, what is your reason for counting the AL as weaker than the NL for this period? I looked at players who played in both leagues in the 1950's once, and found no significant differences in their quality of play from one league to the other."

That comment makes it appear that whatever adjustment for league quality he used for the 1950s, it wasn't based on players who move between leagues. The subsequent discussion on that thread talks about other data, such as a study by Dick Cramer from The Hidden Game of Baseball. But how the bbref league quality adjustments for the 1950s were calculated appears to be a mystery.

Kiko Sakata, 103. Thank you very much for summarizing your Won-Loss system and pointing me to information about it. There's a lot on your website and I will need to spend some more time trying to understand your system. I have a few questions for you:

= Reading the article on the basics of your system, it appears that individual events in each game are weighted according to the change in win probability due to the event. Is that correct? And does that remain true after all the various normalizations are applied? Should I expect the numbers for batters to be similar to Fangraphs WPA totals?

- Fielding. I see that for hits vs. outs on balls in play, you split the credit 70% fielders and 30% pitchers. I may have missed seeing how you split responsibility among fielders for hits. For example, a ground ball single to left field - is that split 50-50 between the shortstop and third baseman? Or do you have a formula for splitting responsibility for plays not made? And how do you split credit for outs when they involve multiple fielders?

- Play-by-play data. My understanding is that prior to the 1970s there are some missing games in the play-by-play data from Retrosheet (though a box score might be available instead). How did you handle incomplete or missing data?

- When you say, for example, "My system is a big fan (relative to other systems) of above-average "inning eater" pitchers," it wasn't clear to me which metric you are looking at. Do you prefer pWOPA or pWORL or eWORL?

- I'm confused about how should I interpret the difference between pWOPA and eWOPA. Is it removing the context play by play (similar to the difference between WPA and WPA/LI on Fangraphs)? You talk about expected context, but I'm not sure what that means.

Dr Chaleeko, 105. Thank you for your kind welcome.

Thanks for the interest, Brent!

"it appears that individual events in each game are weighted according to the change in win probability due to the event. Is that correct?" Yes

"And does that remain true after all the various normalizations are applied?" All plays for a given team within a given game get the same normalization, so, within a particular game, a ranking of players by net pWins would match a ranking of players by WPA, but the magnitudes of the numbers would differ.

"Should I expect the numbers for batters to be similar to Fangraphs WPA totals?" Not necessarily, because of the normalization process, which varies by game.

"For example, a ground ball single to left field - is that split 50-50 between the shortstop and third baseman?" The way I split fielding credit on hits is kind of complicated but explained here. The simple math answer is that a ground ball single to LF is debited about 56% to 3B and 44% to SS and that's based on working with location data from Retrosheet for the 10 years or so that they have it. All fielding credits go to the first fielder involved in a play except for double (and triple) plays where the credits go to the first fielder involved in each of the outs. So, a 6-3 groundout, all fielding credit goes to the SS; a guy thrown out at home 8-6-2, all fielding credit goes to the CF. The only shared fielding credits would be on double (or triple) plays as well as on force-outs in DP situations - e.g., runner on 1st, one out; on a 6-4 force-out, the second basemen will take a small loss for failing to turn the double play.

"Play-by-play data. My understanding is that prior to the 1970s there are some missing games in the play-by-play data from Retrosheet (though a box score might be available instead). How did you handle incomplete or missing data?" For games which are missing play-by-play, Retrosheet has begun to "deduce" these games based on newspaper game stories and box scores. I've done a lot of these deductions as has fellow HOMer Rob Wood. Retrosheet has released deduced games to fill in all of the gaps back to 1928. For 1916 - 1927, though, yes, there are missing games. This article details what we have.

For seasons with missing games, the default presentation will just exclude those games (e.g., Babe Ruth). There is a link on that page that says "Player records with missing games extrapolated"; clicking that will blow up the player's numbers based on how many games he's missing (e.g., player actually played 150 games; we have 100 - my "extrapolation" would just multiply all of his numbers by 1.5 (150/100). Here's Babe Ruth with his numbers extrapolated.

"Do you prefer pWOPA or pWORL or eWORL?" - Yes. One of the things I like best about my system is that it's not a single number, so people can choose their own preferences. In a "yes/no" Hall-of-Fame kind of environment, I tend to be fairly liberal in terms of evaluating players based on what makes their case the strongest (my personal Hall would include, for example, both Tommy John and Dwight Gooden). That doesn't quite work when you have to rank the players but my system doesn't force you to be a "career" or a "peak" or a "prime" voter. Certainly, Tommy John looks better the lower the comparison (i.e., he looks better in pWORL than in pWOPA) but, really, he looks pretty good in both.

"Is it removing the context play by play (similar to the difference between WPA and WPA/LI on Fangraphs)?" - Basically, yes. All home runs hit at Wrigley Field in 2016 have the exact same value.

"You talk about expected context, but I'm not sure what that means." - When I calculate a player's eWins and eLosses, I hold his total player decisions constant (by season) so if, doing the context-neutralizing thing, a player has a pRecord of, say 50-50, and an eRecord of 50-45, I blow up that player's eWins and eLosses so that he has the same win percentage but his eWins + eLosses equals his pWins + pLosses (so, this guy's record would become 52.6 - 47.4). This tends to have very little effect on non-pitchers. For pitchers, it tends to matter more - in effect, I'm building relief-pitcher leverage into my eWins (same as BB-Ref and Fangraphs do). One reason I do this is because it makes it a little easier to compare pWins and eWins - in the above example, this player's performance led to about 3 fewer wins (50 - 52.6 = -2.6) than would have been expected. Whether that matters in how you rank that player is up to you (and could reasonably vary player by player; pWins are absolutely affected by the quality of a player's teammates).

Hey, gang, I wanted to direct attention to part of an article we posted today at my website. Not trying to draw clicks, I promise, but I think it's thought provoking in terms of what we do around here. The part that's relevant to the work of the HOM is in the section called "Imagining a Better World," a little below the fold. There's some research and reasoning there that's of potential importance to our evaluation of the remaining pre-expansion candidates, both MLB and MLE players. I thought it might be worth some discussion because it could impact every player before 1958 and provide some additional thinking around chronological balance.

Again, not trying to clickbait anyone.

It's a great piece with interesting points for discussion but I have one thought.

Should we assume that in a hypothetical integrated baseball that the league remains at 16 teams? Or should we add the official Negro League teams to the count?

If we take 1926 as an example year (wiki page with all relevant league standings) - there were 8 teams in each of the NL, AL, NNL, and ECL, which is 32 official Major League teams. Now, it probably makes sense to toss out some of bottom tier Negro League teams that really didn't seem to be competitive at that level - the Brooklyn Royal Giants, Newark Stars, Dayton Macros, and Cleveland Elite Giants all had abyssmal records in league play, far below even the '62 Mets or the '03 Tigers. At the same time, we can add the clearly major league level Homestead Greys. That puts you at 27 major league teams as opposed to 16.

If we take an average hitter in the 16 team all white league (say Irish Meusel for 1926) and put him in a 16 team integrated league, he's definitely not an average hitter. But in an integrated 27 team league? I think he'd still be at that level.

Jaack, the way we thought it through was that had MLB integrated from the start, there would only have been 16 teams during the Negro Leagues era, but quality of play would be higher due to the presence of players of color. In essence that the Negro Leagues would never have existed if MLB (and the country in general) hadn’t been run by racists. Rather than 28 or 30 teams worth of players with all the replacement and below average hitters that entails, we are talking about a single league with best available talent, just as it became after integration. (I think it’s possible the NL of the 1960s might have been had the highest quality of play ever seen because the balance of players of color were in the NL, really two starting nines of All-Star players of color.) We felt that when we went by a 28-30 team expansion scenario, we would elect lesser MLB players who should not have been elected but should have moved aside for the better players of color. To take an example from current HOM elections, Bob Johnson still gets votes because he is a borederline candidate due to his performance as COMPARED TO MLB. But compared to the entire potential talent pool, he would drop far enough from the in/out line that he probably wouldn’t draw m/any votes. Hurley McNair among Negro Leaguecorner outfielders would push Johnson down the rankings too. The problem is that none of us, that I recall, and pls correct me if I’m wrong, adjust our rankings to reflect the effect of combining the talent pools. If blacks and whites had played together NONE of them would have been as good as their raw, value, or MLE stats currently show. This impacts latter-day players in important ways. We have been a little less generous with modern players and a reason for that could be that moderns are compared to a fully integrated league and pre-1960s players are not so the oldsters have an advantage that we calculated at around 14.5%.

Does that make sense? This is a little meta, so forgive me if I’m not as clear as I could be.

The problem is that none of us, that I recall, and pls correct me if I’m wrong, adjust our rankings to reflect the effect of combining the talent pools.

Correct. HoM has clearly treated NGL as a de facto expansion. The MMP project treats all the years before 1962 as if there were 20 teams.

NGL players per election
1901-1910 17/213 = 8%
1911-1920 46/201 = 23%
1921-1930 52/195 = 27%

This assumes I counted correctly, I could be off by a couple.

Another fun fact - only one Negro Leaguer has won an MMP award - Josh Gibson in 1940. 39 black or Hispanic (Canseco, A-Rod) players have won MMP in the 73 seasons since integration.

@112

You're making perfect sense – I don't really disagree with anything there, except pegging the replacement level to a sixteen team league. Well, maybe I don’t even straight up disagree with it. I kind of see three approaches that have some sort of logic to them.

1. Integrate the leagues by kicking out the bottom 10-15% of white players from the NL/AL and replacing them with the best available non-white players. Here you have a 16 team league.

2. Integrate the leagues by adding non-white players to the NL/AL so that they make up 10-15% of the league. In doing so, you’d have an 18-22 team league.

3. Integrate by just merging the NL/AL with the Negro Leagues, and redistributing the players. Here you end up with a 26-32 team league.

I do think the Hall of Merit has elected mostly in line with the second option, and I’m inclined to continue to vote in line with that standard on the basis of precedent. I also like that option as it pegs the level of competition to the strongest existing league, which follows in line with how I treat the seasons during WWII.

I do agree that option one seems the most plausible of the in a non-racist league counterfactual, but I can’t really back that up with anything.

I'm wouldn't argue that anyone should change their approach to your 1, 2, and 3 points above. I would advocate that regardless of which of those things you use, we need to adjust players downward in the pre-integration era because they currently have an unfair advantage over their more modern peers. Take for example the ultimate two borderline guys: Jake Beckley and John McGraw. One's borderline because he had an extremely shallow peak and an extremely long career. The other is borderline because he had an extremely high peak and a very short career. Not set them next to a couple of modern borderliners who are not in. Say John Olerud and Sal Bando who have more normal looking careers. If a massive, systematic, and non-baseball influence on Beckley and McGraw's play made their performance look better than it was, you'd probably want to adjust for it, right? That way Olerud and Bando could be on a level playing field with Beckley and McGraw. And that's exactly what I'm saying. I've measured the effect of integration in one way and, to speak reductively, found it cost top white players 14.5% of their WAA on a seasonal basis. (You don't have to take my word for it, of course, anyone could do their own study.) If you adjust Beckley's WAA and McGraw's WAA down by 14.5% each year, you'll find that neither of them is likely a borderline candidate anymore who would have received strong support. They would both likely occupy a section of the backlog where guys like Tony Perez, Frank Chance, Ned Williamson, and Matt Williams live. I'm bringing this to everyone's attention because I think this is potentially a really big deal, an elephant in the room that none/most of us realized was there. Of course, I could be wrong, but it seems really big to me.

If you assume a 4 team expansion when you go through the exercise of integrating players 1920-1947 onto the ballot the "average" point should stay in approximately the same place. The players who get pinched by that method would be those who played 1947-1962 because integration would force a "contraction" before it expanded back to that 20 team level.

I think this also applies to NGL MLE projections. NGL players would see a 14.5% drop in MLE WAA. That means (barring new data) we've found all of the Negro Leaguers and we may have over-inducted there as well.

DL, your first point is accurate. That's one of the reasons I prefer the 16-team model for 1871-1960.

Yes, this definitely applies to MLEs. The do not account for the integration effect and were designed to place one player into MLB at a time, not en masse. To put this in a nutshell:
A) Variance in the Negro Leagues is higher, so MLEs use z-scores to bring MLEs into an MLB range of variance.
B) Quality of play in the Negro Leagues is generally lower overall, so MLEs use an adjustment for that.
C) This new adjustment applies to all players because the MLE doesn't assume full integration and neither, of course, do the value stats many of us use for MLB value stats.

prefer the 16-team model for 1871-1960

12 is probably enough teams for 1892-1900 and 8 for 1871-1891.

those who played 1947-1962

Who gets underrated here? Nellie Fox, Phil Rizzuto, Johnny Pesky, Bus Clarkson, Luke Easter, Don Newcombe, Bob Lemon, Ralph Kiner, Ken Boyer, Minnie Minoso, Billy Pierce, Early Wynn, Richie Ashburn, Larry Doby, Duke Snider, Pee Wee Reese. Then there's your stars like Mays, Williams, Musial, Aaron, Mantle, Roberts, Banks, Kaline, Spahn, etc.

12 is probably enough teams for 1892-1900 and 8 for 1871-1891.
Yes, in effect they would be treated the same way as a 16 team league, but the only really important players with MLEs from that time are Grant Johnson and Bill Monroe, and Monroe hasn't proven HOM-worthy. (There's just not enough data from that time for Frank Grant.) Really, we're talking 1895-1957. The adjustment for 1871-1946 is set at 0.855, and from 1947-1957 generally rises as the degree of integration rises.

Who gets underrated here?
No one in that period (1947-1962) would be underrated, they would all be overrated, some by more than others, because they all would receive some downward adjustment for any seasons that fall in 1871-1957. Among backloggers whom I seem to recall getting votes any point, we're talking Stephens, Ellie Howard, Rizzuto, Elliott, Pesky, Clarkson, Easter, Marv Williams, Dandridge, Trout, Walters, and Newcombe.

No one in that period (1947-1962) would be underrated

I think we are treating it differently. I'm assuming a de-facto expansion to 20 teams. As integration happened that would mean an increase in WAA for that period until expansion recovered it.

Dr. Chaleeko, thanks for linking that research.

I am inclined to incorporate your findings into my rankings (probably slightly softened but I haven't decided yet). But the result would most likely mean a ballot that only includes players from the integrated era. As I ponder that, I'm a bit torn. We're all well aware (I think) that certain eras of history, in particular the pre-integration era, are already over-represented in the HOM. I firmly believe your research pinpoints the reason why.

So, would a ballot consisting entirely of players from 1960-present represent fairness to all eras? Certainly I think the argument could be made for yes, based on representation already in HOM, and assuming the voter has systematically and consistently considered pre-integration players against modern players. I have often semi-formally considered the requirement a moratorium on ballots with only modern players, as a way to ensure that voters with such ballots actually have studied/considered players from older eras. This would mean it is harder to verify that they have/haven't just from looking at their ballot.

At this point I'm just rambling a bit. But I do think this research is valuable.

Thanks for the share Doc, great systematic look at adjusting raw WAR totals.

To you and others, by the same token, how well does WAR adjust for expansions, strength of one league versus another (1950s/1960s NL vs AL, 1990s/2000 AL vs NL), NO expansion since 1998, WWII depleted talent?
At what level do you or others adjust these?
All factors to consider, though your research suggests that THE BIGGEST is looking at the pre-integration era ballplayers and assessing them properly.

Doc, when I look at your files at the HoME, what type of discount should be in play for Negro League MLEs?
Taking a player with a robust data set, I have Ben Taylor coming in at ~97/98% of a HOF career using your WAR/WAA translations?
Should I be docking ~14.5% from this?

how well does WAR adjust for expansions, strength of one league versus another

It really doesn't try to answer that question. It's trying to determine how many wins the player put up in that season compared to other players. Standard deviation adjustments normalize everything to the same runs/wins but even they don't try to assess league strength.

Bleed, you should dock 14.5% off of Taylor’s WAA. If Taylor had 1.0 WAA and 3.0 WAR, he’d end up at 0.86 WAA and 2.86 WAR. Please see the article for the adjustments for 1947-1957, which are less drastic as MLB moved toward fuller integration.

Is Baseball Gauge offline now? My browser won't go there anymore

Nevermind. Found the news item on Seamheads. RIP Baseball Gauge.

I've used the baseball gauge war as part of my HoM system. Hope we can get it somewhere after this

cookie, someone tipped me off to this previously, I was able to save the raw Excel file of data for Gauge/DRA WAR, post your email here and I can send to you, same goes for others.

Bleed, I'd be interested in that file. carlgoetz5@yahoo.com

Carl, I sent through and CC'd myself, we have both have Yahoo, so it should transmit ok :), let me know if it did not.

I was also able to download an excel copy of gWAR and also, if people are interested, Win Shares, and will be glad to send to anyone interested.

I was also able to download an excel copy of gWAR and also, if people are interested, Win Shares, and will be glad to send to anyone interested.

It would be great if someone could post the top Win Shares each year into the MMP thread

cookie, someone tipped me off to this previously, I was able to save the raw Excel file of data for Gauge/DRA WAR, post your email here and I can send to you, same goes for others.

cook9049@yahoo.com

Cookie, I sent through and CC'd myself, we have both have Yahoo, so it should transmit ok :), let me know if it did not.

I would love a copy of that database as well - my BTF email should work, but let me know if it causes trouble.

Can you list your email out Eric J, I'm not finding where I can send an attachment from BTF.

Fair enough. twototenth at gmail dot com.

Eric, I sent through and CC'd myself, hopefully it transmits ok :), let me know if it did not.

Got it, thanks!

Dr. Chaleeko, 110, 112, 116. Thanks for posting. I do have a methodological concern, though. To me, it doesn't make sense to apply a fixed percentage to a player's WAA. If we imagine an integrated league, the white players who would slip below replacement level and lose their jobs are all below average players, so someone who used to be average will now be below average compared to the new population of players. That implies that someone who used to be just above average (say a WAA of 0.3) is not going to lose 14.5% of of their WAA, but 100%. Conversely, someone with a very high WAA of 6.0 might only lose 5% or something like that. It's complicated, because both the mean and standard deviation would change, but I'm quite sure that a fixed percentage is not going to work. I hope this makes sense.

Brent, you make perfect sense. In a hypothetical integrated MLB of 1935, Satchel Paige and Dizzy Dean would both be dominant aces; Mel Ott and Josh Gibson would both hit 40+ home runs per season. The players hurt the most would be the ones who performed - in real life - around league average in their respective segregated leagues. Those men would suddenly find themselves at or near replacement level.

I think to make it work you need to reset "average" at 57.5% instead of 50% and replacement at .345 winning percentage instead of .300.

Brent, you are right. It’s the same trap as additive vs multiplicative park effects. Well, I’ll fix it at some point soon. But keep in mind the bigger point. MLEs and MLB stats are not adjusted in any way that accounts for the boost that segregation gave players. In my opinion it is very important to make such an adjustment, however you might do so, because we risk being unfair toward integrated modern leagues by not doing so.

Ardo, i don’t think you are quite right in one assumption. Or amd Gibson may but also may not hit their forty homers. It depends upon the quality of Black pitchers who enter the league and replace the innings of lesser white starters with higher quality innings. If Satchel Paige enters the league and replaces, say, Monte Weaver’s innings plus some by a fringe player, the league gets a little tougher. When the entire gamut of Negro Leagues pitching entera the league, the QoP should rise significantly making it harder to hit those forty homers.

Apropos of nothing...Speaking of Mel Ott, the most amazing thing about his 511 homers? He hit 40 just once (42 to be precise). But he hit 25 or more 11 times.