Or, the Perception Deficit Score

            I have tackled this general topic before.  I always say that, because it is always true; I’ve been doing this stuff for a long time.  I’ve written about this before, but I have some new ideas about how to make it work it, so let’s try it out and see if it works.  Let’s run it up the flagpole and see who salutes. Let’s put the pedal to the metal and see what this baby can do.   Let’s knock off the cliches and get to work.

            For many years, I would never address the question of whether a player was overrated. "Overrated" and "Underrated" lack clear definition.   Where are they rated?   Who rates them?  What does it actually mean to say that a player is overrated, or that he is underrated?  This is what I used to say, when somebody would ask me whether Tony Armas  was overrated.

            I gave up that approach sometime in the 1990s, in part because the development of the tools we all use to evaluate players gave each player a rating address, so to speak, so that this was no longer as true as it used to be.   Beyond that, a way of thinking about a problem can be true without being productive; it can even be true but destructive.   My old way of thinking about the problem was true, perhaps, but not productive. 

            And there is also this:  nobody owns the language.  I try to speak the same language that everybody else does.  That is why I don’t use acronyms unless they are universally understood; when you do that, you lose connection to those you are talking to.  Almost everybody uses those terms, overrated and underrated, and I know what they mean by them even if I can’t precisely pin it down, so what was I really accomplishing by refusing to participate in that discussion?

            OK, the current idea, which, I am sure, is actually merely a refinement of a previous idea.  Suppose that whether a player could be  described as overrated or underrated could be stated in the same form as a won-lost ratio?  Suppose that we could say that a player’s overrated/underrated score was 121-178, indicating that:

1)     He was underrated by 57 points, or

2)     That he was underrated by 47%, or

3)     That his Perception Deficit Score was .406, and anyone under .500 was at least a little bit underrated. 

Point (2) there turns out not to work, but I’m getting ahead of myself; at the time I wrote that I thought it might work.  (1) and (3) still work.  I like to call it the Perception Deficit Score, because once in a while I like to pretend to be a academic who can make up terms like that.   He’s got a PDS, now.    He doesn’t just have an OPS and a WAR and an oWAR and a dWAR; he’s got a PDS as well. 

I have in my mind a list of about 15-20 rules for establishing a player’s Overrated and Underrated Points.  Some of those rules are for pitchers, and this article does not get to the pitchers; the article is 11,000 words and 26 pages, but it doesn’t get to pitchers.  The rules are of two different types:  (1) rules that say that a player of this type, a player who does these things well, may be considered underrated or overrated because players who do those things tend to be overrated or underrated, and (2) rules that say that, comparing this player’s actual value to his recognition, we may observe that he IS overrated.   Some of the rules say that he SHOULD PROBABLY BE overrated or underrated; some say that he HAS BEEN overrated or underrated. 

And then there will have to be a "Backstop Rule", or "Mickey Mantle Rule".  The backstop rule is an override, to prevent the system from occasionally reaching stupid conclusions. I’ll have to figure out the details later, but a few players are so exceptional that you can’t evaluate them on this scale; it’s like weighing an elephant on a postal scale.  Mickey Mantle did many things in his career that would be characteristic of an underrated player.  He had a very high walk rate, for example—usually characteristic of an underrated player—and the number of times that he won the MVP Award (3) is much lower than the number of seasons that he was actually the best player in the league.   Mickey Mantle, or Mike Trout, or Ted Williams, or a few others in their group; it’s not a big room. 

But you can’t say that Mickey Mantle was underrated, because it is obviously not true.  He was worshipped.  He is legendary.  The voters don’t give the MVP Award to Mike Trout every year; that doesn’t mean he’s underrated.  It just means that they choose to give that award to somebody else sometimes.  It’s fine.

On to the list.  RBI men have historically been overrated, and are still overrated to a certain extent.  Any number of players who clearly were not the best player on their own team, let alone the best player in the league, have won MVP Awards because they led the league in RBI, or, occasionally, came close to leading the league in RBI while also having some auxiliary claim to value such as playing for a team which has a surprisingly good season. 

Our first rule, then, is:

1.    If a player has more RBI in a season than Runs Created, he is charged with overrated points.  If he has fewer RBI than Runs Created, he is credited with underrated points.

I don’t actually use Runs Created; I use .9 times Runs Created.  The reason for that is that not all Runs Scored are driven in, so if you just use Runs Created, the totals don’t balance.   Also, it’s not one to one; it is one overrated point for each 10 RBI more than .9 * Runs Created, rounded off to the nearest whole number.

 At this point I am only tracking position players, not pitchers, and  I am only tracking players who (a) started their careers no later than 1920, and (b) played at least 1,000 games.

The RBI rules are of type (1), rules that say that a player of this type is USUALLY overrated or underrated, rather than that we have after-the-fact evidence that he was.  At this point, after just these two rules and don’t get ahead of us, we’ve got a long way to go, but just after these two rules, the system would say that the most overrated players in history were:

1.     Joe Carter                       (37 to 0)

2.     Dave Kingman               (36 to 0)

3.     Lee May                          (33 to 1)

4.     Ruben Sierra                  (32 to 0)

5.     Juan Gonzalez               (32 to 0)

While the most underrated players ever would be:

1.     Rickey Henderson        (0 to 85)

2.     Pete Rose                       (1 to 68)

3.     Richie Ashburn             (0 to 66)

4.     Barry Bonds                   (1 to 61)

5.     Brett Butler                    (0 to 57)

Of course, there would be a serious problem with saying that all of these Hall of Famers and Hall of Fame type players are underrated, but we’ll deal with that when the time comes. 

            Somebody out there will tell me, if I don’t take a moment to head it off,  "What about if a player drives in runs because he hits well with men in scoring position, or what about if he doesn’t drive in runs because he never gets an extra base hit with men on base?  Is it fair to say that the guy who hits .350 with runners in scoring position is overrated?"

            Sure.  If you can document that a player’s RBI total is NOT a function of where he was in the batting order and who was on base, then go for it.  I don’t have the programming skill to get into that, but the details are negotiable.   What I am trying to explain here are the principles. 

Batting Average historically is the Master Statistic which controls (controlled) the perception of value.  People 50 years ago would argue vociferously that Dick Groat was a great player and site his batting averages as clear proof of this, with the same unbounded confidence that people now place in WAR.  This led high-average hitters to be overrated.  It still does; there are still people who want to put Bill Madlock in the Hall of Fame because he won several batting titles.  

            Our next rule, then, is that

2.   If a player has a significantly higher Batting Average than Secondary Average, he is charged with Overrated Points.  If he has a significantly higher Secondary Average than Batting Average, he is credited with Underrated Points. 

The actual formula for the points awarded here is

Batting Average, minus Secondary Average, +.002,

Times at bats,

Divided by 30, and rounded off to the nearest whole number.

The formula for Secondary Average is Total Bases minus Hits, plus walks, plus Stolen Bases, divided by At Bats.  The average batting average for all players in my study is .264; the average secondary average is .260.  That’s why the formula is designed that way, so that the scale for batting averages rests parallel to the scale for secondary average. 

In 1927 Lloyd Waner (Little Poison) had a batting average of .355 with 223 hits, but, since he drew only 37 walks and hit only 17 doubles and 2 homers, he had a secondary average of only .137.  This makes his batting average 218 points better than his secondary average (.355 - .137  =.218).  We subtract .002 and multiply that times his at bats, which were 629.   .216 * 629 is 136, divided by 30, is 4.53.  So Waner gets 5 "Overrated points" for that discrepancy, which is the highest total of all time. Lloyd Waner in his career is also the most overrated player all time, in this regard.  These are the top 6:

1.     Lloyd Waner      (46 to 0)

2.     Doc Cramer        (46 to 0)

3.     Nellie Fox            (40 to 0)

4.     Ichiro Suzuki      (39 to 0)

5.     Dick Groat          (35 to 0)

6.     Pete Rose           (34 to 0)

Let me point out that Lloyd Waner and Dave Kingman are as close to exact opposites as you can get—a little singles hitter who stuck out only 173 times in an 18-year career, and Kingman, a giant home run hitter who once hit .204 with 156 strikeouts in a season.   Which was considered a lot of strikeouts at the time.

And yet, Kingman and Waner both rank at or very near the top of different "overrated" lists.  How is that?

They’re specialists.  Specialists are always overrated.  Players who do one thing exceptionally well will always be overrated, because it is easier for the mind to grasp what it is that they do well than it is to find the balance of a bunch of things that a player might do well and poorly.

Equally interesting here is Pete Rose.  Rose ranked among the most UNDERRATED players on the previous list; here, he is among the most OVERRATED.  But both of those make perfect sense, and follow from these four true statements:

1.     Players who don’t drive in runs are generally underrated,

2.     Pete Rose was not an RBI man,

3.     Players who hit for a higher average than their overall skills are generally overrated,

4.     Pete Rose was a high-average hitter who didn’t do a tremendous number of other things. 

And these are the five most underrated hitters in this regard—that is, players who were far better than their batting averages:

1.     Barry Bonds                   0 to 105

2.     Rickey Henderson        0 to 69

3.     Jim Thome                     0 to 59

4.     Mark McGwire              0 to 57

5.     Ted Williams                  0 to 54

It may seem odd to describe Ted Williams, a career .344 hitter, as a hitter who was better than his batting average—but he was.   He was a much more productive player than your average .344 hitter. 

Historically, as Batting Average and RBI have dominated the casual, intuitive evaluation of players, walks have been invisible.  Into the 1970s, a casual baseball fan had no source that would tell him whether a player walked 20 times a year or 100, and most fans did not know whether a player who hit .300 did so with a .450 on base percentage, or a .325 on base percentage.  Historically, the "walks" and "on base percentage" categories were simply not part of a player’s evaluation.  They were invisible because they were not considered important.  "Walks" were something that a pitcher did, and something the batter received.  This caused players who had high walk rates to be underrated, often to the point at which they had difficulty staying in the lineup. 

You would be correct if you were to point out that Rule 2 gave some credit to the underrated player who drew walks, because "walks" are a part of secondary average.  You would not be correct, however, if you were to criticize this system for double-crediting walks, once in Secondary Average and once by themselves.  This would only be a valid criticism if the sum total of credit given for high walk rates was greater than the extent to which it caused players to be underrated. 

Giving credit for the same thing in different stages is not only allowable; it is preferable.  It is always better to look at an issue in different ways, just like camera angles.   You look at a play from one camera angle, the player looks safe; a different angle, he looks out.  You look at a political issue from one angle, it looks one way; you look at it from a different angle, it looks different.   The same with underrated and overrated; the more different angles you look at it from, the more accurate picture you have.   Dividing credit for something between different categories allows you to look at the issue in different ways. 

            These are the rules for underrated/overrated points directly in this area.   I don’t give any points here for seasons of less than 500 Plate Appearances.  Then:

            Rule 3)  Credit the player with 1 underrated point if his on base percentage is at least .0730 greater than his batting average, with 2 underrated points if his on base percentage is at least .0840 greater than his batting average, and 3 underrated points if his on base percentage is at least .0990 greater than his batting average.

Charge the player with 1 overrated point if his on base percentage is no more than .0633 points higher than his batting average, with 2 overrated points if it is no more than .0545 points higher, and 3 overrated points if it is no more than .0435 points higher than his batting average. 

            The standards are set so that there are equal numbers of players who are in each of seven groups.  Referring to underrated points as "+" points, the seven groups are +3, +2, +1, 0, -1, -2 and -3.   Of course, everybody with less than 500 plate appearances is at zero, but the rest of it balances.   Barry Bonds is at the top of the walks scale, of course; the highest seasons other than Bonds are by Gene Tenace and Eddie Yost.  Ozzie Guillen is at the bottom of the scale, bottom two seasons are both Ozzie.  Combining all three positive and negative categories, the five most underrated players so far would be:

            Yes, I see the problem, and I knew that was coming; we’ll deal with that later.  The next time I give you a list of the most overrated players so far in the analysis, I’ll just ignore those five players and give you the next five.  And these are the 5 most OVER-rated players, so far in the process:

            That looks like it could develop into a pretty good list, but I will note that Willie Davis, who I would tend to regard as more of an underrated player than an overrated player, shows as tenth on the overrated list, so we’ll keep our eye on that as the system develops. 

            Let’s move now to MVP Awards.  You may remember that a few weeks ago I published an article about players who had more Win Shares than the player elected as the Most Valuable Player.  That would certainly be relevant to a discussion of who was overrated and who was underrated.   Hence, the next set of rules:

         4)  All players who have more Win Shares than the elected MVP of their league receive underrated points for the season, the number varying from one to ten according to a pattern described below. 

All points in the league counted as underrated for one player are counted as overrated for the player who did win the League MVP Award. 

            Essentially, a player gets one point under rule 4 for each Win Share that he had above the number that the elected MVP had.  In 2019 Cody Bellinger, who had 31 Win Shares, won the MVP Award although Christian Yelich had 33 Win Shares.  That’s simple; Yelich is credited with 2 underrated points, while Bellinger is charged with 2 overrated points.  In 2018 Mookie Betts won the MVP Award with 36 Win Shares, although Mike Trout had 39.  Again, a simple one; Mike Trout gets three underrated points, and Mookie Betts is charged with 3 overrated points. 

            About 50% of the time the player who leads the league in Win Shares does win the MVP Award.  Most of the time, when there is a discrepancy, it’s just a few Win Shares.  Occasionally, however, a player wins the MVP Award who is not seen by the Win Shares method as a serious candidate for the Award.  Juan Gonzalez won the American League MVP Award in 1998 although he had only 25 Win Shares.  Ten players in the league had more than that, including Albert Belle, who had 37.  The other 9 of those are credited with one Win Share for each point of advantage that they had over 25.  Belle, however, is credited with only 10, because of a sub-rule:  No player gets more than 10 points under rule 4.

            When there is a large gap between the league leader in Win Shares and the elected MVP, it is always or almost always because the elected MVP had a total under 25.  In 1934, for example, Mickey Cochrane was the elected MVP with only 23 Win Shares, although Lou Gehrig had 41.   Lots of players had more than 23.   Mel Harder, to pick a name almost at random, had 27.  

            But is the fact that Harder had four more Win Shares than the elected MVP actually meaningful evidence that Harder was an underrated player?   The vote is strong evidence that either Mickey Cochrane was a very overrated player, or that Cochrane had value which escapes the understanding of Win Shares.   It doesn’t have anything to do with Harder; it has to do with Cochrane.   Harder is incidental.  It is not the common case that a player way down the Win Shares list wins the MVP Award, but it does happen once or twice a decade.  In 1944 Marty Marion won the National League MVP Award although there were 23 players who had more Win Shares than Marion.  Were all 23 of those players underrated?  Of course not.  

            To avoid implicitly making a false statement about those 23 players, I use a 10-6-5-4-3-2-1 pattern.  The player who leads the league in Win Shares cannot be credited with more than 10 Underrated points (by this rule; he will get more later, under the next rule.) The player who is second in Win Shares is not credited with more than 6 Underrated points.  The player who is third gets no more than 5, etc.  But there are two exceptions.   First, if two players are tied, the second one has to be treated equal to the first.   And second, every player who has more Win Shares than the MVP gets at least one overrated point. 

            Another reason for doing that—another reason for putting that 6-5-4-3-2-1 limitation on the points—is that I don’t want these points to swamp the system.  Under rules 5 (below), we’re going to give the player who should have won the MVP Award (the player with the most Win Shares) another 25-point bonus.  Without these bumper rails, Marty Marion in 1944 would be charged with 153 Overrated Points.  It would swamp the system.  It might make him the most overrated player of all time, not just in a season but in his career.  Marion’s selection as MVP is an instructive event, in regard to how he was perceived at the time.  It deserves a large "overrated" number.  But it doesn’t deserve to be larger than everything else in the system, so we limit the system so that it isn’t.   I hope that is clear. 

Rule 5:

5) The player who leads the league in Win Shares (that is, the other player who could have won the MVP Award) is given 25 "underrated" points.  These 25 points are also charged to the elected MVP as overrated points. 

"Having more Win Shares than the MVP" and "Not winning the MVP Award despite having the most Win Shares in the League" are overlapping concepts, like walk rate and secondary average, but they are not the same thing.   Mitch Webster in 1987 had 23 Win Shares, while the elected MVP, Andre Dawson, had only 20.  We give Webster an underrated point, but that’s nothing at all like being the best player in the league and being denied recognition for it.  The best player in the league was Tim Raines (who, by the way, basically idolized Andre Dawson.)   But it is Tim Raines who is REALLY denied recognition here, not Mitch Webster. 

The points given/charged under Rule 5 are 25, but they’re not always 25.  There are two situations in which they are not.  If the player who wins the MVP Award does not lead the league in Win Shares but it is  close, then we don’t award the full 25 points.  If the margin is just one Win Share, then it isn’t 25 points; it’s 5 points.   If the margin is just two Win Shares, then it’s 10 points; if three Win Shares, 15 points, if four Win Shares, 20 points. 

When the margin is close, we should lack confidence that the player with more Win Shares was actually more valuable.  In 2018 Cody Bellinger beat Christian Yelich in the MVP Voting although Yelich had two more Win Shares.  It would be silly to have immense confidence that my system was right, and the MVP voters wrong.  WAR believes that Bellinger was the right choice.  Maybe they’re right; I don’t know.  I go with Yelich, but he gets only 10 underrated points, not 25.  As the margin gets larger, I become more confident that the league leader in Win Shares has been shafted. 

The other situation in which the points are diminished is if there is a tie for the most Win Shares in the league between two players, neither of whom won the MVP Award.  That has happened about 10-15 times in baseball history.  When that happens, we divide the 25 points between the two players who tied for the league lead in Win Shares, giving the extra point (if necessary) to the player who had more WAR. 

Combining these two exceptions into one, in 1932 Chuck Klein won the MVP Award with 31 Win Shares, although two players (Mel Ott and Lefty O’Doul) had 33 Win Shares each.   Because the margin is only 2 Win Shares, the league leaders don’t have 25 points to split; they have 10.  Because they are tied, they get 5 underrated points each. 

Let’s update the charts.  Through 5 Rules, the most underrated players in the data (not counting the five superstars who made up the last chart) would be:

That list is not appreciably better than the last one, but we’re working on it.   And the overrated list is:

Again, these lists will change a great deal as the process continues to move forward. 

The next thing, the next set of rules, has to do with the Run Environment.  There are two different things involved here:

6)   Hitters who play in hitter’s parks, and pitcher’s who pitch in pitcher’s parks, can be overrated, while pitchers who pitch in hitter’s parks, and hitters who play in pitcher’s parks, can be underrated.   There will be an adjustment for this.

7)   Hitters who play in big-hitting eras like the steroid era, and pitchers who pitch in pitching-dominated eras (like the 1960s), tended (at least in the past) to be overrated, while pitchers who pitched in big-hitting eras and hitters who played in low-run eras can be underrated.  There is an adjustment for this. 

While these are different effects, we will adjust for them in one pass, in this way.   First, take the league average of runs per game, and then modify that by the park effect, creating the Park Run Context.   This will average something very close to 4.50. 

If the Park Run Context is over 6.00, each regular on the team (500 or more PA) is charged with 6 overrated points for the season.

If the Park Run Context is 5.75 to 6.00, each regular on the team (500 or more PA) is charged with 5 overrated points per season. 

If the Park Run Context is 5.50 to 5.75, each regular on the team is charged with 4 overrated points per season. 

If the Park Run Context is 5.25 to 5.50, each regular on the team is charged with 3 overrated points per season. 

If the Park Run Context is 5.00 to 5.25, each regular on the team is charged with 2 overrated points per season. 

If the Park Run Context is 4.25 to 4.75, no adjustment. 

If the Park Run Context is 4.00 to 4.25, each regular player on the team (500 or more plate appearances) gets 1 underrated point per season.

If the Park Run Context is 3.75 to 4.00, each regular player on the team gets 2 underrated points per season. 

If the Park Run Context is 3.50 to 3.75, each regular player on the team gets 3 underrated points per season.

If the Park Run Context is 3.25 to 3.50, each regular player on the team gets 4 underrated points per season.

If the Park Run Context is 3.00 to 3.25, each regular player on the team gets 5 underrated points per season.

I don’t believe any team ever played in a Run Context lower than 3.00 or higher than 6.00, but if they did, you can figure that out.  I do not adjust the 500-PA standard for strike shortened seasons.  (Later, after writing this, I found one.  The 1936 St. Louis Browns played in a Run Context higher than 6.00 Runs.)

I can’t update the standings at this point, because I don’t have the data organized in such a way that I can do that.  It’s not too difficult to do that for one player at a time; if I’m just doing a list of 5 or 10 players, it’s not hard to do that, but dealing with 18,000 player/seasons, I don’t have the data in the spreadsheet to do that.   Let’s move on. 

OK, the next one on our list is going to seem wrong to a lot of you, but I know this is right, so I’m going to do it.

8)    All players who have 600 or more at bats in a season are charged with one overrated point.  Players with 610 or more at bats are charged with a second overrated point.

Players who have 400 to 499 at bats in a season are credited with one underrated point.

This has to do with standards, or counting numbers.  Counting numbers were central to the evaluation of baseball players for a century, and still are to some extent.  Standards were the signals which made the counting numbers look like value.  There is a vast array of "counting number" standards—100 runs scored, 200 hits, 100 RBI, 30 homers, etc.—but the "almost" numbers had huge impact on how players were evaluated, as well.  90 RBI is a lot different than 70; 180 hits is a lot different than 160.  40 doubles is or was a standard of excellence, and 10 triples, and 20 homers and 40 homers and 50 homers.

When a player has 625, 650 at bats in a season, he has full access to those standards.   When he bats 400, 450, 480 times in a season, he has almost no access to those standards—even if he was, in fact, a better hitter than the 625-at bat guy.  Of course, the player who is in the lineup every day, the player who plays 157 or 160 games is most often a more valuable player than a platoon player who plays 135 games and bats 440 times; I’m not saying he isn’t.   I’m saying that it isn’t proportional.  Those "topping off" at bats have a greatly disproportional impact on the perception of the player, and that is what this article is about—distorted perceptions. 

In my data from the years 1920 to 2020, only players whose careers began 1920 or later. . . in my data there are 144 players who had 600 or more at bats with a batting average between .275 and .300 and an OPS between .725 and .775.   There are 256 players, almost twice as many, who had 400 to 499 at bats with a batting average between .275 and .300 and an OPS between .725 and .775.   Same quality of hitters in both groups.

But in the 600-PA group, there were 35 players who scored 100 runs, 3 who had 200 hits, 7 who had 100 RBI, 7 who hit 30 homers, 17 who hit 40 doubles, and 11 who stole 50 bases.  Just focusing on those standards, there are 80 positives with 144 players.   In the 400-499 At Bat group, there is no one who scored 100 runs or had 200 hits, one player who drove in 100 runs, one who hit 40 doubles, and two who stole 50 bases.  They are four players who met a standard, in 256 players.  The density of standards met is 36 times higher when a player bats 600 or more times in a season.

In a sense this is obvious, but what is less obvious is the impact these has on distorting the value perception of these players.   Norm Cash was a VASTLY better player than Bill Bucker.   According to Baseball Reference, Cash leads Buckner in WAR, 52 to 15.1.   Cash, playing through the hitting dearth of the 1960s, had a career OPS of .862. Bill Buckner, not playing through any hitting dearth, and playing much of his career in the great hitter’s parks of Wrigley Field and Fenway Park, had a career OPS of .729  

But Buckner had five seasons with 600 or more at bats, whereas Cash had one, and Cash had eight seasons with 400-499 at bats.  Because of that, and TOTALLY because of that,  Buckner had 200 hits twice, led the league in doubles twice, had 46, 41 and 39 doubles in seasons in which he didn’t lead the league, and drove in 100 runs three times.  I asked people on Twitter "Please do this without checking WAR.  Who was a better player, Bill Buckner or Norm Cash?"   In the early voting, Buckner was beating Cash 80-20.  After a while the question got bruited about among my Twitter followers and people saw tweets from others who DID check WAR, the dirty cheaters, so the voting evened out, but Buckner still won, 57-43, among more than 1,000 votes.  Because he batted more times in a season, Buckner was perceived as more valuable than a player with essentially four times as many Wins Above Replacement. 

            Another one. . .Nellie Fox and Willie Randolph.  Randolph and Fox were very similar players, and Nellie Fox was a very good player, and a player and man who was worthy of admiration.  But Willie Randolph was easily a better player than Fox, beating him 65.9 to 49.5 in WAR, and also collecting more Win Shares in a shorter career.   He played for more successful teams, and he played in New York.

            Yet Fox won an MVP Award, and is in the Hall of Fame.  Willie Randolph did not win an MVP Award, and dropped off the Hall of Fame ballot after one year, drawing 1% in the voting.  Why?  Fox had 12 seasons with 600 or more at bats, leading the league in at bats several times.  Randolph had no seasons with 600 at bats.  Fox thus scored 100 runs four times, and led the league in hits four times as well as leading in other categories.  Randolph, although he scored more runs per game, per at bat or per plate appearance than Fox did, never scored 100 runs in a season, and never led the league in anything except one season with 119 walks. 

            So, regardless of whether other people know it or not, I know that this is a significant factor in players becoming underrated or overrated, and I’m going to put it into the system.    These are now the 5 most underrated players, ignoring the 10 superstars that were listed before. 

            We’re creeping closer to having a meaningful list.  Raines and Mel Ott, although they are Hall of Famers and their scores will be adjusted for that, are actually underrated players.  The "Overrated" list is the same as it was the last time I posted it, so I’m not going to update that one.  In fact, this is the last time I am going to update the lists; the math on that is becoming unwieldy. 

            My next rule has to do with making the All Star team without solid evidence of deserving it.   The rules here will be:

            Rule 9) A player who does not make the All Star team despite being credited with 20 or more Win Shares for the season will be credited with one underrated point for each Win Share over 19., up to a limit of 10.  A player who DOES make the All Star team despite earning less than 20 Win Shares for the season will be charged with one overrated point for each Win Share less than 20, without limit.

            Jimmie Foxx in 1933, Dick Allen in 1964 and Jeff Bagwell in 1996, for example, did not appear in the All Star game despite earning 41 Win Shares each. Foxx and Bagwell were on the All Star roster, but did not appear in the game.  For this, they received 10 "underrated" points each.  Which actually is not the best example, because the guys this is really intended to credit are more like Scott Rolen, who was not named to the All Star team in 1997, 1998 or 2001 despite having 29 Win Shares in 1997, 30 in 1998, and 29 in 2001.  This interfered with Rolen’s receiving the recognition that he deserved for his outstanding play.   Ken Singleton was not named to the All Star team in 1972, when he had 28 Win Shares,  or in 1975, when he had 33 Win Shares,  or in 1976 (24 Win Shares), or 1978 (28) or 1980 (23).   (In 1975 Fred Lynn, John Mayberry and Ken Singleton tied for the league lead in Win Shares, with 33 each.   Lynn and Mayberry finished first and second in the MVP voting.  Singleton finished 10^th.)

            Luis Aparicio, on the other hand, appeared in 8 All Star games in six different seasons in which he had less than 20 Win Shares.  In 1971 Aparicio earned only 8 Win Shares and had negative WAR for the season, but started the All Star game and played the entire game ahead of Freddie Patek, who had 24 Win Shares that season, Leo Cardenas, who had 22, and Mark Belanger, who had 21.  Cardenas was on the All Star team as the backup shortstop, but never got into the game.    

            There are many examples like that, of players who earned star reputations early in their career and appeared in All Star games for years thereafter, sometimes as an honor to a legendary veteran, but many times simply as a misperception of their value.  1940s catcher Walker Cooper built a "star" reputation in 1942-1943, and appeared in the All Star game in 1946 despite earning only 6 Win Shares on the season (0.7 WAR).  1960s first baseman Bill White appeared in six All Star games in seasons in which he had less than 20 Win Shares. 

            Another thing that people THINK is a factor in a player being overrated or underrated is playing in a really big city, like New York or Los Angeles.  Well, not LIKE New York or Los Angeles; actually New York or Los Angeles.

            People believe that’s a factor, but I’m not convinced that it is.  The larger the city, the more the local press will pick holes in the performance of the players.  A bright spotlight exposes small flaws.   Whenever a smaller-city player doesn’t win an award, people complain about their players not getting treated fairly, but the only franchise which has been around since 1980 and has never won an MVP Award is the New York Mets.  Since 1960, the Pirates have had more MVPs than the Dodgers have.  Since 1970, the Rangers have had more than the Dodgers.   Since 1960, the Cardinals and the Reds have had more than the Pirates or Rangers.  Since 1960, the Cardinals and the Reds have had more than the Yankees have, even though the Yankees started up by four, winning MVPs in 1960, 1961, 1962 and 1963.   When a player does not win an award that he deserved, we’ll deal with that.   But I don’t want to presumptively say that this happened because he didn’t play in a big city, and then pile that on top of the other. 

            One thing that plausibly might cause a player to be overrated, however, is getting the opportunity to play in the World Series.  Within my data—within this data set I am working with, 18,134 player/seasons—the ratio of career games played to World Series games played is almost exactly 250 to 1.   Let us say, then, that for each 250 regular season games a player plays, he has an expectation of playing in 1 World Series Game. 

Rule 10) For each World Series game that he plays above expectation, he is charged with 1 overrated point, up to a limit of 20 points, rounded off to the nearest whole number. For each World Series game that he doesn’t play below expectation, he is credited with one underrated point.

            This list in a raw form is absurdly asymmetrical.   No one in history is more than -11 (11 underrated points), while Yogi Berra would be +67.   Accepting for the sake of argument the premise that Yogi’s regular appearances in the October Classic may have made him overrated in his era, a 67-point overrated charge would seem to be grossly excessive. 

            The next rule a small one, probably only effects maybe 10 players in history. 

            Rule 11)  If a player wins the Rookie of the Year Award while another player eligible for the award earns more Win Shares, credit the player who did not win with one underrated point for each one difference in Win Shares, and charge the player who did win the award with offsetting overrated points. 

            Rule twelve will have to be summarized here; the words may not make sense at first.

        Rule 12) Every player who has more than 150 Career Win Shares will be assigned a "HOF Vote Equivalent" based on his performance in Hall of Fame Voting, and will then be assigned overrated points or underrated points based on the relationship between his Vote Equivalent and his actual Win Shares. 

            The Vote Equivalent Score works like this.

          &nbs​p; If a player is Elected to the Hall of Fame in his first year of eligibility with a vote of more than 90%, his Vote Equivalency is 500.

            If a player is Elected to the Hall of Fame in his first year of eligibility but with a vote of less than 90%, his Vote Equivalency is 450.

            If a player is Elected to the Hall of Fame within his first five years of eligibility, but not in his first year, his Vote Equivalency is 400. 

            If a player is Elected to the Hall of Fame by the BBWAA, but not within his first five years of eligibility, his Vote Equivalency is 350. 

            If a player is elected to the Hall of Fame by the Veteran’s committee, his Vote Equivalency is 300. 

         &​nbsp;  If a player appears on the BBWAA ballot but has not been elected to the Hall of Fame, his Vote Equivalency Score is 150, times the highest percentage that he achieved (or has achieved) in the voting, plus 150. 

          &nb​sp; If a player never appears on the BBWAA ballot, his Vote Equivalency score is 150. 

            Having then established his Hall of Fame Vote Equivalency Score, we compare that to his Career Win Shares.   If the Win Shares are higher than the Vote Equivalency Score, the player is credited with Underrated Points, in the Ratio of 1 to 4, rounded down.  If the Vote Equivalency Score is higher than the player’s career Win Shares, he is charged with Overrated Points, in the Ratio of 1 to 4. 

            To understand the process. . ..Joe Morgan had 512 Career Win Shares.  He was elected in his first year on the ballot, but with less than 90% of the vote, so that’s a Vote Equivalency of 450.  His Win Shares are 62 greater than his Vote Equivalency Score, so he is credited with 15 Underrated Points.

            Eddie Mathews had 450 Career Win Shares.  He was elected to the Hall of Fame in his 5^th year on the ballot, so he is credited with 12 Underrated Points.   (450 – 400) = 50 / 4 = 12.5  (12)

            Tony Gwynn had 398 Career Win Shares.   He was elected to the Hall of Fame in his first year on the ballot, receiving 98% of the vote.  His Vote Equivalency Score is thus 500, so he is charged with 25 Overrated Points.   (398 – 500) = -102 / 4 = 25.5 (25). 

            Lou Whitaker had 351 Career Win Shares.  He dropped off the ballot after one year, receiving 2.9% of the vote, so his Vote Equivalency Score is 154.  He is thus credited with 49 Underrated Points—a huge number.   (150 + .029 * 150) = 154.35 (154).   (351 – 154) = 197 / 4 = 49.25 (49). 

            Tony Perez had 349 Career Win Shares.  He was elected to the Hall of Fame in his 9^th year on the ballot, so that’s a Vote Equivalency Score of 350.   Since his Career Win Shares almost match his Vote Equivalency Score, he has neither Underrated or Overrated Points arising from this part of the system. 

            Dennis Eckersley and Buddy Bell, onetime Cleveland teammates, retired with 301 Win Shares each (and with similar WAR, Bell being a point ahead.)  Anyway, Eckersley, with 301 Win Shares, was elected to the Hall of Fame in his first year of eligibility but with less than 90% of the vote, for a Vote Equivalency Score of 450.   This translates to 37 Overrated Points (450 – 301) = 149 / 4 = 37.25.  Bell, also with 301 Win Shares, drew 1.7% of the vote, thus dropping off the ballot.  This makes a Vote Equivalency score of 153 [(150 * .017) = 2.55 + 150 = 152.55.]  So while Eckersley gets 37 Overrated Points, Bell gets 37 Underrated Points.

            Daryl Strawberry retired with 252 Win Shares.  He drew 1.2% of the vote, a Vote Equivalency Score of 152.  He thus is credited with 25 Underrated Points.

            Gary Gaetti’s data is almost exactly the same as Strawberry’s.  Strawberry had 252 Win Shares, 42.2 WAR, and 1.2% of the vote in his first year.  Gaetti had 249 Win Shares, 42.1 WAR, and 0.8% of the vote.   He also gets 25 Underrated Points.

            And finally, let’s do Jim Sundberg, Mo Vaughn and Lee Smith together in Chart Form

            Obviously, the Hall of Fame Voters like relief pitchers (Eckersley and Smith) far better than the analytical systems do.   But that doesn’t necessarily mean we’re right.   It could be just that we’re missing something. 

            OK, we have two more rules now to close it out.  One is a "positional correction". 

      ​  Rule 13:  The Points Awarded under the previous 12 rules will be adjusted to remove a bias against players at key defensive positions. 

            The system as I have outlined it so far is unfair to catchers and shortstops.  This system, because it is dependent on hitting stats to some degree, has a strong tendency to classify catchers and shortstops as Overrated,  Catchers, as a group, are not overrated; they are treated unfairly by the analytical process.  To correct for that, we credit players with "underrated" points equivalent to .073 times Win Shares for a catcher, and .064 times Win Shares for a Shortstop—applied season by season, so that if a player is a shortstop one season and not a shortstop some other season, the two seasons are treated differently.

            On the other side of the ledger—all of these things must balance, at least generally—on the other side of the ledger:

            Right Fielders are charged with .025 Overrated Points per Win Share,

            Center Fielders are charged with .037 Overrated Points per Win Share,

            Left Fielders are charged with .039 Overrated Points per Win Share,

            First Basemen are charged with .040 Overrated Points per Win Share, and

            Designated Hitters are charged with .089 Overrated Points per Win Share. 

            Second Basemen and Third Basemen do not have adjustments, as both positions are within 1% of balance without any adjustment.

            Rule 14:  Superstar Correction Rule:  For Players who win MVP Awards and are elected to the Hall of Fame, but who still show up as "underrated" under rules 1-12, we will apply a correction to prevent the system from reaching an obviously false conclusion.

            As I explained early in the article, players like Mantle, Ted Williams, Musial, Bonds and Mike Schmidt have characteristics consistent with being underrated players.  But it is absurd; you can’t say that Mickey Mantle is underrated.  So here’s what we do.

        &nbs​p;   For players who show as underrated, and who either won an MVP Award or made the Hall of Fame, we subtract the underrated points from the overrated points, and remove some of the underrated points. 

            10% of the margin (the underrated points minus the overrated) for the first big award (MVP Award or Hall of Fame selection),

            20% of the margin for the second one,

         &nbs​p;  30% of the margin for the third one,

            40% of the margin for the fourth one, and

            50% of the margin for the fifth one.

            That’s not 150% total; that’s 85%. 

            After you remove the first 10%, you have 90% left.

       &n​bsp;    If you remove another 20% of that, you have 72% left.

          &nbs​p; If you remove another 30%, you have 50.4% left,

            If you remove another 40%, you have 30.24% left.

            If you remove another 50%, you have 15.12% left. 

            There are Hall of Famers who are still underrated players, and there are certainly Hall of Famers who are overrated players.   This rule just focuses on the exceptional cases whose scores would otherwise be misleading. 

            OK, that’s the whole system.   Now let me pick 10 players at random, and illustrate the process. 

        ​    I asked my computer to pick 10 players at random, and it did, and I’ll create over and underrated profiles for those ten players, starting with the weakest of the ten, Gates Brown.

            For those of you not old enough to remember, Gates Brown was a Tigers player of the 1960s and early 1970s.  I think . . ..if I remember right, and I sure hope I do. . . I think he was discovered playing baseball in prison for some youthful offense, despite which he was a well-liked, popular player and, as best I understand it, a good teammate.  He was short and thick, listed at 5-10 and 225, despite which he ran fairly well, going 30-for-38 in his career stealing bases.

            As a rookie in 1963 he mostly pinch hit, then got a shot as a regular in 1964.  He wasn’t bad, hitting .277 with some power, but his defense was poor, and he (a) lost his job to Willie Horton, who was a similar player but better, and (b) pinch hit for the rest of his career.  People think he was a great pinch hitter, because he had a great season in 1968, hitting .370 with power to help the Tigers win 100-some games and the World Series.  He also had a very good season as a pinch hitter in 1971, although honestly most of his other seasons were. . . well, pinch hitting is a tough job. 

            The incident that Brown is most remembered for is one time when, eating a hot dog in the clubhouse, he was unexpectedly called upon to pinch hit.  He quickly stuffed the hot dog in his pocket, apparently forgetting that it had mustard on it.  He hit a double and slid in to second base; when he got up he had a giant mustard stain emanating from his pocket. 

            Anyway, this is Brown’s overrated/underrated profile:

            Our process suggests that Brown was not overrated or underrated to a significant extent, which I would probably agree with.   Next, an active player.

            The system believes that Calhoun has been meaningfully underrated.  I don’t know whether I agree or disagree, but I do very distinctly remember an announcer in a game this summer (fall) saying that Calhoun was an underrated player.  I remember it because I wasn’t sure whether I agreed or not.

            Candy Maldonado.

            Although there is some counterbalancing information, Maldonado was probably overrated, based on

1)     Being a better RBI man than overall hitter,

2)     Appearing more than average in World Series games,

3)     Being an outfielder in a system that overrates outfielders. 

Phil Nevin would appear to be not likely overrated or underrated.

          &nbs​p;  

            Omar Infante appears to have been likely a somewhat overrated player:

            Again, this is not to say that he WAS an overrated player; merely that it appears to me, as best I am able to measure such a thing at this point, that he has the characteristics of an overrated player.   He didn’t walk, and his batting average was much higher than his actual offensive value. 

            I can see, now that we’re here, that I have made a mistake in how I set up the test players display.   The problem with running the data for Omar Infante and Phil Nevin is that nobody cares whether they are overrated or underrated.  It is not just that nobody cares; it is that nobody cares enough to HAVE an opinion on this issue; therefore, a statistical approach to find that opinion is like a well-funded mission to find Bigfoot:  there is no Bigfoot there to find, no matter how you go about it.  I need to change my rules for identifying test players. 

        &n​bsp;   I’m going to look for players between 215 and 335 Career Win Shares.   This discussion sort of organizes around the Hall of Fame and a few special players.  Below 215 Win Shares, generally, you’re not a Hall of Fame candidate.  Above 335, you’re pretty much automatic unless you have an issue of some kind, so let’s focus on the players between those two posts.   We’ll start with Orlando Cepeda.

            Well, that’s a little more interesting.  The data suggests that a player with Orlando Cepeda’s profile would be likely to be overrated, which I believe that he probably was.  Cepeda’s Hall of Fame Equivalent Score (300) is almost the same as his career Win Shares (310), suggesting that that part of the system works sometimes.  Note that we are not suggesting that Cepeda is unworthy of Hall of Fame selection; indeed, I would say that he IS worthy of Hall of Fame selection.   But one can be both a legitimate Hall of Famer, and overrated within that group of players, the Hall of Famers.   I believe Cepeda was; I think it is a fair comment.

            The other note is that Cepeda’s All Star selections match very well with the criteria we established for that.   The rule we established was that if you have 20 Win Shares, you should make the All-Star team, and if you don’t, you shouldn’t.  Cepeda, who played in 11 All Star games, made the All Star team in every season that he had 20 Win Shares except his rookie season of 1958, when he had exactly 20, and 1970, when he had 21, and Cepeda did NOT make the All Star team in any season when he did not have 20 Win Shares.  He had 19 Win Shares in 1966, 17 in 1968 and 19 in 1969, but did not make the All Star team in any of those seasons.  (It is jumping ahead of our narrative, but Paul O’Neill is also like that.  He appeared in the All-Star game in 1991, 94, 96, 97 and 98, and had 20 Win Shares in 1994, 96, 97 and 98.  In 1991 he didn’t have 20, but he had 19. 

            Jim Bottomley has an overrated/underrated profile very similar to Cepeda:

            Both Bottomley and Cepeda were first basemen who were more RBI men than complete offensive players, although both were tremendous offensive players, but they were not players like Musial and Mays and Trout who were just all-around great hitters.  They might drive in as many runs as Mays or Musial or Trout, but not have the same offensive value; that’s what we rely on to say that this is an indication of being overrated.   The basic difference between Cepeda and Bottomley is that Cepeda played through a low-hitting era and played in several parks that did not favor hitters, whereas Bottomley played in a big-hitting era and in good hitter’s park.   Set those points aside, and Cepeda would score at 102-11, and Bottomley at 105-12. 

        &nbs​p;   A REAL parallel between Bottomley and Cepeda is their MVP Awards.  Bottomley was the Cardinal’s first baseman in 1928, led the National League in RBI, and the Cardinals won the pennant, and Bottomley was named the MVP.  Cepeda was the Cardinal’s first baseman in 1967, led the National League in RBI, and the Cardinals won the pennant, and Cepeda was named the MVP.  Neither man is credited with leading the league in Win Shares, although both have MVP-territory numbers.   Bottomley had 30 Win Shares in 1928, but the league leader was the Pittsburgh right fielder, Paul Waner, who had 34.   Cepeda had 34 Win Shares in 1967, but the Pittsburgh Right Fielder, Roberto Clemente, had 35.  Clemente was not actually the leader; the league leader in Win Shares in 1967 was Ron Santo, but still. . .pretty neat parallel there. 

            Bottomley’s score has several tricks in it, and you could score it differently.  I was really intending only to score BBWAA MVP Awards, not the old league awards, and Bottomley’s MVP was before the BBWAA took that over, so you could ignore it.  Still, he won the MVP Award, and he probably wasn’t the best player in the league, so it seemed to me best to mark it that way.   A similar thing with the All Star games; Bottomley did not play in the All Star game in six seasons in which he had 20 Win Shares, so you could credit him with underrated points for that, but he didn’t play in those All Star games because, at that time, there were no All Star games.  It doesn’t seem reasonable to me to say that he was underrated because he wasn’t selected to play in games that were never played.

            The Hall of Fame did not exist, either, at the time that Bottomley was active, so if Bottomley had not been elected to the Hall of Fame, this might be a cause to argue that those points should not be  counted against him.  But since Bottomley (a) WAS elected to the Hall of Fame, and (b) pretty clearly did not really need to be, it is difficult to see how Bottomley suffered any disadvantage there.  So we see Bottomley as seriously overrated, which, to be frank, seems to be obviously true.   

And now for something entirely different, Darrell Porter:

            The chart suggests the likelihood that Porter was significantly underrated.  

            Which, in my opinion, was absolutely true.  He earned 222 Career Win Shares, but didn’t draw a single vote when his name appeared on a Hall of Fame ballot.   Bob Boone had 210 career Win Shares,  Tim McCarver 204, Elston Howard 203, Benito Santiago 190, Del Crandall 179, Tony Pena 175, Terry Steinbach 173, Rick Dempsey 158, Manny Sanguillen 157, Terry Kennedy 150, and Sandy Alomar Jr. 115—yet all of those men, all catchers from essentially the same era, all received SOME support in Hall of Fame voting.   Even Steve Yeager, with 106 career Win Shares, picked up a vote from a Hall of Fame voter.  If you prefer WAR to Win Shares, Porter not only had more WAR than any of those other catchers, he had at least 45% more WAR than any of them.  Porter is credited by Baseball Reference with 40.9 WAR; the highest figure for any of those other catchers, who were mentioned in the voting, was 28.3, by Tim McCarver.  So. . .of course Porter is underrated.  (Porter also had more Win Shares and WAR than Jim Sundberg, also mentioned in Hall of Fame voting; however, since Sundberg had 200 Win Shares and 40.5 WAR and got only 1 Hall of Fame vote, he is actually more like Porter than the other catchers on that list.)

            Paul O’Neill’s overrated/underrated profile is almost perfectly balanced:

       &​nbsp;    We couldn’t say that O’Neill is likely to be overrated or underrated.  O’Neill did get a bad deal in Hall of Fame voting.  O’Neill had 259 Career Win Shares, one more than Jim Bottomley.  He also leads him in WAR, 38.8 to 35.  Bottomley is in the Hall of Fame; O’Neill dropped off the ballot after drawing just 12 votes in his first look. 

            This isn’t really because O’Neill got screwed in Hall of Fame voting; it is mostly because Bottomley got lucky.  Still. . .O’Neill could reasonably have stayed on the ballot for a longer look. 

            And finally, Brian Downing:

            Brian Downing is nearly the complete underrated player, with an overrated percentage of 14.6%. 

            Reading this just before publishing it, I realize that this article is long and technical.  I wanted to explain everything, so that, if you choose, you can create an overrated/underrated score for any player.   But part of the theory of this bit is that I will respond to your questions about players you think are overrated or underrated, and I will do that, a little bit, as much as I have time to do.  It does take time to do these profiles; I can semi-automate most of the process, but some things I have to dig through item by item, so it takes time.  Please suggest players you would be interested in, but remember that my time is limited, so if you suggest more than one, I’m just going to ignore you.  Thanks for reading.