Let me ask you a question which you have probably never thought about and certainly don’t have any method to approach, but nonetheless know the answer to.  Pick a player at random. . .Aaron Rowand of the Giants.  What was his best number last year?

            His best number is his doubles, right?   Thirteen homers, 44 walks, 2 steals, .271 average. . .who’s impressed?   His good number is that he hit 37 doubles.

            Take these five players (below, in order). . .Mike Aviles of the Royals, Fred Lewis of the Giants, Curtis Granderson of the Tigers, Orlando Cabrera of the White Sox, Adrian Gonzalez of the Padres.   What was the best number for each player?

            Aviles’ best number is his .325 batting average.   Lewis’ best number is his triples, 11.  Granderson hit more triples than that, 13, but his best number is his runs scored, 112.   Cabrera’s best number is his hit total, 186, and Gonzalez’ best number is his home runs, 36.   

Let’s do five more. . .Justin Morneau of the Twins, Jeff Keppinger of Cincinnati, Willy Taveras of Rockies (last year), Russell Martin of the Dodgers, and Carl Crawford of the Rays:

            Morneau’s best number is his RBI count, 129.  Keppinger’s best number is his strikeout rate—24 Ks in 459 at bats.   Willy Taveras’ best number by far is his stolen base count, 68.  Russell Martin’s best number is his .385 on-base percentage, and Crawford’s best number is his triples, 10. 

            You might not agree with all of those, but. . .we can agree on eight out of the ten, right?   But have we ever talked about this, ever studied it, ever outlined any method to determine what is each player’s best number?  A consensus exists about a subject which we have never discussed.  

            A player’s best number is the number that the opposing team’s announcers will point to first.   Announcers assume (correctly) that a lot of people listening don’t really know much about the opposing team’s players, and they don’t want to diminish or insult these players, so they will point first to their best number.   “Willy Taveras stole 68 bases for the Rockies last year,” the announcer will say, his voice rising just a little to suggest the excitement that this generates, “and it would have been a hundred if he had been able to bunt his way on just a little bit more often.   His on base percentage, which was an outstanding .382 in 2007, dropped to .296 last year.” 

            “Jeff Keppinger struck out only 24 times all last year,” the announcer will say.  “One of the best hit-and-run men in baseball.    Kept his average at a respectable .266, although he is not much of a power threat and not the quickest shortstop in the league.” 

            The question I was trying to get to is, “How do we know these things?”   How do we know that Justin Morneau’s 129 RBI are better than his 23 homers and better than his .300 batting average, not that anybody is complaining about a .300 batting average? 

            We just do; it comes with being a baseball fan.   We have “scales” in our head that weigh and measure each number as quickly as we can scan a batting line, and pick out the numbers that are biggest and best relative to the others.  

            Wouldn’t it be fun, I thought, to try to re-create those scales in an organized process?  What could we learn by doing that?

            It turned out that it wasn’t as much fun as I thought it would be.   It’s complicated and time-consuming, and I made a lot of mistakes and had to re-do things too many times.   One mistake was, I tended to assume, going in, that the “scales” for the more important categories should be bigger than the scales for the lesser categories.   If a player has 40 doubles and 40 homers, we have to be more impressed by the home runs because a home run is worth more than a double, right?

  But that doesn’t work, because if you expand the scales it tends to place everybody’s “best number” in one of the three or four big categories.   I wound up with what is essentially a 1-to-10 scale for each category, except that we can go as high as 13 in some categories and as low as zero in all of them.  The all-time record number in each category, sometimes the top two or three numbers. . .those are “13s”.   70 homers is a “13”.   A .420 batting average is a “13”.  

            Another mistake I made was trying to proportion the scales to represent the frequency of occurrence.   That was the general idea of the scales, but sometimes it works, sometimes it doesn’t.   Two-thirds of regular players, historically, hit five triples in a season or less.    If a player hits 9 triples in a season, he’s pretty well up the ladder on the frequency scale, but it’s not a terribly impressive event.   If a player scores 75 runs and hits 6 triples, which will your eye go to first?  More regular players historically have scored 75 runs than have hit 6 triples, but still. . .

            And then there’s the zeroes; I started out thinking of it as a one-to-ten scale with zeroes and numbers above ten used for historic exceptions.   That works fine in most categories.   It’s a “zero” if a regular player drives in less than 20 runs.   There aren’t a lot of players in history who have driven in less than 20 runs, so that works.

            But there are 25 players every year who steal zero bases, so what are you going to score that, other than zero?

            What I’m trying to get to is this:  The real-life scales that we use to evaluate these things are complicated and respond to many different pressures in the data.   A simple summary of these such as would be dictated by the kind of analysis they teach you in Statistics classes won’t work—which actually is why I like questions like this.  I like questions that are math-based but which escape the borders of straightforward mathematical or statistical analysis, and force us to think in ways that imitate intuition.   This gets a negative reaction from a lot of readers, many of whom wish I would stick to the pathways of formal analysis, but it’s just way I like to do things.  I think problems in real life are more complicated than the mathematical images of them that we like to construct, so to gain traction against them you have to combine the math with intuition, guesswork, and trial-and-error.

            We normally, in sabermetrics, discuss batting statistics as interactive elements.  Hits are meaningful relative to at bats, runs scored relative to times on base.  Here we are forcing ourselves to look at them as free-standing elements, the way naïve baseball fans do, and the way we all do when we are first learning the game.     

            Anyway, I wound up with 15 scales, representing the fifteen categories in the player data charts I gave you above.  This is the chart for home runs:

            This is the chart for Batting Average:

            So if a player hits .285 with 22 homers, these two figures are considered equally impressive, both “6s” on our scale.  If a player hits for a little higher average but with a couple less home runs—let’s say .305 with 19 homers—then the batting average is a better number than the home run count.  If he hits .275 with 27 homers, the home runs are better than the batting average.  

            If a player hits .305 with 19 homers, how many runs would you figure he would drive in?   He should probably drive in 80-some runs, right?   If he hits .275 with 27 homers, how many runs should he drive in?  About the same number.  

            (Parenthetically, there are 29 players in history through 2007 who have averaged .303 to .307 with 18 to 20 home runs.   They have driven in as many as 133 runs—Vic Wertz, 1949—and as few as 61, by Ray Fosse in 1970.   The average is 87.  I knew it would be 80-something, but I wrote that before I checked, so then I thought I had better check.) 

            So 80-some RBI would have to be a “6”, since this is the number you would expect to get if you combined a “7” and a “5” (.305 with 19 homers) or a “5” and a “7” (.275 with 27 homers) or if you combined two “6s” (.285 with 22 homers.)   This is our chart for RBI:

            I wound up using the same chart for Runs as RBI.   I started out with different charts, reasoning that there are more Runs than RBI (1) and the standard deviation of RBI among players is higher than the standard deviation of Runs Scores (2), so the charts would be similar but slightly different.   But if a player scores 70 runs and drives in 68, it seems wrong to say that his RBI count is more impressive than his runs scored, or vice versa, so I came back to a unified chart. 

            So anyway, Vic Wertz in 1949 hit .303 with 20 homers, 133 RBI.   That’s a 7 for batting average, a 6 for home runs, but a 10 for RBI (7-6-10).   His good number is his RBI count.   Randy Winn in 2003 hit .306 with 20 homers, but only 63 RBI.   That’s a 7-6-4, in those categories.   His good number in that set is his batting average, although actually his best numbers on the season are his hits total (189) and his doubles (47).   We score those both as “8s”.  

            Of course, one can evaluate how great a hitter’s season has been by looking at the numbers in this way, and adding up the total.  I don’t want to get into that very deep, because (a) we already have 2,748 established methods to evaluate a hitter’s season, and (b) there are obvious defects in the process for that purpose (since that is not what the system is designed to do.)   But I’ll give it two paragraphs, or three including this one.

            The ten most impressive batter’s seasons in history, if scored by this method, are 1. Babe Ruth, 1921 (134); 2. Babe Ruth, 1923 (128); 3 tie. Rogers Hornsby, 1922 and Lou Gehrig, 1927 (127); 5 tie. Lou Gehrig, 1930 and Lou Gehrig, 1931 (126); 7 tie. Chuck Klein, 1930, Lou Gehrig, 1936, and Stan Musial, 1948 (124); 10 tie. Babe Ruth 1920, Babe Herman, 1930, Chuck Klein, 1932, Jimmie Foxx 1932, and Lou Gehrig , 1934 (122).

            And, with regard to the MVP race—the player with the most impressive collection of individual stats very often DOES win the MVP Award.   The last ten MVPs, if the MVP Awards were decided by adding up the “impressive number scores” from this system, would be: 2004 NL, Barry Bonds; 2004 AL, Vladimir Guerrero; 2005 NL, Derrek Lee: 2005 AL, Alex Rodriguez;  2006 NL, Albert Pujols; 2006 AL, Grady Sizemore; 2007 NL, Matt Holliday; 2007 AL, Alex Rodriguez; 2008 NL, Albert Pujols; 2008 AL, tie, Dustin Pedroia and Josh Hamilton.  

            Another thing you can do with the system is look at players year by year, and ask “what was usually this player’s best number?”   What was the defining skill of this player?   I’ll do ten players at random, ignoring seasons with less than 400 Plate Appearances:

            Suppose that we add up all of Rickey’s “points” for his career, counting only the seasons with 400 or more Plate Appearances.   We have:

            Whereas for. . .let’s see, marginal Hall of Famer.   Leadoff man.   Richie Ashburn.  For Richie Ashburn we would have these career totals:

            Don’t know where any of that goes. 

            Anyway, another thing you can do with this method is to use it to identify similar seasons.   I already have “similarity scores”, of course, but using this to cast a wider net. . ..Let’s take a season as a starting point.    Robin Ventura, 1996.  These are his numbers:

Ventura, 1996

            We can append to this a “scan” of the season, like this:

            Ventura’s best numbers are home runs, RBI and slugging percentage, all “8s”.   Since Ventura is a “6” in games played, we will eliminate from the data base all seasons which are lower than “5” or higher than “7”.   Since Ventura is a “5” in at bats, we will eliminate from the data base all seasons that are lower than “4” or higher than “6”.   In this way, we can find all seasons which scan as being similar to Ventura on all points.   

            We wind up with 27 seasons that scan as similar to Ventura’s:  Hank Sauer, 1952 (National League MVP), Rocky Colavito, 1962, Reggie Smith, 1971, Sal Bando, 1973, Johnny Bench, 1974, Jeff Burroughs, 1974 (American League MVP), Eddie Murray (1978, 1979, 1982, 1985 and 1987), Jack Clark, 1982, Gary Carter, 1982, Alvin Davis (1984 and 1987), Kent Hrbek (1984 and 1986), Mike Schmidt, 1986 (National League MVP), Wally Joyner (1987), Dave Winfield (1992), Fred McGriff (1993 and 1996), Manny Ramirez (1996), Jeff Bagwell (2003), Hideki Matsui (2004), Moises Alou (2004) and Garrett Atkins (2007).   These are their stats:

            That’s actually a useful method, because very often, in my work, I need to identify groups of similar seasons to establish a “comparison group” for one reason or another.  

            I have developed a “best numbers” system for pitchers, too, but it’s a little raw and this article’s a little long, so I’ll let that go.   The chart at the bottom gives the scoring system for the other eleven categories.   Thanks for reading.

Bill James

            Strikeouts are entered as “Strikeouts per 1000 at bats”.