Baseball Statistics and the Consumer Price Index

Faithful readers of this blog will have noticed that I like to invoke baseball when addressing matters far afield from America’s pastime. (See this, this, this, this, this, this, this, this, and this.) It lately occurred to me that baseball statistics, properly understood, illustrate the inherent meaninglessness of the Consumer Price Index (CPI).

What does the CPI purport to measure? The Bureau of Labor Statistics (BLS) — compiler of the index — says that it “is a measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.” Read that statement carefully. The CPI does not measure the average change in prices of the goods and services purchased by every urban consumer; it measures the prices of a “market basket” of goods and services that is thought to represent the purchases of a “typical” consumer. Further, the composition of that “market basket” is assumed to change, over time, in accordance with the preferences of the “typical” consumer. (There is more about the CPI in the note at the bottom of this post.)

To understand the arbitrariness of the CPI — as regards the construction of the “market basket” and the estimation of the prices of its components — one must read no further than the Bureau’s own list of questions and answers, some of which I have reproduced in the footnote. As a measure of your cost of living — at any time or over time — the CPI is as useful as the statement that the average depth of a swimming pool is 5 feet; a non-swimmer who is 6 feet tall puts himself in danger of drowning if he jumps into the deep end of such a pool.

The BLS nevertheless computes one version CPI back to January 1913. If you believe that prices in 1913 can be compared with prices in 2013, you must believe that baseball statistics yield meaningful comparisons of the performance of contemporary players and the players of bygone years. I enjoy making such comparisons, but I do not endorse their validity. As I will discuss later in this post, my reservations about cross-temporal comparisons of baseball statistics apply also to cross-temporal comparisons of prices.

Let us begin our journey into baseball statistics with three popular measures of batting prowess: batting average (BA), slugging percentage (SLG), and on-base plus slugging (OPS). The “normal” values of these statistics have varied widely:

Average major league batting statistics_1901-2012
Source: League Year-by-Year Batting at

Aside from the upward trends of SLG and OPS, which are unsurprising to anyone with a passing knowledge of baseball’s history, the most striking feature of these statistics is their synchronicity. Players (and fans) of the 1920s and 1930s enjoyed an upsurge in BA, SLG, and OPS that was echoed in the 1980s and 1990s. How can the three statistics rise in lockstep when BA usually suffers with emphasis on the long ball (captured in SLG and OPS)? The three statistics can rise in lockstep only because of changes in the conditions of play that allow batters to hit for a better average while also getting more long hits. By the same token, changes in conditions of play can have the opposite effect of causing offensive statistics to fall, across the board. But given constant conditions of play, there usually is a tradeoff between batting average and long hits. A key point, to which I will return, is the essential incommensurability of statistics gathered under different conditions of play (or economic activity).

There are many variations in the conditions of play that have resulted in significant changes in offensive statistics. Among those changes are the use of cleaner and more tightly wound baseballs, the advent of night baseball, better lighting for night games, bigger gloves, lighter bats, bigger and stronger players, the expansion of the major leagues in fits and starts, the size of the strike zone, the height of the pitching mound, and — last but far from least in this list — the integration of black and Hispanic players into major league baseball. In addition to these structural variations, there are others that mitigate against the commensurability of statistics over time; for example, the rise and decline of each player’s skills, the skills of teammates (which can boost or depress a player’s performance), the characteristics of a player’s home ballpark (where players generally play half their games), and the skills of the opposing players who are encountered over the course of a career.

Despite all of these obstacles to commensurability, the urge to evaluate the relative performance of players from different teams, leagues, seasons, and eras is irrepressible. is rife with such evaluations; the Society for American Baseball Research (SABR) revels in them; many books offer them (e.g., this one); and I have succumbed to the urge more than once.

It is one thing to have fun with numbers. It is quite another thing to ascribe meanings to them that they cannot support. Consider the following cross-temporal comparison of baseball statistics:

Top-25 single-season offensive records
Source: Derived from the Play Index at (Most baseball fans will recognize all of the names but one: Cy Seymour. His life and career are detailed in this article.)

Take, for example, the players ranked 17-25 in single-season BA. The range of BA for those 9 seasons (.384 to .388) is insignificantly small; it represents a maximum difference of only 4 hits per 1,000 times at bat. Given the vastly different conditions of play — and of the players — what does it mean to say that Rod Carew in 1977 and George Brett in 1980 had essentially the same BA as Honus Wagner in 1905 and 1908? It means nothing. The only thing that is essentially the same is the normalized BA that I concocted to represent those (and other) seasons. Offering normalized BA in evidence is to beg the question. In fact, any cross-temporal comparison of BA (or SLG or OPS) is essentially meaningless.

By the same token, it means nothing to say that prices in 2013 are X times as high as prices in 1913, when — among many other things — consumers in 2013 have access to a vastly richer “market basket” of products and services. Further, the products and services of 2013 that bear a passing resemblance to those of 1913 (e.g., houses, automobiles, telephone service) are demonstrably superior in quality.

So, it is fun to play with numbers, but when it comes to using them to make cross-temporal comparisons — especially over a span of decades — be very wary. Better yet, resist the temptation to make those cross-temporal comparisons, except for the fun of it.

Whose buying habits does the CPI reflect?

The CPI reflects spending patterns for each of two population groups: all urban consumers and urban wage earners and clerical workers. The all urban consumer group represents about 87 percent of the total U.S. population. It is based on the expenditures of almost all residents of urban or metropolitan areas, including professionals, the self-employed, the poor, the unemployed, and retired people, as well as urban wage earners and clerical workers. Not included in the CPI are the spending patterns of people living in rural nonmetropolitan areas, farm families, people in the Armed Forces, and those in institutions, such as prisons and mental hospitals. Consumer inflation for all urban consumers is measured by two indexes, namely, the Consumer Price Index for All Urban Consumers (CPI-U) and the Chained Consumer Price Index for All Urban Consumers (C-CPI-U)….

The Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W) is based on the expenditures of households included in the CPI-U definition that also meet two requirements: more than one-half of the household’s income must come from clerical or wage occupations, and at least one of the household’s earners must have been employed for at least 37 weeks during the previous 12 months. The CPI-W population represents about 32 percent of the total U.S. population and is a subset, or part, of the CPI-U population….

Does the CPI measure my experience with price change?

Not necessarily. It is important to understand that BLS bases the market baskets and pricing procedures for the CPI-U and CPI-W populations on the experience of the relevant average household, not of any specific family or individual. It is unlikely that your experience will correspond precisely with either the national indexes or the indexes for specific cities or regions….

How is the CPI market basket determined?

The CPI market basket is developed from detailed expenditure information provided by families and individuals on what they actually bought. For the current CPI, this information was collected from the Consumer Expenditure Surveys for 2007 and 2008. In each of those years, about 7,000 families from around the country provided information each quarter on their spending habits in the interview survey. To collect information on frequently purchased items, such as food and personal care products, another 7,000 families in each of these years kept diaries listing everything they bought during a 2-week period….

What goods and services does the CPI cover?

The CPI represents all goods and services purchased for consumption by the reference population (U or W) BLS has classified all expenditure items into more than 200 categories, arranged into eight major groups. Major groups and examples of categories in each are as follows:

  • FOOD AND BEVERAGES (breakfast cereal, milk, coffee, chicken, wine, full service meals, snacks)
  • HOUSING (rent of primary residence, owners’ equivalent rent, fuel oil, bedroom furniture)
  • APPAREL (men’s shirts and sweaters, women’s dresses, jewelry)
  • TRANSPORTATION (new vehicles, airline fares, gasoline, motor vehicle insurance)
  • MEDICAL CARE (prescription drugs and medical supplies, physicians’ services, eyeglasses and eye care, hospital services)
  • RECREATION (televisions, toys, pets and pet products, sports equipment, admissions);
  • EDUCATION AND COMMUNICATION (college tuition, postage, telephone services, computer software and accessories);
  • OTHER GOODS AND SERVICES (tobacco and smoking products, haircuts and other personal services, funeral expenses)….

For each of the more than 200 item categories, using scientific statistical procedures, the Bureau has chosen samples of several hundred specific items within selected business establishments frequented by consumers to represent the thousands of varieties available in the marketplace. For example, in a given supermarket, the Bureau may choose a plastic bag of golden delicious apples, U.S. extra fancy grade, weighing 4.4 pounds to represent the Apples category….

How do I read or interpret an index?

An index is a tool that simplifies the measurement of movements in a numerical series. Most of the specific CPI indexes have a 1982-84 reference base. That is, BLS sets the average index level (representing the average price level)-for the 36-month period covering the years 1982, 1983, and 1984-equal to 100. BLS then measures changes in relation to that figure. An index of 110, for example, means there has been a 10-percent increase in price since the reference period; similarly, an index of 90 means a 10-percent decrease….

Can the CPIs for individual areas be used to compare living costs among the areas?

No, an individual area index measures how much prices have changed over a specific period in that particular area; it does not show whether prices or living costs are higher or lower in that area relative to another. In general, the composition of the market basket and the relative prices of goods and services in the market basket during the expenditure base period vary substantially across areas….