C
Charmed
Dear Covers:
I am sure there must be at least some, if not many, baseball fans here at the Cove. Ichiro Suzuki's hit in Friday's game was heard around the world and cheered by baseball fans all over the world.
With the first hit, Suzuki tied George Sisler's 84-year old record of 257 hits, set in the 1920 baseball season. With the second hit, he surpassed Sisler and with the third hit he surpassed himself to finish with 259 hits with 695 At bats (the number of times a player is at bat in this game).
His batting average to date, for the 2004 season, BA = 259/695 = Hits /At Bats = 0.373 is lower than George Sisler's batting average 0.407, achieved with 257 Hits and only 631 At Bats. But baseball fans are now celebrating this event not because of a significant new value of the ratio y/x, but because the numerator y in this ratio represents a new record. Will there be an asterisk attached to Suzuki's record, similar to the asterisk added to Roger Maris, when he surpassed Babe Ruth single-season home run record of 60 homers, back in 1961?
Why the asterisk? Babe Ruth, one of the all time baseball legends, hit the most home runs per season for several years (1919-21, 1923-24, 1926-30), tied for the home run lead in 1918 and 1931, and set a record of 60 home runs in a 154-game season in 1927. Roger Maris finally surpassed this record in 1961. But, he hit 61 home runs in a season with 162 games. (Mark McGwire hit 70 homers in the 1998 season and Barry Bonds hit 73 in 2001.) Babe Ruth hit 714 home runs in major league play, a record that held until 1974, when Hank Aaron surpassed it. Sometime in the next year, Barry Bonds might surpass Babe Ruth's 714.
The question of asterisks is thus associated with the number of games now being played in a single season. The more the games, the more the At Bats, or the higher the denominator x. One sportswriter has already suggested that we should never push accomplishments from the past aside -- because the season has more games today . He says, "There should be two records, one for the 162-game season and one for the 154-game season. I believe baseball ought to have two record books for all records, and both sets of records should be held in high esteem."
He adds, "Baseball should not diminish what George Sisler achieved with his 257-hit season. Hitters who played the same 154-game schedule came close several times but never surpassed it. And we'll never know how many more hits Sisler would have had if he'd played 162 games.
Likewise, what Ichiro has done is impressive because baseball has seen more than 30 years of the 162-game schedule and no one has come close until now. So give both Sisler and Ichiro their due."
Not too long ago, as discussed in another recent thread (Number lie and can be deceiving), Vijay Singh surpassed Tiger Woods single-season winnings record. Again, golf fans were celebrating an event related to the "absolute value" of a number that appears in the numerator. Again, there are some questions about the meaning of this new milestone or record. Vijay Singh plays more often than Tiger Woods. Also, the prize money awarded for each tournament victory has changed in the last four years. (For that matter, in his entire career, the legendary golfer Jack Nicklaus earned less than what Woods or Singh did in a single season.) We must also account for the time value of money (inflation, interest, etc.)
Sometimes, as in the case of Suzuki's new record and Singh's new record, it is the absolute value of the numerator y that we celebrate. Yes, there are differences in the number of games played per season, or the number of At Bats, or the denominator x. However, we recognize joyfully the arrival of a new milestone in the numerator y. At other times, however, it is a new milestone of the y/x that we celebrate. The Batting Average of 0.407 set by George Sisler has not yet been surpassed.
Only one other player, Ted Williams has ever achieved this high BA in a single season (0.406, in 1941, with 185 hits and 456 At Bats). Most major league baseball players currently (i.e., in 2001) average between 0.260 to 0.275.
The biologist Stephen Jay Gould, who was an ardent baseball fan, has compared this to the evolutionary processes associated with biological traits, in various species. According to Gould, the “range” in any species declines with time. The average difference between the tallest and the shortest members of a species decreases, as does the average difference between the fastest-running and slowest members of a species. Likewise, the 0.400 hitter has all but disappeared in baseball, and so has the 0.150 hitter.
However, can we compare the performance of great players like Tiger Woods and Vijay Singh, or Babe Ruth, Ted Williams, and Barry Bonds, or Sisler and Suzuki, although the denominator x is obviously not the same?
I hope to discuss point this in more detail in another thread. This has great practical implications. We evaluate not only the performance of great players but also the performance of labor in automotive assembly plants as discussed in another thread (hours per vehicle, now how hours to build a car at the Big 4). The hours per vehicle (HPV) is the ratio of labor hours y and the number of vehicles produced x. The profit margin is also a simple y/x ratio, with y being profits and x being revenues. The defects per opportunity or defects per unit (often measured as defective parts per million), of interest to quality professionals, is also a ratio. But, as in the case of golf and baseball, it is also important to recognize not only the implications of the ratio but the implications of the absolute values of y that appear in the numerator of these widely used ratios.
If the absolute number of defects y increases, the number of parts that are rejected increases and this affects the profits of the corporation, even if the defects per million opportunities (DPMO), or defects per unit (DPU) is low, or has not changed. Or, to cite another example, the survival rate for heart surgeries is 99%. Hence, if 100 surgeries are performed in a small hospital, 99 partients survived. However, if we consider a much larger hospital, where 1000 surgeries are performed, the same survival rate means that 10 patients have died. Can we take comfort in the fact that survival rate is still 99%? Former U. S. President Bill Clinton went through his highly publicized heart bypass operation recently and British Prime Minister is recuperating from his heart operation this weekend.
The ratios or percents are important and so are the absolute numbers x and y. Equally important is the relation between x and y. An appreciation of the nature of the mathematical relation between x and y leads us to a deeper appreciation of the meaning of y and the ratio y/x. It also permits a method of comparing performance when the denominator x is widely different. (Suzuki x = 695, Sisler x = 631, Ted Williams x = 456).
It is sufficient to add here that often the mathematical law relating x and y is the simple linear law y = hx + c = hx - W where h appears to be a universal constant that has a single value for each problem being studied. In my humble view, it is the variation in the nonzero c, or what is the same the work function W = - c, that is responsible for the apparently confusing variation in the ratio y/x. A doubling of x does not always lead to a doubling of y. This is the fundamental significance of the nonzero c. A doubling of opportunities does not double the defects. A doubling of revenues does not double the profits. A doubling of operations does not double the number of deaths, and so on. Amazingly, a doubling of the number of orbits made by a spacecraft (such as the space shuttle or the international space station) does not seem to lead to an exct doubling of the time taken to complete the orbits.
In turn, if c is nonzero, the linear law means y/x is no longer a constant and comparisons can only be made if we also make appropriate corrections that recognize the effect of the nonzero c or W.
Yes, there appears to be a single universal value of h that we can associate with all the great baseball players. Likewise, it appears that there is a single value of h that can be associated with the profits-revenues data for all companies, and so on. We will pursue this discussion in more detail later.
Charmed
I am sure there must be at least some, if not many, baseball fans here at the Cove. Ichiro Suzuki's hit in Friday's game was heard around the world and cheered by baseball fans all over the world.
With the first hit, Suzuki tied George Sisler's 84-year old record of 257 hits, set in the 1920 baseball season. With the second hit, he surpassed Sisler and with the third hit he surpassed himself to finish with 259 hits with 695 At bats (the number of times a player is at bat in this game).
His batting average to date, for the 2004 season, BA = 259/695 = Hits /At Bats = 0.373 is lower than George Sisler's batting average 0.407, achieved with 257 Hits and only 631 At Bats. But baseball fans are now celebrating this event not because of a significant new value of the ratio y/x, but because the numerator y in this ratio represents a new record. Will there be an asterisk attached to Suzuki's record, similar to the asterisk added to Roger Maris, when he surpassed Babe Ruth single-season home run record of 60 homers, back in 1961?
Why the asterisk? Babe Ruth, one of the all time baseball legends, hit the most home runs per season for several years (1919-21, 1923-24, 1926-30), tied for the home run lead in 1918 and 1931, and set a record of 60 home runs in a 154-game season in 1927. Roger Maris finally surpassed this record in 1961. But, he hit 61 home runs in a season with 162 games. (Mark McGwire hit 70 homers in the 1998 season and Barry Bonds hit 73 in 2001.) Babe Ruth hit 714 home runs in major league play, a record that held until 1974, when Hank Aaron surpassed it. Sometime in the next year, Barry Bonds might surpass Babe Ruth's 714.
The question of asterisks is thus associated with the number of games now being played in a single season. The more the games, the more the At Bats, or the higher the denominator x. One sportswriter has already suggested that we should never push accomplishments from the past aside -- because the season has more games today . He says, "There should be two records, one for the 162-game season and one for the 154-game season. I believe baseball ought to have two record books for all records, and both sets of records should be held in high esteem."
He adds, "Baseball should not diminish what George Sisler achieved with his 257-hit season. Hitters who played the same 154-game schedule came close several times but never surpassed it. And we'll never know how many more hits Sisler would have had if he'd played 162 games.
Likewise, what Ichiro has done is impressive because baseball has seen more than 30 years of the 162-game schedule and no one has come close until now. So give both Sisler and Ichiro their due."
Not too long ago, as discussed in another recent thread (Number lie and can be deceiving), Vijay Singh surpassed Tiger Woods single-season winnings record. Again, golf fans were celebrating an event related to the "absolute value" of a number that appears in the numerator. Again, there are some questions about the meaning of this new milestone or record. Vijay Singh plays more often than Tiger Woods. Also, the prize money awarded for each tournament victory has changed in the last four years. (For that matter, in his entire career, the legendary golfer Jack Nicklaus earned less than what Woods or Singh did in a single season.) We must also account for the time value of money (inflation, interest, etc.)
Sometimes, as in the case of Suzuki's new record and Singh's new record, it is the absolute value of the numerator y that we celebrate. Yes, there are differences in the number of games played per season, or the number of At Bats, or the denominator x. However, we recognize joyfully the arrival of a new milestone in the numerator y. At other times, however, it is a new milestone of the y/x that we celebrate. The Batting Average of 0.407 set by George Sisler has not yet been surpassed.
Only one other player, Ted Williams has ever achieved this high BA in a single season (0.406, in 1941, with 185 hits and 456 At Bats). Most major league baseball players currently (i.e., in 2001) average between 0.260 to 0.275.
The biologist Stephen Jay Gould, who was an ardent baseball fan, has compared this to the evolutionary processes associated with biological traits, in various species. According to Gould, the “range” in any species declines with time. The average difference between the tallest and the shortest members of a species decreases, as does the average difference between the fastest-running and slowest members of a species. Likewise, the 0.400 hitter has all but disappeared in baseball, and so has the 0.150 hitter.
However, can we compare the performance of great players like Tiger Woods and Vijay Singh, or Babe Ruth, Ted Williams, and Barry Bonds, or Sisler and Suzuki, although the denominator x is obviously not the same?
I hope to discuss point this in more detail in another thread. This has great practical implications. We evaluate not only the performance of great players but also the performance of labor in automotive assembly plants as discussed in another thread (hours per vehicle, now how hours to build a car at the Big 4). The hours per vehicle (HPV) is the ratio of labor hours y and the number of vehicles produced x. The profit margin is also a simple y/x ratio, with y being profits and x being revenues. The defects per opportunity or defects per unit (often measured as defective parts per million), of interest to quality professionals, is also a ratio. But, as in the case of golf and baseball, it is also important to recognize not only the implications of the ratio but the implications of the absolute values of y that appear in the numerator of these widely used ratios.
If the absolute number of defects y increases, the number of parts that are rejected increases and this affects the profits of the corporation, even if the defects per million opportunities (DPMO), or defects per unit (DPU) is low, or has not changed. Or, to cite another example, the survival rate for heart surgeries is 99%. Hence, if 100 surgeries are performed in a small hospital, 99 partients survived. However, if we consider a much larger hospital, where 1000 surgeries are performed, the same survival rate means that 10 patients have died. Can we take comfort in the fact that survival rate is still 99%? Former U. S. President Bill Clinton went through his highly publicized heart bypass operation recently and British Prime Minister is recuperating from his heart operation this weekend.
The ratios or percents are important and so are the absolute numbers x and y. Equally important is the relation between x and y. An appreciation of the nature of the mathematical relation between x and y leads us to a deeper appreciation of the meaning of y and the ratio y/x. It also permits a method of comparing performance when the denominator x is widely different. (Suzuki x = 695, Sisler x = 631, Ted Williams x = 456).
It is sufficient to add here that often the mathematical law relating x and y is the simple linear law y = hx + c = hx - W where h appears to be a universal constant that has a single value for each problem being studied. In my humble view, it is the variation in the nonzero c, or what is the same the work function W = - c, that is responsible for the apparently confusing variation in the ratio y/x. A doubling of x does not always lead to a doubling of y. This is the fundamental significance of the nonzero c. A doubling of opportunities does not double the defects. A doubling of revenues does not double the profits. A doubling of operations does not double the number of deaths, and so on. Amazingly, a doubling of the number of orbits made by a spacecraft (such as the space shuttle or the international space station) does not seem to lead to an exct doubling of the time taken to complete the orbits.
In turn, if c is nonzero, the linear law means y/x is no longer a constant and comparisons can only be made if we also make appropriate corrections that recognize the effect of the nonzero c or W.
Yes, there appears to be a single universal value of h that we can associate with all the great baseball players. Likewise, it appears that there is a single value of h that can be associated with the profits-revenues data for all companies, and so on. We will pursue this discussion in more detail later.
Charmed
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