RELATIVITY AND NORMALIZATION What is it?

• Relativity and Normalization can be used when making comparisons between and among players, teams and eras. • Helps “level the playing field” when comparing stats • Can help determine whether it was “more difficult” for to home runs in the 1920s, or to hit home runs in the 1990s. • Transforms raw statistics into a new number, up to four decimal places. Example

• , of the Pirates, in 1947: • Kiner hit 51 HR in 565 at-bats, for an HR to at-bat ratio of 51/565 = .0903 • Shows that he hit about 9 HR for every 100 at-bats, normally • In the Major Leagues in 1947: All players on the 16 teams hit a total of 1,565 home runs in 84,436 at-bats. What is the ratio? • 1565/84436 = .0185, or showing the “average” player hit slightly less than 2 HR per 100 at-bats • To find the normalization number, divide Kiner’s number by the overall number • .0903/.0185 = 4.8689 Interpretation

• How do we interpret the normalization number? • One possibility is that Kiner was nearly 5 times better than the the average home hitter of 1947. • By figuring these out for certain statistics, you can compare players from different eras — or even narrowing down between the AL and the NL. Demonstrating

• In 1928, Hall of Famer had a of .575. If the slugging percentage of the AL was .397, find his normalized ratio and give an interpretation to this number. • .575/.397 = 1.4484 • Manush was nearly 45 percent better than the average AL hitter in 1928. • Generally, any normalized offensive number greater than 1 means the player was better than the average player. Below 1 means below average, and 1 means average. Demonstrating Sabermetrics

• At the end of the 1959 season, the AL HR leader, of the Indians, was traded for the AL champion, , of the . Compare their relative performances using normalization, given the following information: (1) Kuenn had an avg. of .353, while the league batted .253; (2) Colavito had 42 HR in 588 At- Bats, while the league had 1,091 HR in 41,964 at-bats. • Kuenn’s normalization: .353/.253 = 1.3953 • Colavito’s: 42/588 = .0713; League: 1091/41964 = .0260. Dividing .0713/.0260 = 2.7462 • Can any conclusions be drawn from comparing these numbers? Demonstrating Sabermetrics

• Hall of Famers , , and were all right-handed pitching aces for their teams. Compare their relative ERA to league ERA:

Year Player ERA League ERA 1913 Johnson 1.14 2.93 1940 Feller 2.61 4.38 1966 Marichal 2.23 3.60 1968 Gibson 1.12 2.99 Pitching cont.

• If we compare the individual ERA to the league ERA, then the lower ratio is the better ratio: • Johnson (.3891); Feller (.5959); Marichal (.6194); Gibson (.3746) • You could go the other direction, as well, dividing the league ERA by the individual ERA: • Johnson (2.5702); Feller (1.6782); Marichal (1.6144); Gibson (2.6696) • The second method shows that Johnson and Gibson were better than two-and-a-half times the average .