PROFICIENT YEARS AT SPORTS 42 professional world billiard records were broken. The solid line of Figure 12 reveals the ages at which 136 professional world champion- ships were either won or retained.* Figure 12 suggests that professional world billiard championships are most likely to be won or retained by players of ages 25 to 29 inclusive, and that world records at billiards are most likely to be broken by players when they are from ages 30 to 34 inclusive. Figure 12 suggests once again that the very best per- formance is likely to be attained during a somewhat narrower age range than is performance of lesser merit. Thus, the age range for world championship performance is from 19 to 55, but the age range for the breaking of world records is from 26 to 49. GOLFERS Figure 13 presents the ages at which 48 American and British golfers held the Professional Golf Championships of their respective countries.f In Figure 13 the apogee of the age curve occurs very defi- nitely at ages 30 to 34 inclusive, and the findings are quite similar when separate age curves are constructed for the two national groups. When data were assembled separately for 88 American and British Open Golf Championships, it was found that 24 of them had been won at ages 25 to 29, and that 23 of them had been won at ages 30 to 34. Thus, 47 of the Open Golf Cham- pionships of England and of Amer- ica (53 per cent) were won dur- ing the ten-year interval 25 to 34 inclusive. Since the difference be- tween the 25 to 29 and the 30 to 34 age groups amounts to only one championship out of 88, it will per- haps be best to postpone decision regarding the five-year interval of greatest success at winning Open Golf Championships. However, de- tailed analysis of the data for amateur golfers reveals that the national amateur golf champion- ships (both the British and the i. L iL i i. i i 4. 20 25 30 3 40 45 50 55 60 65 FicurE 13. Chronological ages at which 48 American and Britishers became pro- fessional golf champions of their re- spective countries. American) have been won most often by individuals who were from ages 25 to 29 inclusive. Some readers may wonder why *In Figure 12, and in Figure 13, no correction was made for population differences at successive age levels because census data for the various countries of the world were not easily available to the writer. Data regarding the birth dates of the golfers were supplied by Mr. R. W. Treacy, former Secretary of the Professional Golfers’ Association of America, and by Mr. R. C. T. Roe, Secretary of the Professional Golfers’ Association [of England]. Supplementary information was obtained also from the Tournament and Player Record Book for 1935. Chicago: Published by the Professional Golfers’ Association of America.