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Should the long throws be measured to the nearest centimeter?

In 1997, the IAAF rules committee has voted to measure the discus, hammer, and javelin to the nearest centimeter, instead of the nearest even centimeter, as it was previously. The main argument for the rule change was that modern measuring equipment is more accurate.

While this is true, the marking of the throw still relies on a human official whose accuracy has not improved. Anyone who has ever spotted the landing of a discus, hammer, or javelin knows how difficult it is to measure the mark. I have done a paper that determines that the hammer mark can vary as much as one centimeter depending upon the softness of the ground. According to the rules, the measuring point is the edge of the crater closest to the circle. However, the hammer lands at approximately a 45-degree angle; therefore the same throw on harder ground leaves further marks. This difference can be as much as 1cm.

The difficulty with the javelin is that after the javelin lands, it may vibrate down as it hits the ground, resulting in a mark shorter than where it actually hit upon first impact. This difference can be a few centimeters. Discus can be the most difficult to spot because the implement does not always leave a visible mark on hard ground.

Going to the nearest centimeter is going to place the decision more in the fate of the official's spot. Therefore, I am proposing a new rule that would expand the role of the athlete's second best throw to determine placing when their best throws are very close. I don't think there is anything particularly undesirable about going to the next best throw to break a tie, for throws that are that close together. I believe it is better than only considering the best throws that are not statistically different.

Many other sports have a smallest increment of improvement. In land speed records, it is 1 percent improvement. This means that the previous speed record must be improved by at least one percent in order to be broken. In weightlifting, competitions, the weight must be increased by at least 2.5 kg., which amounts to about 1 to 2 percent, depending upon the amount of weight lifted. In contrast, a 2-cm improvement of a 90-meter javelin throw is only a 0.022 percent improvement; much less significant.

We want the outcome of the competition to be as much in the hands of the competitors as much as possible. If we go to 1cm accuracy, we transfer the outcome to the hands of the field judge. Most field judges would agree: they would not want to be in a position where the competition is determined by their spot.

Here is a proposition for a modified rule for determining placing based on a minimum significant difference in the measured distances:

In all field events where the result is determined by distance, placing shall be determined by the best performances of each competitor. If the best performances are not significantly different from each other, the tie shall be resolved by comparing the sum of the best two performances of each competitor.

The minimum difference required for distances to be significantly different are event specific, regardless of the actual distance. They are: Long Jump: 2cm Triple Jump: 4cm Shot Put and all weight throws (weight, superweight, ultraweight): 5cm Discus, Hammer, and Javelin throws: 10cm.

Example 1 (straightforward): Discus throw Competitor A series: 50.11, 40.00, f, f, f, f 1st Competitor B series: 50.01, 48.00, f, f, f, f 3rd Competitor C series: 50.00, 49.00, f, f, f, f 2nd A is 1st place because his best throw (50.11) is at least 10cm firther than any other competitor's best throw. B and C's best throws are not separated by at least 10cm. In this case, we consider the sum of their best two throws: Competitor B: 50.01+48.00=98.01 3rd Competitor C: 50.00+49.00=99.00 2nd Competitor C is 2nd because the sum of his best 2 throws is at least 10cm further than the sum of Competitor B's best two throws. Example 2a (more involved): Shot Put Competitor A series: 15.06, 14.70, f, f, f, f 1st Competitor B series: 15.03, 14.80, f, f, f, f 1st Competitor C series: 15.00, 14.90, f, f, f, f 2nd In this case, A and B are not significantly different, B and C are not significantly different, but A and C are further than 5cm apart. So we have overlapping tied pairs. In this case, ties are resolved pairwise starting from from a 1st place tie, and working down. First, resolving A and B: Competitor A: 15.06+14.70=29.76 Competitor B: 15.03+14.80=29.83 1st Then A is 2nd and C is 3rd based on best performance only. Example 2b: Shot Put Competitor A series: 15.04, 14.70, f, f, f, f 1st Competitor B series: 15.03, 14.80, f, f, f, f 3rd Competitor C series: 15.00, 14.90, f, f, f, f 2nd This is identical to Example 2a, except that all three are less than 5cm apart, so we go to the sum of the best two throws for the entire triplet. Competitor A: 15.04+14.70=29.74 Competitor B: 15.03+14.80=29.83 Competitor C: 15.00+14.85=29.85 A is 3rd place because he is more than 5cm lower than B and C. For B and C, we would then go to the sum of the best 3 throws, etc. for all six throws. Since the rest of the throws were fouls, ordinarily, these two competitors would remain as tied. However, ties for 1st place shall be broken by extra throws. Each competitor gets an additional throw, and then the best of all seven throws are compared. If the difference is not more than 5cm, then we sum the best two, etc. until the sum of all 7 throws are considered. The throwing order does not change from the previous throw. Successive throws are added and compared in this way until a tie for 1st place is broken.

This rule applies only for the purpose of determining placing in a competition (determining who is first, second, third, etc.) It does not apply to a minimum distance required to break a record. Records can still be broken by a margin of 1 cm in all events.

This is not unprecedented in sport; in tennis, you must win a match by two serves, in volleyball, you must win by two points. In the vertical events (high jump and pole vault), you have a minimum increment to raise the bar, which is a greater increment than the accuracy of the measurement.

To get more technical, we want to use an increment of measurement that is significant enough to determine who threw the farther while being reasonably sure that, using that level of accuracy, that Athlete A's throw was actually farther than Athlete B's throw. In marking the spot, there is the actual distance thrown, and there is a spot, which will have a distribution centered at the actual thrown distance.

Now, in statistics, a Type-I error is going to the next highest throw when Thrower A and Thrower B's actual thrown distance was more than the minimum winning measurement increment. A Type-II error is marking and measuring Thrower B's throw as further when the actual distance thrown was less than Thrower A. A Type-II error is considered more serious than a Type-I error.

As the increment of measurement decreases, the probability of making a Type-II error approaches 50%. If the measurement were 1mm, for instance, two throws that were measured as 1mm apart is almost like tossing a coin to see who wins.

Some analogies: In justice, a Type-I error is letting a guilty criminal go free because of lack of proof beyond a reasonable doubt, and a Type-II error is convicting an innocent person. In business inventory, a Type-I error is overordering a product and having too much on hand, and a Type-II error is running out of inventory and thus losing sales by having to turn away customers willing to buy at that moment.

Most societies consider a Type-II error more serious than a Type-I error. We would rather commit more Type-I errors to be safe, so as to avoid almost all Type-II errors. Going to nearest centimeter in the long throws greatly increases the incidence of Type-II, but decreases the incidence of Type-I error only slightly.