Let us start from the beginning. What is the Gundersen method? It's a method due to G. Gundersen and used in the Nordic Combined event (a winter sport in which the athletes compete in ski jumping and then in cross-country skiing). The winner of the jumping starts first in the cross-country, the remaining athletes starting with a time handicap according to their jumping score. The idea is that whoever crosses the finish line first is the winner of the event.
Recently the IAAF decided to introduce the Gundersen system in the combined events of the U20 World Championships. The fear is that once tested in the junior category it will be introduced in the senior one as well. This is a disastrous situation. I cannot understand how people, supposedly expert in athletics, could have accepted this. (I could not believe my eyes when I read somewhere that K. Mayer himself is in favour of such a system).
So, let us see what is not OK with the Gundersen system in combined events. The Gundersen scale attributes a fixed number of seconds to a point interval: it is a linear table. The scoring table on the other hand is not linear. The precise formula for 1500 m is (time given in seconds)
points = 0.03768*(480-t)^1.85
which means that a difference of 1 point at 3 min 30 s corresponds to 0.12 s, to 0.15 s at 4:30, and 0.20 s at 5:30. So in order to apply the Gundersen method a choice must be made concerning the correspondence time-points. Let us make the reasonable assumption that for the application of the handicap the reference time will be 4 min 30 s. In this case the Gundersen formula would look like this.
points=2545-t/0.15
It is simpler to illustrate the difference between the two by a graphic.
And now for a small experiment. Two decathletes, A and B have a point difference of exactly 100 points after the 9th event. Following the Gundersen procedure A starts first and B starts after 15 seconds, i.e. some 83 metres of initial handicap. B is a far better runner than A and chases him all along the race. They both sprint towards the finish line where A manages to maintain his advance by a very small margin. Their respective times are 4:30.01 for A and 4:15.07 for B. So A is the winner of the decathlon. True? No! When one calculates the real points corresponding to the performance, A gets 745 points and B 846. So the winner is B despite that fact that A crossed the line first. This is a direct effect of the nonlinearity of the scoring table. And I do not think anybody in their right mind would be ready to abandon it in favour of a linear table. That would amount to going back a century or so in scoring.
Why does the Gundersen method work for the nordic combined event? Simply because there is no overall score for the final performance. The only thing that counts are the relative places of the athletes. The same is true for modern pentathlon. Given that one event (fencing) depends on the athletes present, there can be no absolute score for this discipline, no world record. But this is not true for the combined events of athletics. The world records have a great emblematic value and even those who are in favour of the Gundersen method would never seriously consider to forego the record in favour of a simpler classification.
But wait, it gets worse. I computed the point difference, after 9 events, between Mayer, during his Decastar world record, and the 2nd, 3rd, 5th, 9th and 11th athlete. The difference in points is respectively 831, 958, 1230, 1786, and 1929 points. Converted into time handicap this gives 2:05, 2:34, 3:04, 4:28, and 4:50. So the second and third decathlete would start when Mayer would be completing his second 400 m lap, the 9th would start when Mayer would be sprinting towards the finish line while the 11th would have to wait a few more seconds after Mayer's arrival before starting. Is that something we would like to see? And how the average Joe watching the event on television would be able to tell who is first (remember this is the rationale behind the introduction of the Gundersen method) when athletes are lapping each other? Again, why the method works for the Nordic Combined? Simply because we are talking about a kilometres long cross country cross (typically 10 km) not a mere 400 m long stadium.
And things could get even worse when we consider a competition with massive participation. There will be 24 decathletes and heptathletes present next year in Doha for the World Championships. Could we have them run one after the other applying the Gundersen handicap? That would lead to a total chaos on the track. But separating them into heats would defeat the whole handicap idea.
To my eyes the Gundersen method creates more problems than it solves. It puts emphasis on the victory rather than the record and while everybody agrees that the former is more important than the latter my example above shows that the handicap method is not a sure-fire one.
Would we like to have a combined event where we wouldn't have to bother about the record and where only the victory would matter. Well, look no further. It has been invented almost three millennia ago. I am talking about the ancient pentathlon. I have dedicated one of my very first posts to this great sport of Ancient Greece. And in case you wonder who would have been victorious in an ancient pentathlon contest between Eaton and Mayer, I am convinced that Mayer would carry the event, although he would have had to wrestle Eaton for this (not an akoniti, dustless, victory).
Recently the IAAF decided to introduce the Gundersen system in the combined events of the U20 World Championships. The fear is that once tested in the junior category it will be introduced in the senior one as well. This is a disastrous situation. I cannot understand how people, supposedly expert in athletics, could have accepted this. (I could not believe my eyes when I read somewhere that K. Mayer himself is in favour of such a system).
K. Mayer at the end of his wolrd record decathlon
points = 0.03768*(480-t)^1.85
which means that a difference of 1 point at 3 min 30 s corresponds to 0.12 s, to 0.15 s at 4:30, and 0.20 s at 5:30. So in order to apply the Gundersen method a choice must be made concerning the correspondence time-points. Let us make the reasonable assumption that for the application of the handicap the reference time will be 4 min 30 s. In this case the Gundersen formula would look like this.
points=2545-t/0.15
It is simpler to illustrate the difference between the two by a graphic.
And now for a small experiment. Two decathletes, A and B have a point difference of exactly 100 points after the 9th event. Following the Gundersen procedure A starts first and B starts after 15 seconds, i.e. some 83 metres of initial handicap. B is a far better runner than A and chases him all along the race. They both sprint towards the finish line where A manages to maintain his advance by a very small margin. Their respective times are 4:30.01 for A and 4:15.07 for B. So A is the winner of the decathlon. True? No! When one calculates the real points corresponding to the performance, A gets 745 points and B 846. So the winner is B despite that fact that A crossed the line first. This is a direct effect of the nonlinearity of the scoring table. And I do not think anybody in their right mind would be ready to abandon it in favour of a linear table. That would amount to going back a century or so in scoring.
Why does the Gundersen method work for the nordic combined event? Simply because there is no overall score for the final performance. The only thing that counts are the relative places of the athletes. The same is true for modern pentathlon. Given that one event (fencing) depends on the athletes present, there can be no absolute score for this discipline, no world record. But this is not true for the combined events of athletics. The world records have a great emblematic value and even those who are in favour of the Gundersen method would never seriously consider to forego the record in favour of a simpler classification.
But wait, it gets worse. I computed the point difference, after 9 events, between Mayer, during his Decastar world record, and the 2nd, 3rd, 5th, 9th and 11th athlete. The difference in points is respectively 831, 958, 1230, 1786, and 1929 points. Converted into time handicap this gives 2:05, 2:34, 3:04, 4:28, and 4:50. So the second and third decathlete would start when Mayer would be completing his second 400 m lap, the 9th would start when Mayer would be sprinting towards the finish line while the 11th would have to wait a few more seconds after Mayer's arrival before starting. Is that something we would like to see? And how the average Joe watching the event on television would be able to tell who is first (remember this is the rationale behind the introduction of the Gundersen method) when athletes are lapping each other? Again, why the method works for the Nordic Combined? Simply because we are talking about a kilometres long cross country cross (typically 10 km) not a mere 400 m long stadium.
And things could get even worse when we consider a competition with massive participation. There will be 24 decathletes and heptathletes present next year in Doha for the World Championships. Could we have them run one after the other applying the Gundersen handicap? That would lead to a total chaos on the track. But separating them into heats would defeat the whole handicap idea.
To my eyes the Gundersen method creates more problems than it solves. It puts emphasis on the victory rather than the record and while everybody agrees that the former is more important than the latter my example above shows that the handicap method is not a sure-fire one.
Would we like to have a combined event where we wouldn't have to bother about the record and where only the victory would matter. Well, look no further. It has been invented almost three millennia ago. I am talking about the ancient pentathlon. I have dedicated one of my very first posts to this great sport of Ancient Greece. And in case you wonder who would have been victorious in an ancient pentathlon contest between Eaton and Mayer, I am convinced that Mayer would carry the event, although he would have had to wrestle Eaton for this (not an akoniti, dustless, victory).
VERY USEFUL ONE
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