The results of the competition in alpine skiing (for example) are recorded in the form of a protocol in which the participants are separated in accordance with the times shown. Despite the high accuracy of measurements, these are relative results (as opposed to 100 meters running or high jumps). That is, the participant can only assess their gap with respect to the leader, in seconds or as a percentage. However, not everyone is “chasing” with the leader, they more often look at their position relative to the familiar participants.
At the next competition everything will be different, other times shown, another leader. Another deviation is possible with respect to the leader and friends.
Is it possible to transfer these indicators: an accurate measurement of the times and the relativity of deviations from familiar participants into absolute indicators, as in the race for the one hundred meters? Yes! And pretty simple.
The question of transfer the results of competitions in some absolute times was put up for myself about 30 years ago. At that time, SCAS (a sports club of the Academy of Sciences) did a competition every Sunday. Either inside the club, or match meetings, most often SCAS-MSU, or city-scale competitions.
I noticed that there is a clear feeling of how I drove: better or worse than my usual capabilities. My position was in the lower half of the protocol, so deviations from the leader did not give much for analysis. But I really wanted to translate a clear feeling in the same clear indicators. For example, “rode better for half a second”.
Familiarization with the then adopted system of penalty points of the competition showed that for our case it is not particularly suitable. The system (with a claim to absoluteness) of penalty points is based on the percentage lag behind the leader, with sometimes the leader is not zero points, but some initial penalty points in accordance with the rating of starts. In general, the system is built on the fact that the gap from the leader is absolutely. Either one leader or the other, but your lag is still converted into some absolute penalty points that can be compared from competition to competition. In our case, there could be a noticeable difference in class between the leader and the “traditionally second”. Therefore, if the leader suddenly flew out, or did not come to the competition, the system built on lagging behind the first place immediately showed some fabulous results.
It should be noted that the system of penalty points does not give any information to the leader. He, too, can drive or better or worse, while the penalty points are still zero (well, or a fixed constant of the competition).
The solution was very simple. And why do you need to measure your gap precisely from the leader? From the point of view of mathematics, this is absolutely not important. This is equivalent to your advance from the last place. And in order to earn statistics you need to analyze your deviation from all participants. And so for everyone. Then the translation into an absolute is based on the assumption that the sum of participants ride the same way. Someone is better, someone is worse, but in general the average class of the same participants does not change from competition to competition 🙂
The assumption that a certain “backbone” of the participants goes to different competitions equally immediately leads to the fact that the competition course can lead to some generalized “absolute” course, like a hundred meters distance for the runners.
Indeed, let’s say there are twenty participants, the leader showed the time 18 + 17 seconds (two attempts, the typical time for slalom in Moscow), and the twentieth participant 25 + 26 seconds. At the following competitions, on a different track, in other snow-ice-temperature conditions, the same participants show times from 22 + 23 seconds (for the same leader) to 28 + 27 seconds. If the first competition is taken as a claim for the future absolute distance, then the second competition can be counted in times that can be directly compared with the results of the first competition. To do this, you need to sum the times of all twenty participants at the first competition and divide by the sum of all the same twenty participants at the second competition. And multiply by the resulting ratio the results of the participants of the second competition.
Then I analyzed the harvest year 1988 for the competition. As a reference point for the subsequent calculated absolute times, I took the average indicators for the season of Zhorik (Alexander Mistryukov), which resulted to 20.00 seconds as absolute classification time.
It turned out that the system works fairly accurately, measures sensations with an accuracy of no worse than 0.2 seconds, which corresponds to the accuracy of manual stopwatch timing. There were also pleasant additional features, it was possible to understand what the preparation of skis gives, change of equipment, see growth (or fall) of results for the season and from season to season.
If you look wider, the analysis of the system of absolute times can be turned in the direction to the past. Then, by analyzing the protocols, you can understand who is faster, the current world cup leader Marcel Hirscher or, say, Ingemar Stenmark 🙂
We used the system of absolute classification times for about 10 years. Stopped along with the termination of regular competitions.
I give a description of the algorithm, compiled a year ago at the request of Zhorik (Alexander Mistryukov).
Absolute Classification Time (ACT) was actively used to analyze the results of the SCAS competition in 1989-1999, when weekly SCAS Cup competitions were held. The meaning of ACT was to multiply the results of the competition by the calculated coefficient so that the results of different competitions of each participant could be easily compared.
1. The first competition. Suppose that there were 20 participants, the first one traveled for 17.06 seconds, the last for 28.20 seconds. At this point, you need to decide what will be the ACT of the first participant. For example, it can be taken equal to 20.00 seconds. Thus the coefficient 20.00 / 17.06 is calculated. All participants in addition to the usual times in the protocol receive ACT by multiplying their result by this coefficient.
2. The second and further competition. Suppose that at the second competition successfully finished 20 participants, of which 10 were at the first competition. These 10 already have ACT. These ACTs are summed up (Sum_ACT). And for the same participants the actual results are summed up (Sum_Real). Calculates the correction factor of the competition K_comp = Sum_ACT / Sum_Real. The results of the competitions of these 10 participants are multiplied by this factor. This is preliminary calculation of ACTs for these competition. Then there is a small analysis on the subject of protection from inadequate passage of the course by some participants (fell, got up, lost a ski pole at the start, etc.). To do this, the calculated ACTs are compared for each participant with his current ACT. If the ACT of competition for a participant is one second greater, then such result is excluded from the processing for these competitions. That is, its ACT is calculated, but it does not go either to the summation of the competitions, or further to the database. Suppose, in this way the results of 2 participants were thrown out. For the remaining 8, the K_comp is recalculated. Results of ALL participants are multiplied to this factor and this is the ACTs of competition. That is, new participants get their ACT, and the old ones can compare their previous ACT with the ACT of the competition, and thus understand “in seconds” whether they have rode faster or slower. Then ACT of participants are written to the database. For new ones – ACT competitions, for old ones average between ACT competitions and previous ACT. The protocol show the actual result, plus three ACT: previous, competition, adjusted.
It was done like this (program under MS DOS, with menus and DB). For each participant, only one field was stored in the database – AKB. When processing competitions, it was necessary either to select a participant from the database, or enter a new one. And write down the real results. Then, according to the algorithm, a protocol was printed.