During the summer of 1999 all the MACC data for 1998 and 1999 were rerun (many times) to test various ways of averaging and calculating handicap, and adjust some of the analysis settings. Changes were made to the MACC rules, and the refined methods were finalized. The results of the analysis are summarized on this page.
If you're not familiar with handicap calculations, you might want to read the handicap introduction page.
Tracking Slalom and Giant Slalom Separately
We now track handicaps independently for slalom and GS. When a slalom race is processed, only past slalom HC averages are used to derive the new ZPT and CF. Ditto for GS. Most racers can be seen to be better in one discipline than the other. Some of the variation seen prior to 2000 for individual racers was due to the preference for one discipline over the other. As a result, we now see more consistent results for most racers, including pacesetters.
Processing First and Second Runs Separately
In the past (before 2000), separate HC analyses were done for dual races (red and blue), but not for conventional races. However, Bill Orrell did an analysis several years ago and found that course conditions changed significantly between first and second runs, even in GS. This means that most of the time HC values have been too low for the first run and too high for the second.
Each run now has its own HC equation with separate ZPT and CF values.
HC values for racers are now more consistent, particularly in slalom—the group averages are the same for the first and second runs now.
Refining the Definition of "Average HC"
All the new HC values for a run are based on a "class curve" obtained by trying to match the established averages for the participating racers. The details of how a racer's average HC is defined are important, but turn out to be tricky.
If all past HC values are just a little high, than all new HCs will also be a little high. And worse, if the process adds a little error that usually raises the HCs, then the error will build. Even if the error for a run is only 0.1, over time it accumulates. A similar problem occurs if a small error exists that usually reduces the HCs. In that case, the HCs for everyone will slowly go down over time. By considering all of the data from 1998 and 1999 (46 runs per class!), gradual trends like this were found and investigated.
For each racer, we need a "best guess" of what the HC should be. The best guesses for each racer are fed into a fairly well-established method for computing ZPT and CF. The problem is that it's not clear how to make a best guess automatically. Racers naturally have some variation between runs. In one run, racer A beats racer B; in the next run, racer B beats racer A. For some kinds of events we might take the average of recent runs for racers A and B to make our "best guesses" about how each will do in the next run.
Here are some other complications.
- If we take the simple average of the most recent runs, the averages are too high for most racers. The reason is that when a racer has a bad run, it adds seconds. When a racer has a good run, it subtracts tenths of seconds. They don't average out—those bad runs really raise the averages. It was found that if simple averages were used over two seasons, most racer HCs go up 5 or more points. To avoid this problem some results must be thrown out.
- If we take the simple average of a fraction of the most recent runs (say the fastest 50%), the averages are too low. Most racers don't achieve those good results consistently, so the new HCs come out too low. As the season progresses, everyone's average goes down.
- In order to treat all past results equally, it is important that they all have similar significance. This implies that they should represent the same number of races. If the number of recent races is low (say, 4 for SL and 4 for GS), then the statistics are not very stable and are strongly affected by unusual conditions. If the number of recent races is high (say 12 for SL and 12 for GS), the statistics are more stable but many racers are excluded because they did not make the required number of races.
In 1998 and 1999 we took the best 6 of the last 12 results. In rerunning the results for 1998 and 1999 with the improvements in processing, the drift in HC was more noticeable. Everyone's HC went down.
The error increases with the number of races thrown out. If half are thrown out, the drift is about 2 HC points for elite racers and over 5 points for the slower classes.
The Solution (Current Method)
The solution that has been programmed is to take the average of a fraction of the most recent runs, and recognize that that average is lower than the "best guess" because we have removed the slow runs. The "best guess" average is calculated by adding a term proportional to the standard deviation of the racer's best runs. The numbers that are currently in the database are shown in the following table.
For GS, the best 6 of the last 8 runs are used. For SL, the best 6 of the last 9 are used. For both GS and slalom, the best guess is defined as the average of the best 6, plus 0.3s where s is the standard deviation of those 6 runs.
The number of runs to consider and the fraction of those runs to use was determined by trial and error (running the entire 1998 and 1999 seasons and evaluating the results over the 1999 season).
In other ski racing programs with handicaps or points, minor adjustments are made each year to redefine "Zero" and also the course factors used to compare SL with other events. We don't have a definition for "zero" so seasonal adjustments are not always required for the MACC system. However, they are occasionally made as needed to compensate for drift between handicaps for SL and GS.
No adjustments were made for the seasons 2000 - 2006. Adjustments were made prior to some seasons as noted below. When adjustments were made, handicaps for the previous one or two seasons were recalculated before the start of the next season.
After years of using the handicap system, we found that more and more recent upgrades were due to giant slalom handicaps. Therefore, we adjusted the SL handicaps between seasons 2005 and 2006, lowering them by about 1%.
A minor adjustment was made to bring down the SL handicaps and raise GS for the slower classes, while doing the opposite for the open Elite. The adjustments are typically less than a point for most racers.
Slalom and GS handicaps have drifted apart again. Slalom handicaps were reduced for all racers by 5% for the 2014 and 2015 handicaps in the computer database used to calculate handicaps for the 2016 season. We checked to ensure that no racers would be upgraded because of this change.
Slalom handicaps were still higher than GS for most racers at the end of the 2016 season, especially in the slower classes, so we reduced the slalom handicaps for 2017 by 5%. Starting with the 2017 season, handicap lists are archived on the web site. With five weekends, there are six lists: one pre-season, and one after each weekend. All are available from the Racing Results page for the season.
Slalom handicaps were still higher than GS for most racers at the end of the 2018 season, especially in the slower classes. On the other hand, the fastest racers have slalom HCs a little lower than their GS HCs.
This year we applied a formula to change from old slalom HC (HCslOld) to new slalom HC (HCslNew):
HCslNew = 0.95 • HCslOld + 1
We also changed the multiplier for standard deviation in slalom from 0.4 to 0.3, the same value as used in GS.
A handicap system is used to place MACC racers in appropriate ability classes, and to determine when racers should upgrade or downgrade to different classes.
The handicaps are determined largely by past histories of most of the racers competing on a course. Pacesetters provide quality control, and influence the handicaps of racers who are much faster or much slower than the average racer for the course.
Calculating and Reporting Handicaps
Handicaps are computed for all race times. However, the handicaps shown in the results on a race day are subject to adjusment and are not considered "final" until after the first MACC meeting that follows the race.
Handicaps are calculated using different equations for the first and second run, in order to compensate for differing course conditions. Therefore, identical times on the first and second runs can result in different handicaps.