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Year: 2020

Importance of Skiing and Shooting in biathlon

Posted on 2020-08-27 | by real biathlon | 1 Comment on Importance of Skiing and Shooting in biathlon

The z-scores for last season’s basic statistics are a good tool to take a more theoretical look at biathlon. One of the things which always interests me on a general level is the question: what is more important, skiing or shooting?

The two charts show the z-scores for median ski speed and shooting efficiency (a.k.a. lost time at the range) for all 2013–14 World Cup starters (arranged by World Cup rank). The men’s and women’s chart is quite similar in how skiing and shooting seemingly influences the Overall World Cup rank. Generally, the performances get worse the farther down the rankings you go (as you would expect), however, it appears the higher ranked half of the World Cup field, on average, is better at skiing, while the bottom half are better shooters than skiers (per definition, negative values are good, positive values are bad here).


In order to quantify the effect that skiing and shooting has on an athlete’s World Cup rank, I came up with the idea to interpret the three sets of data – ski speed, shooting efficiency and World Cup rank – as a system of linear equations (all in z-scores). I don’t want to go into too much detail, but I explained it a bit more here before. 


Mathematically speaking, the system is overdetermined, i.e. there are more equations than unknowns, and inconsistent, i.e. it has no solution. However, using the method of least squares, you can find an approximate solution. The ratio between the least squares coefficients indicates the approximate influence of these elements (here the influence of skiing and shooting for the World Cup rank).

  Men Women
        Skiing       Shooting        Skiing     Shooting
Top 20 54.8 45.2 61.1 38.9
Top 40 57.9 42.1 56.3 43.8
Top 60 65.8 34.2 61.4 38.6
Top 100 61.2 38.8 65.2 34.8
All 66.1 33.9 66.2 33.8
average 61.2 38.8 62.0 38.0
Importance of Skiing and Shooting 
for Overall World Cup rank  (in %)  | 2013–14

For last season, all groups I looked at, both male and female, produced pretty consistent results. On average, skiing (61%-62%) was the more important factor for the World Cup rank than shooting (38%-39%). For both genders, skiing has the biggest influences if you look at where an athlete is ranked among the entire field; shooting gets slightly more important for smaller groups (most among the men’s top20 → 45%). However, the fewer athletes (i.e. linear equations) you take into account, the less robust and more random the results get. 

Taking it one step further, I split up general shooting into shooting accuracy and shooting speed (range time). This leads to a linear system with three unknowns (ski speed, shooting % and range time), and the influence of each category can again be approximated with the least squares coefficients’ ratio.

The results you get for three elements are very consistent with the results above: the influence of skiing for the World Cup rank is at about 60% (on average). The shooting accuracy is more important (about 25%) than the shooting pace (about 15%). Still, the range time is probably a lot more important than you would expect (especially compared to shooting percentage). Again the results for men and women are very similar. 

  Men Women
  Skiing Shooting %

Range Time

Skiing

Shooting%

Range Time
Top 20 52.0 30.5 17.5 59.2 25.1 15.7
Top 40 60.1 23.8 16.1 53.8 24.1 22.1
Top 60 67.7 23.6 8.7 57.4 21.0 21.5
Top 100   64.3 23.9 11.8 60.9 20.6 18.5
All 60.0 27.5 12.4 64.2 27.0 8.8
average 60.8 25.9 13.3 59.1 23.6 17.3
Importance of Skiing, Shooting % and Range Time 
for Overall World Cup rank  (in %)  |  2013–14

All of this is only a very imprecise approximation of course, based on a small sample size (no group is larger than 200 athletes). However, the fact that the results, which are highly theoretical, are quite similar across all groups and genders, might be an indication there is some merit to it. Also, using a sightly different method, I got results along the same lines in the past (then 65-35, now 60-40). Using z-scores should be methodologically more sound though.

The fact that shooting is equally important for men and women is actually surprising, because women must ski a longer penalty loop relative to their total course length. Shooting penalties should have a bigger effect in female competitions, however the larger skiing differences among women apparently compensates for that perfectly.

Posted in Statistical analysis | Tagged shooting, skiing

The Queen of Pursuit

Posted on 2020-08-27 | by biathlonanalytics | Leave a Comment on The Queen of Pursuit

by
Puck Possessed

I did research on Pursuit races of the 2019-2020 season to find out who the real Queen of Pursuit was for the last season. Here’s a summary of my findings:

Posted in Statistical analysis | Tagged Puck Possessed, pursuit

What’s more important, Shooting or Skiing?

Posted on 2020-08-25 | by real biathlon | 2 Comments on What’s more important, Shooting or Skiing?

The sport of biathlon combines two disciplines, shooting and cross-country skiing. That leads to the obvious question which of those two elements has the bigger effect on the overall result.


I came up with the idea to use the three statistical values which I talk about often – shooting percentage, shooting time and skiing speed – and put them into relation with the Overall World Cup rank. One way to do that is by looking at the data as a system of linear equations (a general system looks like this):

Of course the four sets of data are incompatible (i.e. the World Cup rank is a dimensionless quantity, the shooting time has a physical dimension, seconds). A way around is making all four values ranks, more precisely a ranking for each category among athletes with World Cup points. That leads to a linear system which looks something like this:

This system of linear equations is overdetermined, i.e. there are more equations than unknowns, and inconsistent, i.e. it has no solution. Luckily there are ways to finding an approximate solution, for example the method of least squares. Technically speaking, he linear system Ax = b has the approximate (least squares) solution x = (A’A)-1A’b.


After finding the least squares solution, the ratio between x1, x2 and x3 gives us the approximate influence of the shooting percentage, the shooting time and the skiing speed for an athlete’s World Cup rank.

 Men   Non-Team 
       Shooting %
          Shooting 
Time
Skiing 
          Speed %
Top 100.190.130.67
Top 200.490.010.50
Top 300.50-0.040.54
Top 400.230.060.71
Top 600.260.100.64
Top 104     0.240.070.70
Average:0.320.050.63
Influence of Shooting and Skiing on World Cup rank | Men
(0 = no effect, 1 = single factor)

Among all 104 male athletes who won World Cup points last season, the skiing speed was clearly the most important factor. The skiing speed influence on the World cup rank varied between 50 % and 71 %, depending on what group you look at.

There is the very unusual effect that for the men’s top 20 and top 30 athletes the shooting percentage briefly becomes very important, while it plays a much smaller role overall (top 104) and for the top 10. My best guess would be that that’s the region where the chart of the overall skiing pace flattens out, and therefore the shooting briefly becomes a more important factor.

 WomenNon-Team 
     Shooting %
          Shooting 
Time
Skiing 
          Speed %
Top 100.240.100.66
Top 200.290.090.62
Top 300.430.050.53
Top 400.350.060.60
Top 600.230.020.75
Top 98        0.170.020.81
Average:0.280.060.66
Influence of Shooting and Skiing on World Cup rank | Women  
(0 = no effect, 1 = single factor)

The results for the women don’t look fundamentally different. The skiing speed is slightly more important (81 %) for where an athlete is eventually ranked in the Overall World Cup. Also just like the men’s data, there is the same curious effect that the shooting percentage effect reaches its maximum for the top 30 athletes.

Some general observations:

  • The skiing pace is the most important factor for every group listed above. Overall its influence on the World Cup rank last season was about 65 % on average, pretty much across the board, both for men and women.
  • Shooting percentages play a lesser, but still significant role, with a 25-30 % influence. 
  • While shooting times have by far the smallest effect, it’s not negligible. The shooting speed accounts for about one sixth to one seventh of the total shooting influence. 

The Overall World Cup rank last season was (very roughly) determined like this: Shooting accuracy 30 %, Shooting speed 5 %, Skiing speed 65 %. Interestingly, that seems to be true for men and women alike.

Posted in Statistical analysis | Tagged shooting, skiing

Canadian performances in Biathlon since 2000

Posted on 2020-06-24 | by biathlonanalytics | Leave a Comment on Canadian performances in Biathlon since 2000

By Najtrebor

This article mainly uses data from Senior-level, non-team IBU Biathlon events since 2000, unless indicated otherwise. The data come from the IBU (www.biathlonresults.com) starting with the 2000-2001 season, and going up to (and including) the 2019-2020 season). It combines all race results with Event, Race and Athlete data, although the Athlete data is limited to Senior and IBU Cup level. Unfortunately, the detailed race-data with ski- and shooting times per loop, is only available through PDF-files that so far provide a too-big-a-hurdle to conquer! (Clearly, I wrote this article before this amazing website was re-instated!) But what the current data set provides is ranks, final times and general shooting results.

Participation – all levels and events

While the average number of all participants in IBU events has been very steady in the last 20 years, Canada’s participation has slowly increased, as shown in Figure 1. Although the growth appears to be levelling out in recent years at all three levels, over the 20 year period there is a slow incline, specifically for Junior and Senior events.

Note that the 2019-2020 season was not fully completed due to COVID19, likely leading to lower overall participation numbers.

World Cup Points

The total number of World Cup Points per nation is dependent on the number of participants and how race results are linked to points. But at this level of (semi-)professional sports, to evaluate a nation’s success, the points are usually all that matters. Since the total number of points is more relevant when compared to other nations, the chart below shows national points per season at the Senior level for non-team events, for all nations, with Canada highlighted in red.

Unfortunately, it appears Canada has been in decline in the last couple of seasons.

The chart on the right split some of these nations out so see individual trends and how well nations do and how they are trending. The horizontal dotted line is the base-line (0 points) so the further above the line, the more points nations have scored. It shows that Norway, France and Germany are the main high-scoring nations, Russia has lost touch with the top, and Sweden and Italy are increasing. The other shown nations, including Canada, or relatively stable at this scale.

Canada’s best

The 2019-2020 season was in the middle of the pack of all seasons since 2000, but again note that it was cut short due to COVID19. The 2014-2015 season was our best so far, looking at World Cup points, with very strong performances by Rosanna Crawford and Nathan Smith.

The charts below looks more at the development of Canadian athletes, showing total World Cup points won in individual Senior events on the vertical axis, and the n year of their career on the horizontal axis. The left side shows all athletes to highlight Canadians in the complete picture, where the right side zooms in on Canadians.

Canada’s best seasons: team events

As the last couple of charts, figure 6 shows team events per nation, and how Canada performed since the 2000-2001 season by looking at the average Rank of all seasons (vertical axis) and the number of races started by a nation (horizontal axis).

In contrast to the figure above, the figure below shows the average rank per season as a line starting in ’00-’01 and ending in ’19-’20. As Canada starts in the bottom left (labelled 0001 for season ’00-’01) it starts moving to the right (more races) and up (better average ranking). The upward progression stops after the ’13-’14 season, but the ’19-’20 season shows an improvement again. Hopefully, this can be continued in the next season!

The full pdf of the article above can be downloaded below.

PuckPossessed7_CanadiansDownload
Posted in Statistical analysis | Tagged Canada, Puck Possessed

Contribution from skiing and shooting performance to the overall sprint race performance

Posted on 2020-03-11 | by biathlonanalytics | Leave a Comment on Contribution from skiing and shooting performance to the overall sprint race performance

by Najtrebor
Puck Possessed

I got inspired by a research article by H. Luchsinger†, R.K. Talsnes†, J. Kocbach and Ø. Sandbakk from the Norwegian University of Science and Technology in Trondheim, in which they analyzed the performance of 11 elite male biathletes to “investigate the contribution from overall XC skiing performance … and shooting performance to the overall biathlon sprint race performance”, amongst other purposes. 

This issue of Puck Possessed Biathlon duplicates some of their research based on the women’s sprint races starting in the 2017-2018 season until present to see if and how it matches.

Posted in Statistical analysis | Tagged Puck Possessed, shooting, skiing

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