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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

Ski Speed over the last 14 years

Posted on 2015-12-28 | by real biathlon | Leave a Comment on Ski Speed over the last 14 years

Here’s how the average ski speed of the World Cup top 40 evolved in the last 14 years. Keep in mind I can only approximate the speed through course times and course length; this is not a very precise method (minor mistakes should cancel each other out over the course of a season though). The top 40 athletes should be affected almost equally by possible methodical errors. Thus the speed values might be off by a few decimals, but the comparability season-to-season is still there.

The skiing speed of the men’s top 40 is getting (a lot) faster. Since 2001–02, both the median and the average speed of the top 40 increased by 1.7 km/h. The median skier in 2014–15 (25.8 km/h) was faster than the top skier in 2001–02 (25.1 km/h). All quartiles show a clear upwards trend. Percentage-wise, the ski speed of the median skier improved by about 7.1 %.

Top 40 2001
–02
  2002
–03
  2003
–04
  2004
–05
  2005
–06
  2006
–07
  2007
–08
  2008
–09
  2009
–10
  2010
–11
  2011
–12
  2012
–13
  2013
–14
  2014
–15
   Diff. 
Maximum25.125.324.925.325.225.626.125.725.925.725.926.426.626.2+1.1
1st quartile24.424.524.224.524.524.825.525.325.425.225.325.925.925.9+1.5
Median24.124.424.024.324.324.625.225.125.224.825.125.725.725.8+1.7
3rd quartile23.724.323.624.124.124.525.024.725.024.724.925.425.625.6+1.9
Minimum22.123.622.922.723.523.924.224.424.624.124.425.025.124.9+2.7
Men2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
2013
–14
2014
–15
Diff.
Top 10 avg24.524.724.424.624.624.925.625.325.625.425.426.025.826.0+1.5
Top 20 avg24.324.524.324.524.524.825.425.225.425.225.325.925.825.9+1.6
Top 40 avg24.124.424.024.324.324.725.225.025.224.925.125.725.725.8+1.7
Top 60 avg23.724.323.924.124.224.525.124.825.124.725.025.525.625.6+1.9
All values are average speed in km/h;  Diff.–difference between 2001–02 and 2014–15 seasons

The chart for the women looks distinctively different. The ski speed of the top 40’s median skier increased by 1.0 km/h since 2001–02 (+4.7%). During the first 5 years the speed actually declined. The fastest skier has been pretty stable (between 22.8 km/h and 23.1 km/h) for 6 years in a row (2007-2012), before hitting new all-time highs in the last two seasons.

The big ups and downs in the women’s chart could have reasons beyond pure ski form, e.g. changes in the women’s course difficulty year-to-year, or it could just be a statistical anomaly. I can’t fully explain the curve. It’s possible the courses have slowly been brought in line with the more difficult laps of the men during the first half of the last decade?

Top 40 2001
–02
  2002
–03
  2003
–04
  2004
–05
  2005
–06
  2006
–07
  2007
–08
  2008
–09
  2009
–10
  2010
–11
  2011
–12
  2012
–13
  2013
–14
  2014
–15
   Diff. 
Maximum22.521.922.521.521.621.922.822.822.923.023.023.123.323.6+1.1
1st quartile21.921.221.321.020.921.121.922.322.322.222.122.322.622.8+0.9
Median21.321.021.020.620.620.821.521.922.121.921.821.922.422.3+1.0
3rd quartile21.020.720.720.420.420.721.321.521.821.321.521.822.222.1-1.0
Minimum20.220.219.819.219.819.920.820.820.820.821.021.022.021.7-1.5
Women2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
2013
–14
2014
–15
Diff.
Top 10 avg22.021.321.621.121.021.322.122.522.422.422.422.622.823.0+1.1
Top 20 avg21.821.221.320.920.821.121.922.222.322.322.122.322.622.8+1.0
Top 40 avg21.421.021.020.620.620.921.621.922.021.821.822.022.422.4+1.0
Top 60 avg21.120.720.720.420.420.721.521.721.821.721.621.822.322.3+1.2
All values are average speed in km/h;  Diff.–difference between 2001–02 and 2014–15 seasons

Comparing skiing performances over longer periods is always tricky, certainly more difficult than comparing shooting results. The ski speed is not only affected by the courses (which is a major factor, since World Cup locations change every year), but also by weather. Three or four races during heavy snow fall for example will have a huge impact on the season average.
The increase of ski speed in just 14 years – 4.7% for the women, 7.1% for the men – is substantial. However, a good part of that probably comes down to technology: better working conditions due to waxing trucks, but also general advancements of ski manufacturers and modern waxes will have played its part. The top woman today (23.6 km/h) is just as fast or faster than the slowest male skier before 2006–07 (on easier courses though).

Posted in Long-term trends | Tagged skiing

Shooting Time over the last 14 years

Posted on 2015-12-27 | by real biathlon | Leave a Comment on Shooting Time over the last 14 years

Here’s a closer look at Biathlon World Cup shooting times over the course of the last 14 seasons. The shooting time in biathlon is the time between stepping on and off the shooting mat.

The men’s median shooter needed 32.0 s in 2001–02, 14 years later in 2014–15 only 28.3 s (-3.6 s). If you look at the top 40’s average, the shooting time improved a little less (-3.3 s). In percent, the top 40’s median shooting time improved by an incredible 11.6% in 14 seasons. Interestingly, most of the major improvements happened with the lower ranked athletes; the top 10 are only 1.8s quicker, but the top 40’s slowest shooter was 5.1s slower in 2001–02 compared to last season.

Top 40 2001
–02
  2002
–03
  2003
–04
  2004
–05
  2005
–06
  2006
–07
  2007
–08
  2008
–09
  2009
–10
  2010
–11
  2011
–12
  2012
–13
  2013
–14
  2014
–15
  Diff. 
Maximum39.537.936.737.438.133.934.134.133.333.732.432.531.934.4-5.1
1st quartile33.933.333.334.432.731.432.131.730.630.430.030.029.830.2-3.7
Median32.031.732.032.430.829.830.430.329.829.328.928.828.828.3-3.6
3rd quartile29.630.330.730.729.928.628.628.928.528.027.127.227.827.5-2.1
Minimum26.326.126.928.325.025.824.024.922.724.024.624.523.223.3-3.0
2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
2013
–14
2014
–15
Diff.
Top 10 avg30.531.531.331.829.230.830.630.728.328.828.527.827.728.7-1.8
Top 20 avg30.931.531.632.230.330.029.930.328.928.928.528.228.428.1-2.8
Top 40 avg32.031.831.732.431.030.130.430.229.529.228.528.728.628.7-3.3
Top 60 avg32.432.232.333.031.530.830.530.730.129.729.229.328.829.1-3.3
Diff.–difference between 2001–02 and 2014–15 seasons

On the women’s side, the shooting times improved across the board as well, although generally not by as much (median: -5.6%). The top 40’s median fell by 1.9 s (34.2 s → 32.3 s), the average by 2.7 s (34.8 s → 32.1 s). In 2014–15, the men’s median shooter was 4.0s faster than the women’s. Unlike the men, the women improved almost equally in all categories: the top 10 athletes are 2.4 s quicker, the top 60 athletes 2.9 s quicker than in 2001–02.

Top 40 2001
–02
  2002
–03
  2003
–04
  2004
–05
  2005
–06
  2006
–07
  2007
–08
  2008
–09
  2009
–10
  2010
–11
  2011
–12
  2012
–13
  2013
–14
  2014
–15
  Diff. 
Maximum40.541.444.041.638.938.639.842.738.839.239.538.834.938.0-2.5
1st quartile36.835.936.635.836.435.734.835.034.736.534.934.132.733.1-3.6
Median34.234.134.034.634.533.233.133.632.333.433.032.431.332.3-1.9
3rd quartile32.732.332.633.132.631.931.831.831.231.731.630.430.230.3-2.4
Minimum30.530.130.229.929.328.928.629.927.827.827.625.125.226.8-3.7
2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
2013
–14
2014
–15
Diff.
Top 10 avg34.732.734.435.233.732.533.133.433.033.031.832.231.732.3-2.4
Top 20 avg34.233.434.434.233.533.133.433.532.533.032.332.331.332.3-1.9
Top 40 avg34.834.534.734.734.333.733.433.932.833.933.332.531.332.1-2.7
Top 60 avg35.335.435.135.834.533.934.234.133.233.933.433.031.832.4-2.9
Diff.–difference between 2001–02 and 2014–15 seasons

The gap between genders increased enormously in the last 14 years (for the top 40 from 2.2 s to 4.0 s). However, last season was somewhat of an outlier, the difference was a lot smaller in 2013–14. Ordinarily you wouldn’t expect such a huge gap, because physical strength is probably secondary for shooting pace. I’m not sure if the differences are mainly psychological (risk taking during shooting) or physiological (reaction time for example). The ski times are much closer on the men’s side, maybe gaining just a few second at the range is therefore considered more valuable in the men’s races?

Posted in Long-term trends | Tagged shooting

Shooting percent over the last 14 years

Posted on 2015-12-25 | by real biathlon | Leave a Comment on Shooting percent over the last 14 years

Two years ago I first looked at long-term trends in biathlon statistics, mainly to find out whether today’s athletes are better than previous generations, and how performance levels in the sport are developing in general. I now had another look at it, in order to see if anything had changed during the last two seasons (I haven’t included the currently ongoing season, because partial stats can be misleading). Here are the non-team shooting percentages over the last 14 seasons.
The stats are for the men’s and women’s overall World Cup top 40 (per season). I looked at their non-team percentages, split into quartiles. Quartiles divide the data into four equal groups (of 25 % each), i.e. the grey space between the 1st and 3rd quartile in the chart represents 50 % of the top 40 athletes. Unlike standard statistical methods, such as the average, the use of quartiles (like the median = 2nd quartile) is statistically a more robust method and more resistant to outliers. 

In men’s World cup races, both the top 40’s median and the top 40’s average has improved by more than 3% since 2001–02. Last season was one of the best years shooting-wise, only the maximum (most accurate shooter) is clearly lower than in past years (in the first half of the last decade), but the median and 1st/3rd quartiles were at an all-time high in 2014–15, continuing the upward trend since the early 2000s. The worst shooter of the top 40 hits over 70% since 2009–10, before that the worst shooter always had a hit rate below 70%.

Top 40 2001
–02
  2002
–03
  2003
–04
  2004
–05
  2005
–06
  2006
–07
  2007
–08
  2008
–09
  2009
–10
  2010
–11
  2011
–12
  2012
–13
  2013
–14
  2014
–15
  Diff. 
Maximum91.192.392.792.092.492.188.989.390.090.988.990.691.990.3-0.8
1st quartile85.285.984.786.185.887.084.985.786.086.186.387.387.387.6+2.4
Median81.983.283.382.683.783.181.883.083.784.683.885.285.385.8+3.8
3rd quartile79.080.178.777.778.877.279.679.381.080.881.783.282.983.2+4.2
Minimum69.268.166.567.169.466.968.663.071.975.372.872.875.874.5+5.3
2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
2013
–14
2014
–15
Diff.
Top 10 avg84.282.782.087.784.287.883.985.484.785.485.887.086.886.6+2.4
Top 20 avg83.584.382.284.584.485.883.883.683.684.784.686.585.786.2+2.8
Top 40 avg81.583.081.981.882.482.281.582.183.383.783.784.785.084.9+3.4
Top 60 avg81.081.580.381.182.282.281.281.581.982.682.584.184.383.9+2.9
Diff.–difference between 2001–02 and 2014–15 seasons

The women’s shooting results look very similar to the men’s. For the last 14 seasons they have been creeping higher, although not by quite as much. They improved by more than 2%  (the mean is currently 2.3% higher, the average is 2.5% higher than 2001–02). For 2014–15, the men’s median shooter was slightly better than the women’s (85.8% vs. 84.7%), although there have been seasons where it was the other way around.

Top 40 2001
–02
  2002
–03
  2003
–04
  2004
–05
  2005
–06
  2006
–07
  2007
–08
  2008
–09
  2009
–10
  2010
–11
  2011
–12
  2012
–13
  2013
–14
  2014
–15
  Diff. 
Maximum88.992.489.090.393.391.591.892.691.089.094.395.191.192.6+3.7
1st quartile84.686.183.285.085.286.086.287.186.685.385.287.686.786.9+2.3
Median82.483.080.380.383.082.484.082.185.083.682.285.384.384.7+2.3
3rd quartile78.878.478.478.478.079.581.279.781.981.376.978.980.382.0+3.2
Minimum65.668.264.064.562.866.273.872.975.869.570.871.175.069.8+4.2
2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
2013
–14
2014
–15
Diff.
Top 10 avg83.384.681.281.284.884.185.784.285.983.886.182.985.185.7+2.4
Top 20 avg81.384.381.382.683.783.984.484.485.782.884.483.385.384.8+3.5
Top 40 avg81.382.180.281.181.782.483.783.084.483.081.783.483.983.8+2.5
Top 60 avg80.480.779.479.881.181.482.181.983.681.881.381.782.882.7+2.3
Diff.–difference between 2001–02 and 2014–15 seasons



The shooting results in general continue to improve across the board. It’s impossible to say by how much exactly, results differ a lot depending on what group you look at or what method you use. To put a number on it, I’d say non-team shooting percentages are roughly 2-3% higher now than they were back in 2001–02. It’s unclear how much they can improve further before hitting a ceiling, because unlike ski speed, the hit rate has an absolute limit at 100%.

Posted in Long-term trends | Tagged shooting

Who shoots better: Men or Women?

Posted on 2013-08-27 | by real biathlon | Leave a Comment on Who shoots better: Men or Women?

According to my blog stats the question if men or women are the better shots has always been one of the top search keywords that point people to this site. I wrote a post about that a long time ago, but since it’s of high interest apparently I took a more detailed look at the gender differences in biathlon shooting.

Note: It’s difficult to make any definitive statements about shooting trends, because it all depends on what group of athletes you look at. There isn’t one single group which represents the strength of the whole field perfectly, so it will always be slightly imprecise.

2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
Top 10+3.0-1.4+2.9+6.6-0.3+2.8-2.2+1.7-1.6+1.6-0.8+1.6
Top 20+2.6+1.0+3.0+2.2+1.3+1.9+0.7+0.4-1.9+2.0-0.5+1.2
Top 30+1.2-0.3+2.7+4.1+1.2+1.5-1.0-0.3-1.5+1.6-0.2+0.1
Top 40-0.5+0.3+3.0+2.3+0.7+0.7-2.2+1.0-1.3+1.0+1.6-0.1
Top 60-0.2+0.8-0.2+1.6+1.6+1.2-1.3+0.9-2.0+0.3+1.0+2.3
Top 100+0.2+1.9-0.1+0.5+2.3+0.6-0.1+0.6-2.4+0.2-0.1+2.2
Shooting percentage differences  (in %)    Men / Women   per selected group, last 12 years
Positive values: men were more accurate; Negative values: women were more accurate

During the last 12 seasons, the differences in non-team shooting accuracy between men and women have been small. For two seasons (2007–08 and 2009–10) women were better, in 2004–05, 2006–07 and 2010–11 men are ahead across the board. For most of the other seasons there is no clear picture, although men’s shooting results lead more of the selected groups (and often with bigger margins).


Last year, the shooting percentages for men and women were virtually identical for the top 30 or top 40, however men were over 2 % more accurate in the broader groups (top 60 or top 100). Overall, you probably have to give men a slight edge (of maybe 1 %), even though women were clearly better from 2007–08 to 2009–10.

2001
–02
2002
–03
2003
–04
2004
–05
2005
–06
2006
–07
2007
–08
2008
–09
2009
–10
2010
–11
2011
–12
2012
–13
Top 10+4.2+1.4+3.3+2.4+3.3+1.7+2.8+3.1+4.3+4.3+3.4+5.2
Top 20+3.7+1.5+2.4+1.7+2.6+3.2+3.0+3.2+2.9+3.3+3.4+3.5
Top 30+2.3+1.6+2.3+2.0+3.5+3.7+3.2+3.3+2.5+3.5+3.8+3.7
Top 40+2.3+2.3+2.0+2.2+3.7+3.4+2.7+3.4+2.5+4.1+4.2+3.5
Top 60+2.8+2.9+2.6+2.6+2.6+3.3+3.4+3.1+2.8+3.8+4.2+3.7
Top 100 +2.8+3.1+3.0+2.3+2.6+3.4+2.7+3.2+3.4+4.1+3.9+4.2
Male Shooting Time advantage  (in sec) per selected group, last 12 years

In terms of shooting time, the gender differences are much more obvious. Men shoot considerably faster. In fact, men have increased the gap from about 3 to 4 seconds in the last 12 years. 
Physical strength plays a small part in shooting (relative to their body weight the rifle (3.5 kg) is heavier for most women), but differences of 10 % and more in average shooting time are quite a lot. The large gap might partly be down to a different mental approach (risk taking/range strategy?).

If you combine shooting accuracy and shooting pace and look at the time lost at the shooting range, the gap between men and women becomes much bigger (about 20 s last season for sprints). However, at least half of that range time is spent on skis, so this comparison is unfair: women lose almost 2 seconds approaching and exiting the range and they ski the penalty loop about 3 seconds slower than men.

What’s the bottom line? Generally, men shoot better than women: they are not necessarily more accurate, but on average much quicker (in a sprint about 4*2 = 8 seconds only in “shooting time” last year).

Posted in Statistical analysis | Tagged shooting

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