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Importance of Skiing and Shooting in biathlon

Posted on 2020-08-27 | by

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.

What’s more important, Shooting or Skiing?

Posted on 2020-08-25 | by

real biathlon | 2 Comments

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 10	0.19	0.13	0.67
Top 20	0.49	0.01	0.50
Top 30	0.50	-0.04	0.54
Top 40	0.23	0.06	0.71
Top 60	0.26	0.10	0.64
Top 104	0.24	0.07	0.70
Average:	0.32	0.05	0.63

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.

Women	Non-Team Shooting %	Shooting Time	Skiing Speed %
Top 10	0.24	0.10	0.66
Top 20	0.29	0.09	0.62
Top 30	0.43	0.05	0.53
Top 40	0.35	0.06	0.60
Top 60	0.23	0.02	0.75
Top 98	0.17	0.02	0.81
Average:	0.28	0.06	0.66

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.

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

Posted on 2020-03-11 | by

biathlonanalytics | Leave a Comment

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.

Shooting Time over the last 14 years

Posted on 2015-12-27 | by

real biathlon | Leave a Comment

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.
Maximum	39.5	37.9	36.7	37.4	38.1	33.9	34.1	34.1	33.3	33.7	32.4	32.5	31.9	34.4	-5.1
1st quartile	33.9	33.3	33.3	34.4	32.7	31.4	32.1	31.7	30.6	30.4	30.0	30.0	29.8	30.2	-3.7
Median	32.0	31.7	32.0	32.4	30.8	29.8	30.4	30.3	29.8	29.3	28.9	28.8	28.8	28.3	-3.6
3rd quartile	29.6	30.3	30.7	30.7	29.9	28.6	28.6	28.9	28.5	28.0	27.1	27.2	27.8	27.5	-2.1
Minimum	26.3	26.1	26.9	28.3	25.0	25.8	24.0	24.9	22.7	24.0	24.6	24.5	23.2	23.3	-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 avg	30.5	31.5	31.3	31.8	29.2	30.8	30.6	30.7	28.3	28.8	28.5	27.8	27.7	28.7	-1.8
Top 20 avg	30.9	31.5	31.6	32.2	30.3	30.0	29.9	30.3	28.9	28.9	28.5	28.2	28.4	28.1	-2.8
Top 40 avg	32.0	31.8	31.7	32.4	31.0	30.1	30.4	30.2	29.5	29.2	28.5	28.7	28.6	28.7	-3.3
Top 60 avg	32.4	32.2	32.3	33.0	31.5	30.8	30.5	30.7	30.1	29.7	29.2	29.3	28.8	29.1	-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.
Maximum	40.5	41.4	44.0	41.6	38.9	38.6	39.8	42.7	38.8	39.2	39.5	38.8	34.9	38.0	-2.5
1st quartile	36.8	35.9	36.6	35.8	36.4	35.7	34.8	35.0	34.7	36.5	34.9	34.1	32.7	33.1	-3.6
Median	34.2	34.1	34.0	34.6	34.5	33.2	33.1	33.6	32.3	33.4	33.0	32.4	31.3	32.3	-1.9
3rd quartile	32.7	32.3	32.6	33.1	32.6	31.9	31.8	31.8	31.2	31.7	31.6	30.4	30.2	30.3	-2.4
Minimum	30.5	30.1	30.2	29.9	29.3	28.9	28.6	29.9	27.8	27.8	27.6	25.1	25.2	26.8	-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 avg	34.7	32.7	34.4	35.2	33.7	32.5	33.1	33.4	33.0	33.0	31.8	32.2	31.7	32.3	-2.4
Top 20 avg	34.2	33.4	34.4	34.2	33.5	33.1	33.4	33.5	32.5	33.0	32.3	32.3	31.3	32.3	-1.9
Top 40 avg	34.8	34.5	34.7	34.7	34.3	33.7	33.4	33.9	32.8	33.9	33.3	32.5	31.3	32.1	-2.7
Top 60 avg	35.3	35.4	35.1	35.8	34.5	33.9	34.2	34.1	33.2	33.9	33.4	33.0	31.8	32.4	-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?

Shooting percent over the last 14 years

Posted on 2015-12-25 | by

real biathlon | Leave a Comment

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.
Maximum	91.1	92.3	92.7	92.0	92.4	92.1	88.9	89.3	90.0	90.9	88.9	90.6	91.9	90.3	-0.8
1st quartile	85.2	85.9	84.7	86.1	85.8	87.0	84.9	85.7	86.0	86.1	86.3	87.3	87.3	87.6	+2.4
Median	81.9	83.2	83.3	82.6	83.7	83.1	81.8	83.0	83.7	84.6	83.8	85.2	85.3	85.8	+3.8
3rd quartile	79.0	80.1	78.7	77.7	78.8	77.2	79.6	79.3	81.0	80.8	81.7	83.2	82.9	83.2	+4.2
Minimum	69.2	68.1	66.5	67.1	69.4	66.9	68.6	63.0	71.9	75.3	72.8	72.8	75.8	74.5	+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 avg	84.2	82.7	82.0	87.7	84.2	87.8	83.9	85.4	84.7	85.4	85.8	87.0	86.8	86.6	+2.4
Top 20 avg	83.5	84.3	82.2	84.5	84.4	85.8	83.8	83.6	83.6	84.7	84.6	86.5	85.7	86.2	+2.8
Top 40 avg	81.5	83.0	81.9	81.8	82.4	82.2	81.5	82.1	83.3	83.7	83.7	84.7	85.0	84.9	+3.4
Top 60 avg	81.0	81.5	80.3	81.1	82.2	82.2	81.2	81.5	81.9	82.6	82.5	84.1	84.3	83.9	+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.
Maximum	88.9	92.4	89.0	90.3	93.3	91.5	91.8	92.6	91.0	89.0	94.3	95.1	91.1	92.6	+3.7
1st quartile	84.6	86.1	83.2	85.0	85.2	86.0	86.2	87.1	86.6	85.3	85.2	87.6	86.7	86.9	+2.3
Median	82.4	83.0	80.3	80.3	83.0	82.4	84.0	82.1	85.0	83.6	82.2	85.3	84.3	84.7	+2.3
3rd quartile	78.8	78.4	78.4	78.4	78.0	79.5	81.2	79.7	81.9	81.3	76.9	78.9	80.3	82.0	+3.2
Minimum	65.6	68.2	64.0	64.5	62.8	66.2	73.8	72.9	75.8	69.5	70.8	71.1	75.0	69.8	+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 avg	83.3	84.6	81.2	81.2	84.8	84.1	85.7	84.2	85.9	83.8	86.1	82.9	85.1	85.7	+2.4
Top 20 avg	81.3	84.3	81.3	82.6	83.7	83.9	84.4	84.4	85.7	82.8	84.4	83.3	85.3	84.8	+3.5
Top 40 avg	81.3	82.1	80.2	81.1	81.7	82.4	83.7	83.0	84.4	83.0	81.7	83.4	83.9	83.8	+2.5
Top 60 avg	80.4	80.7	79.4	79.8	81.1	81.4	82.1	81.9	83.6	81.8	81.3	81.7	82.8	82.7	+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%.

Importance of Skiing and Shooting in biathlon

What’s more important, Shooting or Skiing?

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

Shooting Time over the last 14 years

Shooting percent over the last 14 years

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