Feb. 17, 2016: Lars Van Der Haar was incorrectly allocated to the canti group in the data. Shocking error, I know, but fixed now (numbers and plots updated). The effect of moving this #2 ranked rider actually served to move the canti and disc groups closer together in all analyses.
Feb. 17, 2016: Cyclocross Magazine was lovely enough to mention my post. Thanks guys!
But I digress (if that’s possible before I even get started).
Since both the Elite Men’s and Women’s races at the 2016 Cyclocross World Champs were won by riders on canti brakes, I’ve seen several posts lauding the clear superiority of cantis (or at least questioning the supposed superiority of discs).
Twitter was also all aflutter with people posting various quips loaded with their pre-conceived notions of brake superiority:
#CXZolder16 nice conditions for disc brakes
— Éric Laplante (@elaplante74) January 30, 2016
It was amazing race to watch. Great job ladies. #CXZolder16 First and second place no disk brakes. Go figure;)
— Alexander(Sasha) (@belkavelo) January 30, 2016
#CXZolder16 disc vs canti, Van Der Haar vs Van Aert with one to go.
— Tour de Joe (@TourdeJoe) January 31, 2016
One notable blog post made the astute observation that “about half the bikes [were] cantilever- (and carbon-rim) equipped” but also found it notable that the two Elite winners were on cantis. But that simple analysis is a probabilistic oversight: all things being equal, we would expect two canti winners drawn randomly from an equal pool of cantis and discs about one quarter of the time (1/2 x 1/2). In fact, the more riders that cling to cantis, all things being equal, the more cantis will end up on the podium, thus appearing superior.
But of course, all things are not assumed to be equal. We assume that discs, like all major technological advances, should be, well, better. No question, the industry propagates this, and why not? They’re usually right about major tech advances. Think about 1x gearing, STIs, carbon, suspension forks, etc. (and don’t think about Biopace…but then again).
But rather than hash out the perceived benefits (e.g. power, modulation, mud clearance) and drawbacks (e.g. weight, wheel swapping) to discs in ‘cross, I thought I would just crunch some numbers instead. Admittedly, most analyses here rely on good old-fashioned, outdated, misleading frequentist null hypothesis significance testing. Oh well. It serves the purpose and the Bayesian disc brake analysis will have to wait.
I have a real job, so the data had to be pretty quick and easy prepare but representative. I decided to pull the top 20 men and women by points in the 2016 Elite CX fields. The UCI had this information handy, complete with ages and nationalities. Then, assuming that riders used similar bikes all year or at least that World Champs was representative (a big assumption, but it should come out in the wash anyway), I used the sophisticated data repository of Google Images to assign them into either the canti or disc brake class. Using the season rankings rather than a single race ensures that we get a more general sense of whether cantis or discs are “better” (since most non-pros probably have to decide on one or the other). A keen person could look at finishes in each race and class the races according to weather or conditions, but today I am not this person.
Using the top 20 riders should limit the sample to groups of riders who are not limited by physical fitness (as level a playing field as possible). That said, there’s probably a wider range of technical ability in the women’s field simply because the general sample of women who go into CX is smaller*. Technical ability may be something that interacts with brake choice too. For example, a very good technical rider can still perform well in wet and muddy conditions with degrading canti brake performance whereas a less proficient rider may suffer even when braking performance changes only slightly.
Stats note: WC points data were positively skewed, so I log transformed them. Ranks are tough to use because ordinal data kind of sucks. So today I’ll stick mostly with WC points data.
With these data, we’ll first test some expected trends:
- Belgians will tend to ride cantis. It is popular cyclist wisdom (which we all know is never wrong) that Belgians are sticklers for tradition.
- There is a difference in disc use between men and women. First, if we accept that the technical ability range is wider in the top 20 women than men and that discs are more help to less technically proficient riders, a difference should be reflected here. The counter: discs are heavier and bike weight is of more importance to women than men (as higher proportion of body weight). Or maybe female riders are less likely to jump on-board the latest equipment fad because [insert invalid cultural expectation here]. Or maybe it will all even out.
- Younger riders will tend to ride discs. With less technological inertia to cling to, the kids may be less likely to be retro grouches.
Then, we’ll test the big hypothesis:
- Faster riders will tend to ride discs. This one is straightforward and should be true if the industry hype is to be trusted. Given that pros can choose their equipment and that they have ample time to test out a variety of bike setups, we can assume that they’re always riding the bike that’s fastest.
I won’t post the R code here, but I’ll put up the data at the end of this post.
Hypothesis 1: Belgians will tend to ride cantis.
Yup, no question. Whether it’s because they’re traditionalists or because discs are somehow incompatible with motors, they definitely favour cantis, with 14 of the 15 Belgian riders (93%) in the top 20 men and women opting to stay off disc brakes. By percentage, they’re beaten by the French and the Czechs, each with all their top riders on cantis (100%), but the small sample from these countries makes this result a bit suspect (we should have an equal draw from each country for this, but I have a job).
And apparently they’re a wee bit dominant in the sport (in case you didn’t know). 15 of the top 40 men and women are Belgian (38%). While I expected the Dutch to be a strong second, they’re actually just beat out by the Americans with 7 in the top 40 (18%) to The Netherlands’ 6 (15%).
Incidentally, this American showing is largely driven by the women, who make up 5 of the top 20 women (25%), just beating out Belgium’s 4 (20%). Also, the only American rider in the top 20 on cantis is also a woman, and this was Ellen Noble who, at 20th place, just barely got a set of American cantis into the cut (and as a Focus rider certainly would have the option to ride discs).
Another note from the sex breakdown: I hadn’t realised the disparity between the Belgian men and women. While still accounting for 1/5 of all female riders, the women’s dominance is nothing compared to the men. Country-wise, the women’s is a much more even field.
Hypothesis 2: There is a difference in disc use between men and women.
Maybe not surprisingly, there’s no real evidence for this. While the extremely weak trend is for men to choose cantis more often (65%) than the women (55%), given the sample, neither of these proportions are significantly different from 50% (p=0.26 for men and p=0.82 for women).
Hypothesis 3: Younger riders will tend to ride discs.
This one had the potential to be interesting as it weakly trended counter intuitively: the older riders seem to be more prone to switch to discs. The mean (median) age for disc and canti riders respectively is 28.0 (28) and 27.7 (27) years.
But alas, this effect too is not even close to significant (p=0.87). After all, both the youngest rider (Eli Iserbyt, BEL) and oldest rider (The Sven Nys, BEL) were on cantis. And both Belgian. Of course.
Just as a
fishing trip extended analysis, I also considered any potential interaction between age and gender in brake selection. Perhaps we would expect the young males to adopt the new tech because of [insert invalid cultural expectation here]. But this trend doesn’t emerge. Rather, the visible trend is just that of having younger men than women in the top 20.
An ANOVA suggested that the interaction between brakes and sex (p=0.19) was more important than the effect of brakes (p=0.96) or sex (p=0.27) alone on determining age, but it’s still a long way from a significant result.
Df Sum Sq Mean Sq F value Pr(>F) Sex 1 38.0 38.02 1.232 0.274 Brakes 1 0.1 0.08 0.002 0.961 Sex:Brakes 1 54.4 54.41 1.762 0.193 Residuals 36 1111.3 30.87
When plotted, the interaction is there, but its definitely non-significant. I know, boring.
Hypothesis 3: Faster riders will tend to ride discs.
Okay, FINALLY, we get to what we really want to know. If you’ve been paying attention, you should have a pretty good idea how this is going to play out. If not, here it is, in
one three handy plots:
It doesn’t matter if we’re talking about World Cup points (top, note log10 scale) or World Cup rank (bottom), there is no significant difference between disc and canti riders (p=0.54 by points and p=0.75 by rank). Yes, there’s a slight trend in medians towards faster riders on cantis, but we can’t infer (from this small data set anyway) that it’s anything more than would be expected at random. After all, the fastest and slowest riders in the top 20 are both on cantis.
Between men and women, the same statistical result emerges, with no significant difference in World Cup points between discs or cantis among the men (p=0.89) or women (p=0.45).
For interest, the high-point outlier in the men’s disc group is Mathieu Van Der Poel (NED). Without him, the canti group has (just barely) significantly more World Cup points (p=0.04), but only if we don’t talk about multiple comparisons, etc. (which we won’t).
Now that’s a
wide mouth bass convincing result if I’ve ever seen one.
Edit Feb. 17, 2016: Van Der Poel is no longer a high-point outlier now that Lars Van Der Haar has be correctly re-allocated to the disc category.
I could find no significant differences between disc and canti riders, either in demographics or, more importantly, in performance. There are some suggestive trends, but nothing conclusive, at least within the top 20 male and female riders. Sorry, I know that’s a lame result. But it’s a result all the same. I’ve made some assumptions and used a pretty small and potentially biased sample, so it may not be perfect. But it’s a hell of a lot better than the prevailing “hey, look at all the cantis on the podium” argument.
When we expect discs to be superior performers, we risk affirming the consequent when we see cantis on the podium. In fact, there may be no (significant) performance advantage to either. From the data, we should see roughly the same proportions of cantis and discs on the podium as line up at the start line.
Pro riders can choose their equipment, probably on a race-by-race basis too, so they’ll pick what is faster for them individually. And this is almost certainly where the advantage to discs comes in: another equipment option to match to a rider’s skill set on a particular day. Of course, for the rest of us
non soon-to-be pro racers, we have to pick a bike and go with it for at least a season or two. For me, I’ll take discs, even at a slight weight or performance disadvantage, just so I never have to set the toe-in of my G. D. canti pads ever again.
See if you can count the riders in this video that raced on cantis at World Champs!
Use it freely and wisely (and let me know if you do so I can check it out). Data errors? Post a comment and I’ll see what I can do. But remember, I have a job!
Sex Rank Name Country Age Points Brand Brakes M 1 Wout VAN AERT Belgium 22 2360 Colnago Canti M 2 Mathieu VAN DER POEL Netherlands 21 1860 Stevens Disc M 3 Kevin PAUWELS Belgium 32 1835 Ridley Canti M 4 Lars VAN DER HAAR Netherlands 25 1810 Giant Disc M 5 Sven NYS Belgium 40 1620 Trek Canti M 6 Laurens SWEECK Belgium 23 1263 Stevens Canti M 7 Tom MEEUSEN Belgium 28 1203 Ridley Canti M 8 Jeremy POWERS United States 33 1094 Focus Disc M 9 Clément VENTURINI France 23 1086 Look Canti M 10 Michael VANTHOURENHOUT Belgium 23 971 Ridley Canti M 11 Eli ISERBYT Belgium 19 842 Ridley Canti M 12 Marcel MEISEN Germany 27 819 Focus Disc M 13 Francis MOUREY France 36 815 Lapierre Canti M 14 Stephen HYDE United States 29 785 Cannondale Disc M 15 Toon AERTS Belgium 23 770 Ridley Canti M 16 Radomir SIMUNEK Czech Republic 33 760 Stevens Canti M 17 Gioele BERTOLINI Italy 21 740 Guerciorn Disc M 18 Quinten HERMANS Belgium 21 700 Ridley Disc M 19 Tim MERLIER Belgium 24 696 Colnago Canti M 20 Klaas VANTORNOUT Belgium 34 674 Ridley Canti F 1 Sanne CANT Belgium 26 2142 Stevens Canti F 2 Caroline MANI France 29 1540 Raleigh Canti F 3 Nikki HARRIS Great Britain 30 1525 Ridley Canti F 4 Eva LECHNER Italy 31 1520 Ibis Disc F 5 Pavla HAVLIKOVA Czech Republic 33 1424 Ridley Canti F 6 Katherine COMPTON United States 38 1405 Trek Disc F 7 Ellen VAN LOY Belgium 36 1381 Ridley Canti F 8 Helen WYMAN Great Britain 35 1298 Kona Disc F 9 Kaitlin ANTONNEAU United States 24 1190 Cannondale Disc F 10 Sophie DE BOER Netherlands 26 1175 Wilier Disc F 11 Thalita DE JONG Netherlands 23 1136 Giant Canti F 12 Jolien VERSCHUEREN Belgium 26 1086 Ridley Canti F 13 Sanne VAN PAASSEN Netherlands 28 839 Giant Canti F 14 Amanda MILLER United States 30 782 Focus Disc F 15 Loes SELS Belgium 31 768 Ridley Canti F 16 Maud KAPTHEIJNS Netherlands 22 760 Scoppio Canti F 17 Alice Maria ARZUFFI Italy 22 754 Guerciorn Disc F 18 Crystal ANTHONY United States 36 681 Focus Disc F 19 Christine MAJERUS Luxembourg 29 661 Specialized Disc F 20 Ellen NOBLE United States 21 656 Focus Canti
* Okay, before anyone cries foul that I’m slighting the women’s field here, I’m not. There are fewer female cyclists in the world and certainly fewer female cyclists in competition. That means that the sample to draw from is smaller. With the same sample size (i.e. roughly the same number of pros) a proportion of the sample will be drawn from closer to the mean of the “technical ability” curve. I would also argue that this makes for more interesting racing, as results can vary more widely given the conditions, etc.