Mata Architecture for Future Internet

Performance evaluation of Tour de France

cycling teams using Data Envelopment Analysis

Nicky Rogge Daam Van Reeth

Tom Van Puyenbroeck

HUB RESEARCH PAPERS 2012/12 ECONOMICS & MANAGEMENT

FEBRUARI 2012

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Performance evaluation of Tour de France cycling teams using

Data Envelopment Analysis

Nicky Rogge*‡, Daam Van Reeth*, and Tom Van Puyenbroeck*

‡

(*): Hogeschool-Universiteit Brussel (HUBrussel)

Warmoesberg 26, 1000 Brussels (Belgium)

(‡): Katholieke Universiteit Leuven (KULeuven)

Faculty of Business and Economics

Naamsestraat 69, 3000 Leuven (Belgium)

Abstract

This paper uses a robust (order-m) Data Envelopment Analysis approach to

evaluate the efficiency of Tour de France cycling teams for the period 2007-

2011. Since there are multiple ways in which this event can be successful for

a cycling team, we take it that managers face strategic input decisions

regarding team and rider characteristics. Specifically, we distinguish between

ranking teams, sprint teams, and mixed teams, and compute for each of these

an efficiency score as due to the team’s performance relative to similarly

classified teams and an efficiency score that is the consequence of the team

type. We find that ranking teams are generally more efficient than other

types.

Keywords: Data Envelopment Analysis, Tour de France, Cycling, Team

Types, Performance Evaluation; Robust order-m

JEL-classification: L83, D24, L23.

Corresponding author: Daam Van Reeth, Hogeschool-Universiteit Brussel, Warmoesberg 26, 1000 Brussels,

Belgium, Email: [email protected]

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1. Introduction

The Tour de France is the most important cycling race in the world. The three-week race

captures the interest of millions of cycling fans every day. Alongside the cobblestones classics Paris-

Roubaix and the Ronde van Vlaanderen, it is the only cycling race to get worldwide media coverage.

This significant exposure renders the Tour de France the primary season goal for most top cycling

teams and motivates managers to line up their best riders. In fact, Tour de France success sometimes

makes all the difference for a continued sponsorship of a professional cycling team. An analysis of the

performance of Tour de France cycling teams therefore clearly is appropriate.

Performance studies of professional road cycling are, however, still rare in the economics of

sports literature. This is partly due to two distinguishing features of cycling that make such analyses

less straightforward. First, cycling is a sport in which one individual receives the glory of team

production. It is "Lance Armstrong" who appears 7 times on the roll of honour of the Tour de France,

not "US Postal Service" or any of the other teams he was part of when winning the Tour de France.

Still, it would have been impossible for Lance Armstrong to win the Tour de France without the

support of a strong team. Second, there are many prizes to be won in a multi-stage race like the Tour

de France. Evidently, not all cycling teams are able to win the prestigious overall time classification,

but they can still strive for important secondary prizes. This will have an impact on their team

selection. Hence, an appropriate performance analysis should account both for the multiple ways of

being successful in the Tour as well as for the different goals that cycling teams may have in that

respect.

Our focus on teams is one obvious way in which this paper differs from the small body of

literature that has addressed professional road cycling performance earlier. Prinz (2005) and Torgler

(2007) do use team data, but only as explanatory variables for individual performances. Both Sterken

(2005) and Cherchye & Vermeulen (2006) entirely abstract from team importance in their analysis.

Note that team efficiency analyses are rather common in the sports economics literature, especially for

popular European and American team sports. We refer, for instance, to the papers on soccer by

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Dawson et al.(2000), Carmichael et al. (2001), Haas (2003), Espitia-Escuer & Garcia-Cebrian (2004)

and Pestana Barros & Leach (2006). Cooper et al. (2009) and Rimler et al. (2010) analyse efficiency

in basketball, while the baseball and American football team efficiency is addressed by Hadley et al.

(2000), Einolf (2004), Lewis et al. (2007) and Collier et al. (2011).

The multiple-prize nature of the Tour de France is not taken up by Sterken (2005) and Torgler

(2007), who focus on the overall time classification only. Both Prinz (2005), by using total prize

money, and Cherchye & Vermeulen (2006), by aggregating information from different rankings into

one ranking, do embed the multiple prizes context into the analysis. Still, by focusing on individuals,

their assessments neglect an important real element of strategic positioning that is largely at a team

manager’s discretion.

In this paper, we thus broaden the scope of earlier analyses, which focused on individual

performance, used a single (simple or comprehensive) output statistic, and abstracted from ex ante

diversity of team aspirations. Instead, we take it here that actual management decisions relate to

combining individual rider’s quality and experience so as to maximize the chance of winning during

the three-week event, where prizes range from the cherished end-prize, over important side-

competitions (e.g. the best climber) and single stage wins, to minor prizes (e.g. the daily ‘prix de la

combativité’ awarded by a jury for the most combative rider). Adhering to this managerial

perspective, we analyse team efficiency by using a Data Envelopment Analysis (DEA) approach. An

important advantage of our particular set-up is that it enables identifying which part of the

inefficiency is particularly due to the team’s performance relative to its peers, and what part of the

inefficiency is due to the fact that the team is of a certain type. It should be noted further that we have

opted for a robust version of DEA, so as to deal with potential biases in efficiency estimates

originating either from unequally sized team-type groups or from atypical/outlying performances.

We succinctly describe some essential features of the Tour de France in section 2. Section 3

presents the data, while the methodology is explained in section 4. The empirical results are discussed

in section 5. Concluding remarks are gathered in section 6.

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2. The Tour de France

The Tour de France has a long and heroic history going back more than a century. The race lasts

for three weeks, counting 21 stages that differ in length and route. The rider who has taken the least

time overall to cover the entire course wins the Tour de France. Three types of stages exist, each

suitable for a different type of rider. Flat stages are easy to ride and are likely to end in a bunch sprint.

They are of almost no importance to the overall Tour de France win, although occasionally top

favourites suffer time losses when crashes or windy conditions result in peloton splits1. When riders

have to climb steep mountain passes, the race becomes much harder and usually large time

differences between riders are created. Mountain stages are therefore crucial to the overall Tour de

France result. Typically, riders who perform well in flat stages face huge difficulties in mountain

stages and may even struggle to avoid disqualification for arriving out of time. While flat stages and

mountain stages are raced collectively, time trial stages are ridden individually or, sometimes, in

teams. Cyclists start at equal time intervals, usually two or three minutes apart. As time trial stages

might result in significant time differences between riders, they are also very important to the overall

Tour de France result.

The overall time classification is the most prestigious classification to win, the leader wearing the

famous yellow jersey. But there are other competitions of importance too. The points classification,

awarded with a green jersey, is designed so as to award the best sprinter, the rider who is best capable

of winning or ending in top positions in stages where most of the peloton is still together at the finish.

A polka-dot jersey is worn by the leader in the competition for the best climber, while the best young

rider, i.e. under 25 years of age, receives a distinctive plain white jersey. Next to these individual

classifications, there is also a team classification based on the time of each team's best three riders in

every stage. Not all participating teams have a strong enough contender for an overall classification.

These teams might focus on individual stage victories instead. But with 22 teams participating and

only 5 classifications at stake, the stage victories are also hard-fought. In fact, usually about half of

the teams leave the Tour de France empty-handed.

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The mix of several competitions and different types of stages creates a multi-output situation

with many success opportunities. As a result, there are typically three types of teams present in the

Tour de France. Ranking teams aim for the end victory (the yellow jersey) or at least a top final rank

position. Sprint teams particularly compete for stage victories in stages that are well-suited for

sprinters and the green jersey. The third type gathers cycling teams that do not really aim for a good

final ranking position or for winning sprint stages. Mixed teams particularly look for opportunities

during the Tour de France to win a stage that is somewhat in between a sprint stage and a mountain

stage (i.e., the typical transition stages in the Tour de France) or aim for a share in minor prizes.

Teams that have as predominant objective to compete for the end victory or a good final rank

position, like team RadioShack, have a line-up that qualitatively differs from that of teams whose

main goal is to win sprint stages and/or the green jersey, like HTC Highroad. Specifically, a ranking

team will choose riders that are helpful to the team leader throughout the Tour, sheltering him from

the wind in the flat stages and supporting him as strongly as possible in the difficult mountain stages.

A sprint team, on the other hand, will for the most part select riders that are skilled in holding the

peloton together and preparing the sprint for their leading rider.

3. Data

3.1. Teams

The number of teams participating in the Tour de France varies slightly from year to year

between a minimum of 20 and a maximum of 22. In this study we analyse the 2007-2011 period,

leading to a dataset of 105 observations. During this period in total 31 different cycling teams took

part at least once in the Tour de France. A five-year period was chosen for two reasons. First, as

compared to other sports, most cycling teams have a rather short lifespan of on average 5 to 10 years

only. By limiting the analysis to 5 years, our sample contains a large enough number of cycling teams

that participated in all Tours de France under study. Table 1 indeed shows that no less than thirteen

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cycling teams were always present.2 This means that, at the team-level, the Tour peloton remained for

60 to 65% unaltered throughout the years. With a longer sample period of, for instance, 10 years, a

much smaller portion of our dataset would consist of teams that participated in all Tours. Second,

during the 2007-2011 period there were neither significant changes in the prize structure nor in the

number of stages (21) and competitions (5). Since we use these variables as outputs, the unaltered

prize structure allows for a better interpretation of the results. This would be more difficult if we

opted for a longer period.

All cycling teams were subsequently grouped into three team types: ranking teams, sprint teams

and mixed teams. Teams were classified by analysing past Tour de France performances of the

individual riders selected in their Tour de France team. To qualify as a ranking team in year t, for

instance, a team had to line up at least one rider that finished in the Tour de France top 10 in year t-1

or t-2, or in the Tour de France top 5 in year t-3 or t-4. A similar procedure, based on winning sprint

stages in the past, was used to determine sprint teams. If a team qualified for both team types, as for

instance the Rabobank team that during the period 2007-2010 selected overall contender Denis

Menchov as well as sprint winner Oscar Freire, it was categorized as a ranking team, the reason for

this choice being that the final general classification still is the most important prize a team can win.

Finally, teams that didn't qualify for either category were considered mixed teams.3

< Table 1 about here >

Table 1 summarizes the information. It shows that our dataset contains 46 ranking teams, 24

sprint teams and 35 mixed teams. Some teams always were of the same type throughout the sample

period, like Team Saxo Bank (a ranking team for all years), but most teams change type from year to

year, depending on their team composition. Liquigas, for instance, has twice been labelled as a mixed

team first, became a sprint team in 2009, and was twice a ranking team afterwards.

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3.2. Input variables

Apart from random elements like luck and coincidence, success in the Tour de France depends

on a number of team and rider characteristics. We use these characteristics as our input variables in

the DEA analysis. We discern two main categories of input variables: team quality and team

experience. Team quality is measured by the team budget (financial input) and by the number of

Cycling Quotient (CQ) points of the riders selected for the Tour team as earned on the eve of the Tour

(sports input).4 We prefer to use CQ points because they allow comparing team quality over the years,

which is not the case with other point rankings in cycling that often have different point scales from

year to year. Data were collected from the CQ website (www.cqranking.com). We also consider an

alternative in which the CQ points of a team’s Tour selection are expressed as a percentage of the

team total number of CQ points. Team experience is based on past Tour de France performances.

Specifically, the total number of Tour starts by the selected riders were computed. In addition, we

look at team consistency to capture team rather than individual experience. We construct this variable

as the maximum number of riders in a particular Tour team in year t that also rode together in any

Tour team in year t-1. In the rare event a team was temporarily banned, year t-2 was used as a

reference instead. In fact, this correction was only necessary for the Astana team that was denied entry

in the 2008 Tour de France. The Tour team consistency variable measures the importance in cycling

of building a core of domestique riders around a team leader. George Hincapie, for instance, was the

most important domestique to Lance Armstrong, and was part of all his winning Tour teams.


Table 2 summarizes the input data for all teams and for the subsets of team types. The average

team budget amounts to 8.2 million euro, but ranking teams have a 10 to 15% higher budget, on

average, than sprint teams and mixed teams. There is an almost 5:1 ratio between the richest teams

(Katusha and Team HTC Highroad, 15 million euro) and the poorest teams (Barloworld and

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Agritubel, 3.5 million euro). The CQ points show a similar but more outspoken pattern. The riders in

a Tour team are on average worth around 3,700 CQ points. Ranking teams have a CQ value of around

4,500 points, which is almost a third more than sprint teams (3,500 points). Mixed teams only

accumulate about 2,900 points. This results in an almost 10:1 ratio between the strongest team (Team

Saxo Bank, 7,834 points) and the weakest team (Footon Servetto, 879 points). If we look at the CQ

points of the selected riders in the Tour de France team relative to the total number of CQ points in

the cycling team, we notice that the average Tour team represents slightly more than 50% of the

team’s total CQ points. Ranking teams have marginally higher percentage values, on average, than the

other two types. Nevertheless, as can be seen from the minimum and maximum observed percentage

values, there are considerable differences among teams of all types. The nine riders in a Tour de

France cycling team combine on average a total of about 33 Tour starts. Since the start in year t is

included in this total, this means a typical rider has an experience of 2 to 3 previous Tours. Tour

experience does, however, differ importantly between types of teams. Ranking teams (39.74) have far

more experience than sprint teams (30.21) and mixed teams (26.89). At the team level, we note a big

difference between both Skil-Shimano (2009) and Footon-Servetto (2010) that had no experienced

riders in their Tour team, and Team Leopard-Trek (2011) that is the most experienced team in our

sample with 52 previous Tour starts by its nine riders. Finally, with average Tour team consistencies

of 4.89 and 4.88 (meaning that on average about 5 teammates rode the Tour de France together in the

same team the previous year), ranking teams and sprint teams are overall equally consistent

concerning team line-up, while mixed teams are considerably less consistent (3.57).


We have conducted DEA-based performance analyses of Tour de France cycling teams using

five different input selections, as denoted in Table 3. This allows checking for consistency in the

performance evaluation outcomes. In particular, when results would be sensitive to the used input-

output mix in the DEA-model, results should be treated with much caution.

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3.3. Output variables

The complex nature of cycling makes it less straightforward to determine the relevant output

variables necessary for a DEA analysis. Essentially, the results of the Tour de France consist of a

number of ordinal time or points based rankings. However, using the time differences or the points as

output is not very relevant because, just as in many other sports, the order rather than the distance

between two riders ultimately matters. Furthermore, point scales may differ from year to year and

time differences are very much dependent on the race evolution and on the features of the yearly

changing route, which makes a multi-year analysis of such statistics cumbersome at best. Conversely,

sticking to ordinal rankings is also not preferable as it does not allow to discriminate between a one

position difference high in the ranking (e.g. between the winner and the runner-up) and a one position

difference lower in the ranking (e.g. between 100 and 101). Additionally, it is difficult to reconcile

with the all important team element in professional road cycling.

Therefore, we propose three other output variables, all aggregated at the team level: prize money

earned, CQ points collected during the Tour, and prizes won.5 The first two output variables are

related to the ranking but give higher weights to better positions by lowering in a degressive way the

rewards for lower positions. Furthermore, they implicitly weigh the importance of the different prizes

that can be won, by differentiating the rewards between classifications. Data on prize money are made

public each year by the Tour de France. Note that in addition to prize money, all Tour de France

cycling teams also get a lump sump for what is called "participation expenses" and a "presence

bonus", totalling 65,643 euro in 2011. Because this sum is almost unrelated to the team's

performances (it is reduced marginally with 1,600 euro for every rider unsuccessful in finishing the

Tour de France), we did not include it in our total prize money measure. In their capacity as an output

indicator, data on CQ points refer to points as collected during the Tour (whereas, to repeat, the input

counterpart captures the stock of points of a team prior to that Tour). A comparison between the prize

money scale and the CQ points scale reveals an important difference. The Tour de France

organisation pays a stage winner 8,000 euro only, which is less than 2% of the reward the overall

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Tour de France winner gets (450,000 euro). In the CQ ranking, a stage win earns a rider 80 points,

which is over 13% of the points the overall Tour de France winner receives (600 points). Our third

output variable counts the number of prizes won by a cycling team out of a total of 30 possible

important prizes, viz., 21 stage wins, 5 competitions to win (general ranking, points classification,

mountain classification, best young rider and team classification) and the 2nd to 5th place in the final

general classification. As opposed to the first two output variables, this variable gives all prizes the

same weight. The prize money output variable views cycling teams primarily as revenue maximizing

organisations, while the prize count output variable is more in line with a win maximizing situation.

The CQ points variable should be situated somewhere in between the revenue and win maximizing

situation.

Contrary to how we handled inputs, and given the clear importance of all three indicators as race-

related outcomes of the event, we retain all three outputs in the different models. Evidently though,

there is another output that is of special interest to cycling teams and, especially, their sponsors. As

cyclists are promoting these sponsors through the advertising on their shirts as well as by their very

team names, media exposure is very important to a professional cycling team. By way of anecdotic

evidence, while Team Saxo Bank won the 2011 edition of the one-day classic Tour of Flanders with

Nick Nuyens, it only had about 2% of all media exposure through live TV coverage. The team of

runner-up Sylvain Chavanel, Quick-Step, took the bulk of the media attention with over 10% of

exposure. Although Team Saxo Bank won the race, commercially Quick-Step was the more

successful team that day. Unfortunately, media exposure information is unavailable publicly and

could therefore not be used as an output variable in our analysis.

Table 2 also summarizes the output data for all teams and for the subsets of team types. The

average prize money earned by a Tour de France team is almost 100,000 euro. Big differences exist

between teams. The most money was won by Discovery Channel in 2007. The victory by Alberto

Contador earned the team 723,640 euro, more than 70 times the amount Lampre won in 2008, only

9,840 euro. The Tour de France organisation clearly rewards the overall ranking higher than the other

rankings. While ranking teams earn on average 150,000 euro, sprint and mixed teams only receive on

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average 60,000 euro and 50,000 euro of prize money, respectively, for three weeks of hard work. CQ

points awarded for performances in the Tour de France show a similar pattern. On average, teams

gain 620 CQ points in the Tour de France. Ranking teams (822 points) outperform sprint teams (505

points) and mixed teams (434 points). At the team level the differences are very high. In 2009, Astana

was awarded more than 200 times the number of points of Cofidis in 2007: 2059 versus 70. Cycling

teams win on average 1.43 prizes, with a big difference between ranking teams (2.07 prizes) and

sprint teams or mixed teams (0.92 and 0.94). This average is misleading, though, because many teams

are unable to win any prizes at all. Indeed, in our 5 year sample, in 45 out of 105 observations (43%) a

team left the Tour de France empty-handed. Team Saxo Bank in 2008 is the most successful team in

our dataset with 8 prizes.

In sum, Table 2 provides an indication of a positive relation between team inputs and team

output measures for the Tour de France. Looking at the summary statistics in the table, ranking teams

typically use somewhat more inputs compared to other team types, but realize considerably higher

outputs. This signals that, at least at this aggregate level, one could expect type differences in relative

efficiencies (i.e., in aggregated output-input ratio’s) as well. Yet, a comparison of the minimum

observed output values among ranking teams with those of sprint teams shows that there are ranking

teams that realize lower outputs. Consequently, even though ranking teams on average probably do

better in terms of relative efficiency, there will be considerable differences between ranking teams,

some of them even performing worse than the other type teams.

4. Methodology

4.1. Data Envelopment Analysis

To evaluate the efficiency of the Tour de France cycling teams, we use a DEA approach. DEA

was introduced by Farrell (1957) and further developed by Charnes et al. (1978). In its most general

form, DEA can be seen as a non-parametric technique for measuring the technical efficiency of

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similar activity units which utilize (possibly multiple) inputs to produce (possibly multiple) outputs in

environments typically characterized by no reliable information on the prices of inputs and outputs

and/or no (exact) knowledge about the ‘functional form’ of the production or cost function. In the

literature, the activity units are generally referred to by the term Decision Making Units or DMUs. In

our example, it concerns the Tour de France cycling teams in the sample.

The key feature of DEA is that, in the absence of a priori detailed information on the exact

specification of the cost or production function, it estimates the cost or production function from the

observed input and output data themselves (i.e., a posteriori). DEA determines the efficiency frontier

as the piece-wise linear combination that envelops the input-output combinations as observed from

the empirical data. Consequently, only the most efficient cycling teams are situated on this “best

practice” efficiency frontier. It is with respect to this data-driven efficiency frontier that the DEA-

model estimates the efficiency of each activity unit in the sample. More precisely, the DEA-model

computes for each evaluated cycling team the efficiency score as a (radial) distance measure of the

team’s actual position relative to the efficiency frontier. Formally, this yields the following form of

the DEA linear programming model:

( )

1

1

1 2

1 2 1

0 1 2

k

n

k , j j ,i k ,i

j

n

k k , j j ,q k k ,q

j

k , j

x x i , , , p

max s.t. y y q , , ,s

j , , ,n

ϕ

λ

ϕ λ ϕ

λ

=

=

≤ =

≥ = ≥ =

∑

∑

…

…

…

In this formulation, we assume that there are n cycling teams ( )1j ,...,n= that use p inputs j ,ix

( )1i , , p= … in their attempt to realize good performances on the s output criteria j ,qy ( )1q , ,s= … .

In our application of the Tour de France cycling teams for the period 2007-2011, there are 105 cycling

teams (i.e., 105n = ). For instance, recalling Table 3, in our model 5 each of these teams uses four

inputs, viz. ‘budget’ ( 1j ,x ), ‘CQ points in Tour team’ ( 2j ,x ), ‘number of Tour starts’ ( 3j ,x ), and ‘Tour

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team consistency’ ( 4j ,x ) (hence, 4p = ), to compete with other cycling teams in order to do well in

the three output criteria ‘prize money’ ( 1j ,y ), ‘CQ points collected’ ( 2,jy ), and ‘prizes’ ( 3,jy ) (thus,

3s = ). We assume that inputs and outputs are non-negative: 0j ,ix ≥ and 0j ,qy ≥ .

The linear program as in ( )1 is computed n times: one computation per evaluated cycling team.

In each linear programming computation, the input and outputs of the cycling team that is singled out

are denoted respectively by k ,ix and qky , . As can be seen from the program, one basically looks for

the maximal (equi-)proportional expansion in all outputs of this evaluated team ( qkk y ,ϕ for all q),

while keeping its inputs fixed, such that the resulting benchmark projection uses at least as much

inputs and at most as much outputs as a (λ-) weighted combination of the (observed) input-output

combinations of all teams. The efficiency score of a team is then defined as the inverse of this

maximal equi-proportional expansion factor ( kk ϕθ /1≡ ), and is hence situated between zero and one

(i.e., 0 1kθ≤ ≤ ), with higher values indicating more efficient performances. According to this logic,

cycling teams with 1kθ = are perfectly efficient. The λ–vector is the vector of intensities, indicating

how important the other cycling teams in the sample are for constituting the benchmark against which

the evaluated cycling team k is assessed. The subscript “ k ” in k , jλ indicates that the vector of

intensities is specific for each evaluated cycling team. Specifically, for the evaluated cycling team k ,

the intensity vector k , jλ will consist for the most part of zeros except for those cycling teams that are

situated on the efficiency frontier and play a role in defining the benchmark for cycling team k .

Accordingly, this benchmark is a weighted combination of the performances of efficient cycling

teams.

< Figure 1 about here >

The DEA-model can be easily illustrated. Figure 1 displays a fictitious example of 20 cycling

teams being evaluated based on two outputs and one input.6 Instead of requiring an explicit definition

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of the production function, the DEA-model reveals the efficiency frontier by just enveloping the data

points lying most outwards with linear segments. In the example, the cycling teams A , B , C , and D

are situated most outwards. Correspondingly, these teams constitute the empirical DEA-estimate of

the efficiency frontier (i.e., the piece-wise linear ABCD ) and their efficiency scores are equal to one.

They also act as their own benchmark (being situated themselves on the efficiency frontier). All other

teams are situated below the efficiency frontier and are thus inefficient (i.e., 1kθ < ). To determine the

exact value of kθ for the inefficient teams: (1) project the inefficient DMU on the efficiency frontier

in an equi-proportional way and (2) take ratios of radial distances. The projection point on the

efficiency frontier serves the purpose of efficient benchmark team. For the cycling team R , for

instance, the point R' on the efficiency frontier acts as benchmark and the DEA-estimate of kθ

equals the ratio OR OR' . The benchmark for teams R and S , respectively R' and S' , are situated on

the AB -part of the efficiency frontier ABCD , which means that they equal weighted combinations of

the performances of cycling teams A and B . Accordingly, in the DEA-evaluation of teams R and S ,

the intensity vectors R, jλ and S , jλ will consist of zero values for all units except for the teams A and

B . Further note that the value kθ indicates how much a team has to improve in order to become

efficient. The lower the value of kθ , the larger the room for efficiency improvements. When

comparing the efficiency scores of the cycling teams R and S , for example, we see that team S is

less efficient than team R (i.e., ( ) ( )OS OS' OR OR'< ) and thus there is more room for

improvement for team S .

To end this subsection, we point out that many alternative DEA-models exist, and that some of

these may also be suitable in a setting similar to ours. For example, Yang et al. (2011) present a

“fixed-output sum”-model, which hinges on the idea that expanding one’s output can only be

achieved by an offsetting decrease of other competitors’ output. Yang et al. (2011) illustrate their

model with (Sydney 2000) Olympic medals as the fixed-sum outputs. However, in our specific setting

the empirical value added of this additional assumption is small, as the best performers in the Tour

dataset are still far removed from the hypothetical bliss point in which the 9 riders of a team would

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collect all relevant prizes (30 per Tour), obtain their theoretically maximum CQ-points (8,095) and

prize money (1,542,660 euro). Indeed, Table 2 reveals that the actual best practices are still

considerably removed from these theoretical maxima. Thus, they can be taken as targets without the

need of adjusting their outputs downwards. We return to the issue of alternative models in the

concluding section.

4.2. Team efficiency vs. team-type efficiency

The existence of ranking teams, sprint teams, and mixed teams is a crucial element of our

specific setting. It entails that a ranking team will mainly compete with other ranking teams. In the

same vein, the main focus of all sprint teams consists in doing better than the other sprint teams (viz.,

winning sprinting stages and competing for the green jersey). In the basic DEA-model as presented in

the previous section, however, each team is evaluated relative to all other teams in the sample

(irrespective of the team type). This means that the basic version of the DEA-model does not account

for the several sub-competitions that exist between the cycling teams. In terms of Figure 1, this would

imply that a ranking team R might well be deemed inefficient based on a comparison with teams A

and B, which are not necessarily of the same type as R. Put in more abstract terms, and given that we

are gauging efficiency relative to existing best-practices, this feature implies that one should properly

address the selection of relevant peers.

To account for these sub-competitions (and, thus, to account for the several types of cycling

teams in the Tour de France peloton), we use a DEA-framework inspired by Portela and Thanassoulis

(2001).7 The key idea of their approach is straightforward: evaluate any cycling team within its own

group of cycling teams of the same type, and evaluate that team a second time within the complete

sample set. This essentially means that each cycling team is evaluated relative to two efficiency

frontiers: one frontier as determined by the teams that belong to the same group and another, overall

frontier as determined by all cycling teams irrespective of their type. Figure 2 below illustrates the

idea for the ranking teams vs. sprint teams.8

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In Figure 2, both the ranking team R and the sprint team S are located below their respective

own team-type efficiency frontiers (for the ranking teams and sprint teams, the efficiency frontiers are

EFBCD and AGH respectively) and the overall efficiency frontier ABCD . Evidently, given the

existence of two relevant frontiers for each team, two DEA-based efficiency scores can now be

estimated. A first efficiency score is estimated within the sample of cycling teams of the same type.

We formally represent this efficiency score by Own

kθ and label it as “own-team-within-own-team-

type”-efficiency. For the ranking team R and the sprint team S , Own

kθ is computed respectively by

the ratios OR OR" and OS OS" . A second efficiency score is obtained when the team under

evaluation is assessed relative to all teams and, hence, the overall efficiency frontier ABCD . From

now on, we refer to these efficiency scores as the “overall” or “own-team-within-all-team-types”-

efficiency and represent it by Overall

kθ . For cycling teams R and S the overall efficiency scores are

equal to the ratios OR OR' and OS OS' . Combining the outcomes of the two aforementioned

efficiency analyses, we can derive a third efficiency score that is denoted by Type

kθ and is referred to as

“own-team-type-within-all-team-types”- efficiency. In particular, we compute the Type

kθ by taking the

ratio of Overall

kθ and Own

kθ :

( )2Overall

Type kk Own

k

θθ

θ=

Expression (2) implies that we can decompose the overall efficiency score Overall

kθ into an

inefficiency component that is due to the team’s performance relative to similar teams, measured by

Own

kθ , and an inefficiency component Type

kθ which, by construction, isolates the effect of using other

types as well as a basis for comparison. Applying this decomposition to the examples of cycling teams

17

R and S yields own-team-type-within-all-team-types efficiency scores Type

kθ equal to OR" OR' and

OS" OS' . The two components of overall efficiency can be straightforwardly illustrated in Figure 2.

For the sprint team S , for instance, the overall efficiency score Overall

kOS OS'θ = as computed by the

basic version of the DEA-model is seen to consist of an efficiency component Own

kOS OS"θ = that is

due to team S ’s own performance relative to the sprint teams’ best practice and an efficiency

component Type

k OS" OS'θ = that originates from being a sprint team type.

4.3. Robustifying the performance evaluation: robust order-m DEA

Finally, we make one important adjustment so as to deal with two problems that are both related

to the relative perspective taken on in DEA-based efficiency evaluations. A first issue is that groups of

observations are of different size, as should be recalled from Table 1. These differences in group sizes

may cause a bias in the estimation of the different efficiency components. Specifically, given that the

“own-team-within-own-team-type”-efficiency measure is computed within the own group, a ranking

team is evaluated relative to 46 teams in the estimation of Own

kθ , while a sprint team is assessed

relative only to 24 teams. Obviously, this means that the probability for a sprint team of getting a high

Own

kθ is higher than for a ranking team (as the performance of the former is, ceteris paribus, compared

to a smaller group of peers). A second concern is that the impact of teams with atypical or outlying

performances on the assessment of other teams’ efficiency can be quite large.

To account for these issues we use a robustified DEA-analysis that builds on Cazals et al.

(2002).9 The key idea of this approach is to no longer compute the efficiency estimates in one

efficiency evaluation round in which the estimation of Own

kθ builds on a comparison with all cycling

teams of the same type and, similarly, the computation of Overall

kθ is done relative to the frontier

spanned by all cycling teams in the sample. Instead, the efficiency estimates are made in a Monte

Carlo setting in which B runs ( 1, ,b B= … ) are performed (with B a large number). In each of these

18

runs, a subset of the cycling teams is considered in the efficiency evaluation of the cycling team k .

More precisely, in each run, a subset of m cycling teams of the same type (that is, m teams drawn in

an i.i.d. manner from the group of teams of the same type) are considered in the estimation of Own

kθ ,

and a subset of m teams randomly drawn from the full sample of cycling teams are considered in the

estimation of Overall

kθ . The robust versions of Own

kθ and Overall

kθ , denoted by m,Own

kθ and m,Overall

kθ are

computed as the average values of Own

kθ and Overall

kθ defined over the B efficiency assessment runs.

The use of this so-called robust order-m DEA allows, firstly, to neutralize the size bias as due to

different group sizes: m is set equal for all groups of cycling teams in the computations of the

different efficiency scores. Secondly, due to the Monte Carlo simulation with i.i.d. draws of

subsamples, the impact of cycling teams with outlying or atypical performances is mitigated. Before

concluding this section, we also note that because of the sub-sampling approach, it is not necessarily

the case that an evaluated team also appears in the list of m possible comparison partners, which

implies that efficiency scores can now in fact be larger than one, as can be their averages over B runs.

Such robust DEA-estimated efficiency scores larger than one indicate that the cycling team under

evaluation is extremely efficient compared to an average of m randomly drawn comparison partners.

Efficiency scores equal to one reveal that the evaluated cycling team performs efficiently compared to

other teams in the comparison set, and efficiency scores lower than one indicate that the cycling is

inefficient relative to its counterparts.

5. Results

In this section we present the outcomes of the proposed model. Remark that we discuss the

robust (order- m ) versions of the DEA-based efficiency scores. In all calculations, we used B=500

runs and set m=15 for all types. Team performance evaluations were done for five different

input/output combinations (recall Table 3), so as to check for consistency in the evaluation outcomes

(that is, the three different efficiency estimates for the cycling teams). As noted, model outcomes

19

should ideally be insensitive to the input-output constellations used in the DEA-model. Fortunately,

both the descriptive statistics of the “Own-team-type-within-all-team-types”-efficiency m,Type

kθ for the

Tour de France cycling teams (Table 4) as well as the correlations between the three different types of

efficiency estimates (Table 5) for the variant models, indicate that all five models yield largely similar

results. In particular, Table 4 conveys the general “type effect”-result that ranking teams on average

outperform the other two types, thus analytically corroborating the summary indications contained in

Table 2.



In fact, given the high consistency in the findings, it suffices to focus on the outcomes of just one

of the models. In the remainder, we therefore look at the results as yielded by model 5. The

descriptive statistics of all three efficiency scores as yielded by this model (i.e., the overall or “own-

team-within-all-team-types”-efficiency and its two components: the “own-team-within-own-team-

type”-efficiency and the “own-team-type-within-all-team-types”- efficiency) are listed in Table 6.


Some interesting general findings can be discerned from this table. We see that the average

cycling team realizes an efficiency score of 85 18. % when being evaluated relative to the teams of the

own type and an efficiency score of 87 66. % when being assessed relative to all cycling teams

(whatever the type). Both the large standard deviation and the large difference between the minimum

and maximum estimated efficiency scores show, however, that there are considerable differences

between the cycling teams. Note also that Table 6 recaptures some model-specific information

relating to the “own-team-type-within-all-team-types”-efficiency scores m,Type

kθ that was also contained

in Table 4. Ranking teams generally outperform the other two types, with average efficiency estimates

20

of 120 14. % , 80 06. % and 85 44. % for ranking teams, sprint teams, and mixed teams, respectively.

Recalling expression (2), one should thus expect that the “own-team-within-all-team-types”-

efficiency m,Overall

kθ of ranking teams is generally higher than their “own-team-within-own-team-type”

efficiency m,Own

kθ , while the reverse holds for the majority of the teams of the other two types. Table 6

confirms this expectation.

Furthermore, a comparison of the average “own-team-within-all-team-types”-efficiency

estimates for the three types of cycling teams shows that ranking teams generally realize a higher

overall efficiency score compared to sprint teams and mixed teams (i.e., 107 75. % compared to

67 42. % and 75 13. % ). Again though, there are significant differences between individual teams. For

instance, we see that the lowest “own-team-within-all-team-types”-efficiency score is realized by a

mixed team (i.e., minimum efficiency score equal to 12 98. % ). However, also the worst performing

ranking team and sprint team have values near to this minimum (with minimum scores of 16 96. %

and 17 54. % ).


The above findings are further detailed in Figure 3, which displays the scatter plots of the “own-

team-within-own-team-type”-efficiency scores and the “own-team-within-all-team-types”-efficiency

scores. In point of fact, the scatter plot for ranking teams reveals that almost all teams are positioned

below the 45°-line. This shows that a large majority of ranking teams have overall efficiency scores

that are higher than their “within-own-team-type”-efficiency scores. Stated differently, all ranking

teams in our sample get higher efficiency scores when they are being evaluated relative to all cycling

teams (irrespective of the team type) than when being evaluated relative to other ranking teams only.

This result is also intuitive. As noted above, when ranking teams usually outperform sprint and mixed

teams, a within-type evaluation of ranking teams entails a comparison with generally strong teams

only. On the other hand, an overall comparison implies the addition of teams that are generally

performing less well, which makes it easier for ranking teams to realize higher efficiencies. The

21

opposite observation holds for the majority of sprint teams and mixed teams: they realize overall

efficiency scores that are lower than the “own-team-within-own-team-type”-efficiency scores.

The differences between the average “own-team-within-own-team-type”-efficiency scores of the

three types of cycling teams are only slightly different (respectively 86 14. % , 85 61. % , and 83 63. % ).

Ranking teams may do extremely well in terms of realized efficiency (cf. the maximum value of

395 68. % , realized by Astana in the Tour de France of 2010), but may also return home with very

disappointing results when compared with their direct peers. The worst performing team, realizing an

efficiency score m,Own

kθ of only 15 58. % , was indeed also a ranking team (viz., Team Radio Shack with

no stage wins, low prize money and low CQ points in the Tour de France of 2011). In fact, when the

assessment is relative to own-type peers only, all teams face similar distributions of efficiency scores.

We conclude with a brief discussion of the results of some specific teams.10

Table 7 presents the

efficiency scores for three cycling teams for the period 2007-2011, viz. Quick-Step, Team Saxo Bank,

and La Française des Jeux. Apart from the 2007 edition, the Quick-Step team performed rather poor in

the last 5 editions of the Tour de France (although one could argue that the team performed

moderately well in the 2010 Tour de France). The high efficiency scores of Quick-Step in 2007 can be

explained by the good performances of the team in that year. Quick-Step won the green jersey and 5

stage wins, and, thus, a relatively high amount of prize money. It should be no surprise that the impact

of these high outputs on the three efficiency scores is strongly positive. In fact, within the own group

of sprint teams, Quick-Step is even evaluated as highly efficient (i.e., 162 17m,Own

k . %θ = ). A similar

reasoning also helps in explaining the poor efficiency scores for Quick-Step in the Tour de France

editions of 2008, 2009, and 2010. With similar input levels, Quick-Step only realized low output

levels in those editions.


A detailed analysis of the efficiency scores of Team Saxo Bank shows that this team did very

well in the 2008, 2009, and 2010 editions. Particularly the 2008 Tour de France was a good edition for

22

Team Saxo Bank, with high efficiency scores of, respectively, 272 26m,Overall

k . %θ = ,

194 26m,Own

k . %θ = , and 140 15m,Type

k . %θ = . The m,Own

kθ equal to 194 26. % illustrates that Team Saxo

Bank, a ranking team, is evaluated as highly efficient when being evaluated relative to the other

ranking teams. With only one stage win and no other significant performances, the 2011 Tour de

France was an exceptionally bad edition for Team Saxo Bank. Note that these low overall and peer

efficiency scores are obtained despite a significant reduction in some of the inputs.

The performances of the La Française des Jeux team during the last five editions at first sight

seem rather middle-of-the-road, with only one stage win in the editions of 2007 and 2010, moderate

numbers of CQ points won, and moderate amounts of prize money. Nevertheless, both in the 2009

and 2011 editions, La Française des Jeux gets relatively high efficiency scores within the group of

mixed cycling teams (i.e., m,Own

kθ equal to 85.70% and 113.28%). The explanation is found both in the

input and output dimension. Though the outputs of La Française des Jeux seem rather poor, these

performances are rather well when assessed in relation to those of other mixed teams only. On the

input side, a comparison with the inputs used by other mixed cycling teams learns that the levels of

inputs used by La Française des Jeux are rather limited. For instance, with a budget of around 6.5 to 7

million euro in most editions, the budget of the team is among the lowest. Combining both the

relatively high output levels and low input levels explains the relatively high efficiency scores among

the mixed-type cycling teams.

6. Conclusions

The conceptual starting point of this paper is that professional road cycling has its stars and even

its superstars, but that modern cycling requires these leading individuals to operate in strong teams in

order to be successful. Ideally, these teams combine different individual competences in such a way

that the chances of winning are maximized. This insight calls for the assessment of team performance,

just as in many other sports. Furthermore, in a major event like the Tour de France, there are many

23

prizes to be won, which explains why teams, usually those with smaller budgets, may be organized

such as to focus on other aims than on winning the overall individual classification.

We have addressed this issue by using an extensive dataset and a robust evaluation framework.

The latter singles out different efficiency measures, which reveal information about a team’s

performance both relative to teams with similar aspirations and relative to all other participating

teams. Evidently, each of these performance measures yields interesting information from a

managerial point of view. For instance, teams with modest budgets may be expected to play modest

roles, but even then there may be mutual differences in Tour success rates within this type of teams.

In general, neutralizing the type effect effectively instigates a level playing field as far as team

efficiency is concerned. However, it is also clear from our analysis that the (big) teams, which indeed

aim for the big prizes, generally outperform the other team types not only in terms of effectiveness but

also in terms of efficiency. At least in the Tour de France, they seem to deliver, on average, the most

value for money.

While our analysis is robust in the double sense of deriving from models with different

input/output constellations and of being based on (order-m DEA) re-sampling methods, it is also clear

that we have left open some issues. First, lack of public data prevented us from including one output

that is extremely important to sponsors, viz. media coverage of teams. Second, we have focused here

on team types as one important determinant of efficiency in the Tour de France, leaving other

explanatory factors (e.g. a team’s physical condition, comprising indicators such as height, weight and

resulting BMI of selected riders as considered by Prinz, 2005) out of the picture. Adding these

explanatory factors in the (robust) efficiency analysis can be done by using so-called conditional

(order-m) efficiency models (after Daraio and Simar, 2007). We consider this as an interesting avenue

for further research. Third, when it comes to variant models, and as explained in our methodology

section, we have chosen to refrain from a ‘fixed-output sum’-model à la Yang et al. (2011) on the

grounds that even the best teams in our sample are still considerably removed from the (known)

theoretical output maxima. However, one potentially interesting side-product of such a ‘fixed-output

sum’-variant is its endogenous (ex post) identification of a team’s optimal opponents (i.e., those teams

24

for which the output has to decrease when the evaluated team’s output increases). The “own-type

efficiency”-approach of the current paper evidently implies an implicit exogenous (ex ante) selection

of such potential opponents. A comparative analysis of both models therefore also may yield some

interesting insights. Finally, we stress that our analysis relates to the Tour de France only, although it

may be applicable to similar important cycling events such as the Italian Giro or the Spanish Vuelta.

Team managers and team sponsors may find this a prime event, but a bad Tour result may still be

offset by success in the one-day classics, the World Championship road race, etc. Put otherwise, a

team’s success or its efficiency could clearly also be measured over an entire season.

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27

Figure 1: Data Envelopment Analysis (DEA)

0

C

R

R’

D

S

ABCD: All cycling teams

y1/x

y2/x

B

A

S’

28

Figure 2: Team efficiency vs. team-type efficiency

0

E

F

C

R

R’

D

S

H

R’’

AGH: Sprint Teams

EFBCD: Ranking teams

ABCD: All cycling teams

y1/x

y2/x

G

S’’B

A

S’

29

Figure 3: Tour de France cycling teams 2007-2011: Scatter plots

30

Table 1: Tour de France cycling teams 2007-2011: Team types

(R = ranking, S = sprint, M = mixed)

Team Name

2007 Type

2008 Type

2009 Type

2010 Type

2011 Type

#

Participations

#

Ranking

#

Sprint

#

Mixed

AG2R - La Mondiale R R M M M 5 2 3 Bbox Bouygues Télécom / Europcar

M

M

M

M

S

5

1

4

Caisse d'Epargne R R R S S 5 3 2

Cofidis M M S M S 5 2 3

Euskaltel-Euskadi R R R R R 5 5

La Française des Jeux M S M M M 5 1 4

Lampre M M M M S 5 1 4 Liquigas M M S R R 5 2 1 2

Omega Pharma - Lotto R R R M R 5 4 1

Quick-Step S S S M S 5 4 1 Rabobank R R R R R 5 5 Team Highroad / HTC Columbia

M

R

R

M

S

5

2

1

2

Team Saxo Bank R R R R R 5 5

Astana R R R R 4 4

Team Garmin M R R R 4 3 1 Team Milram S S S S 4 4

Agritubel M R M 3 1 2

Katusha M S M 3 1 2 Saunier-Duval / Footon-Servetto

S

M

M

3

1

2

BMC Racing Team R R 2 2

Cervélo Test Team R R 2 2

Crédit Agricole S S 2 2

Team Barloworld M S 2 1 1 Team Gerolsteiner S S 2 2

Team RadioShack R R 2 2

Team Sky R R 2 2 Discovery Channel R 1 1

Saur-Sojasun M 1 1

Skil-Shimano M 1 1

Team Leopard-Trek R 1 1

Vacansoleil M 1 1

Total

21

20

20

22

22

105

46

24

35

31

Table 2: Tour de France cycling teams 2007-2011: Descriptive statistics

Inputs Outputs

Budget CQ points

in Tour

team

% CQ

points in

Tour team

Number of

Tour starts

Tour team

consistency

Prize

money

CQ points

collected

Prizes

All cycling teams

Mean 8.20 3,715.70 54.35 33.28 4.45 96,797 620.61 1.43

Stdev. 2.83 1,394.28 10.73 10.03 1.88 134,413 397.57 1.88

Min. 3.50 879 27.19 9 0 9,840 70 0

Max 15.00 7,834 85.45 61 8 723,640 2,059 8

Ranking teams

Mean 8.79 4,478.63 56.82 39.74 4.89 153,905 822.50 2.07

Stdev. 2.65 1,462.16 10.93 8.98 1.82 184,244 475.42 2.16

Min. 3.70 1,682 30.16 24 1 10,540 163 0

Max 14.00 7,834 85.45 61 7 723,640 2,059 8

Sprint teams

Mean 7.83 3,472.96 53.95 30.21 4.88 59,641 505.71 0.92

Stdev. 2.58 936.67 10.84 6.54 1.26 48,845 239.02 1.77

Min. 3.50 1,715 27.33 20 3 17,760 184 0

Max 15.00 5,572 72.03 45 8 192,370 1,048 7

Mixed teams

Mean 7.68 2,879.46 51.37 26.89 3.57 47,218 434.06 0.94

Stdev. 3.14 987.11 9.83 8.19 2.05 28,350 213.07 1.21

Min. 3.50 879 27.19 9 0 9,840 70 0

Max 15.00 5,372 72.14 39 8 112,550 855 5

32

Table 3: Alternative DEA-models: selections of inputs

Inputs

Budget CQ in Tour team % CQ in Tour

team

Tour starts Team consistency

Model 1 X X

Model 2 X X

Model 3 X X X

Model 4 X X X

Model 5 X X X X

33

Table 4: “Own-team-type-within-all-team-types”-efficiency for the Tour de France cycling teams: descriptive statistics (5 models)

Model 1 Model 2 Model 3 Model 4 Model 5

All teams

Average 97.93% 94.75% 98.56% 99.06% 99.41%

Standard deviation 21.29% 36.10% 20.32% 23.79% 22.40%

Minimum 59.66% 37.71% 56.23% 31.91% 38.20%

Maximum 157.23% 173.07% 151.86% 170.47% 156.92%

Ranking teams

Average 119.09% 133.68% 118.62% 120.43% 120.14%


Minimum 102.44% 116.40% 104.25% 98.96% 98.17%

Maximum 157.23% 173.07% 151.86% 170.47% 156.92%

Sprint teams

Average 82.29% 70.13% 83.92% 76.85% 80.06%


Minimum 71.00% 51.55% 72.23% 50.42% 64.58%

Maximum 95.91% 76.87% 99.17% 90.80% 91.10%

Mixed teams

Average 80.83% 60.47% 82.24% 86.20% 85.44%


Minimum 59.66% 37.71% 56.23% 31.91% 38.20%

Maximum 94.24% 72.26% 97.72% 121.65% 117.56%

34

Table 5: Correlations between the three types of efficiency (5 variant models)

“Own-team-within-own-team-type”-efficiency


Model 1 1

Model 2 0.91 1

Model 3 0.98 0.93 1

Model 4 0.84 0.78 0.87 1

Model 5 0.83 0.78 0.86 0.99 1

“Own-team-within-all-team-types”-efficiency


Model 1 1

Model 2 0.95 1

Model 3 0.98 0.95 1

Model 4 0.84 0.81 0.87 1

Model 5 0.83 0.80 0.87 0.99 1

“Own-team-type-within-all-team-types”-efficiency


Model 1 1

Model 2 0.94 1

Model 3 0.96 0.94 1

Model 4 0.86 0.84 0.88 1

Model 5 0.86 0.87 0.91 0.97 1

35

Table 6: Robust DEA-based efficiency estimates for the Tour de France cycling teams: descriptive statistics (Model 5)

Average Stdev. Min. Max. 25 perc. 50 perc. 75 perc.

All teams

“Own-team-within-own-team-type”-efficiency 85.18% 57.89% 15.58% 395.68% 49.96% 71.77% 100.44%

“Own-team-within-all-team-types”-efficiency 87.66% 72.78% 12.98% 522.96% 45.51% 67.57% 100.40%

“Own-team-type-within-all-team-types”-efficiency 99.41% 22.40% 38.20% 156.63% 81.63% 95.25% 115.95%

Ranking teams




Sprint teams




Mixed teams




36

Table 7: Detailed analysis Quick-Step, Team Saxo Bank and La Française des Jeux (period 2007-2011)

Budget CQ in Tour team Tour starts Team consistency Prize Money CQ points Prizes m,Overall

kθ m,Own

kθ m,Type

kθ

Quick-Step

2007 9 5,125 33 6 101,920 861 5 116.82% 162.17% 72.03%

2008 8.5 3,706 23 5 31,470 351 1 40.57% 52.22% 77.69%

2009 9.5 5,572 45 6 17,760 252 0 17.54% 21.94% 79.95%

2010 9.5 3,285 31 4 78,058 514 2 67.93% 82.99% 81.85%

2011 9.5 3,076 45 4 19,940 297 0 31.33% 40.00% 78.34%

Team Saxo Bank

2007 7 7,834 50 6 136,580 1,034 3 89.92% 73.84% 121.78%

2008 7 7,639 53 6 621,210 1,910 8 272.26% 194.26% 140.15%

2009 7 7,100 51 7 362,850 1,584 6 180.03% 130.24% 138.23%

2010 7 7,451 53 7 292,392 1,269 6 155.77% 120.20% 129.59%

2011 7.5 3,708 40 4 72,290 627 1 61.87% 54.82% 112.85%

La Française des Jeux

2007 7 2,622 20 4 43,840 361 1 53.36% 65.17% 81.88%

2008 6.5 2,437 24 6 45,780 452 0 62.54% 70.76% 88.38%

2009 6.5 2,853 30 3 35,660 596 0 72.72% 85.70% 84.85%

2010 6.5 3,330 35 5 25,922 385 1 42.72% 56.29% 75.90%

2011 8.5 1,940 31 3 90,660 400 0 78.89% 113.28% 69.64%

37

1 Peloton is the word used for describing a group of cyclists packed together. Because of the slipstream-effect

and being sheltered from the wind, riding in a peloton is a lot easier than riding alone resulting in a much

higher pace.

2 Some cycling teams did change names during the sample period but continued under the same management

and with essentially the same riders. In this study, they are considered to be the same teams. For such teams we

use a single name that best describes the team for the entire period. Team CSC (2007), for instance, became

successively Team CSC - Saxo Bank (2008), Team Saxo Bank (2009-2010) and finally Team Saxo Bank -

Sungard (2011), but we will simply use the name Team Saxo Bank for all years.

3 In its yearly Tour guide, the French newspaper l'Equipe characterizes all individual Tour participants as

either a sprinter, a climber, an overall contender, a time trial specialist or a finisher. Apart from merely

reflecting a personal view of the journalist, it proved to be very difficult to aggregate this information into

some sort of team identification measure. Alternatively, we looked at press interviews by team managers on

the eve of the Tour de France to determine a team's main goals. However, although very accurate in some

instances, many teams do not clearly communicate their specific goals or only provide this information to local

media.

4 The CQ-ranking is a world ranking of professional road cyclists, based on their performances during the last

12 months. It can be seen as the non-official successor of the UCI-ranking which disappeared when the

ProTour was introduced in 2005 (www.cqranking.com).

5 Remark that the aggregation of individual output into a team output is to some extent in line with what

happens in reality. In cycling it is customary that prize money is split over all teammates and team staff. Team

leaders therefore do not enjoy any short-term financial benefits from a victory. Glory and long-term financial

benefits through a better contract are their real personal rewards.

6 In point of fact, the few restrictions on the λ-vector in model (1) are such that any rescaled version of an

observed input-output combination is considered to be feasible. This is tantamount to assuming constant

returns to scale, which, in turn, allows drawing Figure 1, where both inputs are normalized by dividing with

the sole output.

38

7 Thanassoulis and Portela (2002) used this adjusted version of the DEA-model to compute and decompose

the pupil under-attainment into inefficiencies that are due to the pupil and the school the pupil attends to. In a

more recent paper, De Witte et al. (2010) applied the approach in a similar setting.

8 Figure 2 could be readily adjusted to also show the situation for the mixed teams. However, in order to

make the figure not too complicated, we just visualize the efficiency evaluations for the ranking and sprint

teams.

9 In what follows, we restrict ourselves to briefly sketching the basic idea of the robust order-m version of the

DEA model. We refer to Cazals et al. (2002) for a more elaborate (technical) explanation of the method.

10 Results for all teams are available upon request.

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