The modified constant time model for the team time trial

Posted on July 25, 2015 by Kevin Murnane

Inclusion of the team time trial (TTT) in stage races like the Tour de France has been the subject of debate for many years. Some think the TTT is fine the way it is and nothing needs to be changed. Some think the TTT has no place in stage races and should be eliminated. And some take the middle ground and argue that the TTT should be included in stage races but the way it is scored needs to be changed. At various times the Tour de France has taken all three of these approaches. In this article I’ll present a model for keeping the TTT and modifying how it is scored.

The TTT is one of the most difficult – maybe the most difficult – discipline in professional cycling. The riders must work together like a well-oiled machine to sustain a level of brutal, intense effort over the entire length of the race. The team rides in a tight formation at extremely high speeds. Corners are negotiated with precision and grace. The line of riders constantly circulates as each rider takes a short pull at the head of the team and then drops back and attaches to the end of the line for a “rest” period until his turn at the front comes around again. The TTT is an utterly unforgiving discipline where a weak rider or a single mistake can dash the hopes of the entire team..

A well-practiced time-trial team is a beautiful sight to behold which is why it would be a shame to see it eliminated from the Grand Tours (the Giro d’Italia, the Tour de France, and the Vuelta a España) . However, it comes with a unique set of problems which detractors justifiably point out in arguments for why it should not play a role in stage races of any kind.

Developing a skilled TTT team takes practice, a lot of practice. And therein lies one of the problems with the TTT; most professional teams have very little motivation to devote the time to train for it. The World Tour events are the premier events in professional cycling. In 2015 there are 149 days of racing in World Tour events, 14 one-day races, 134 individual stages spread out over 13 stage races, and the TTT at the World Championships. Of the 149 days of racing there are only 6 TTTs, one in each of the three Grand Tours, 1 in the Tour de Romandie, 1 in the Critérium du Dauphiné, and the World Championship TTT. Competition in the World Championships is based on nationality, not professional team. Thus the pro teams race in 148 days of World Tour racing of which 5 are TTTs. In other words, TTTs make up only about 3% of the World Tour race days a pro team competes in over the course of the year. It’s not enough to make practicing the discipline worthwhile for most teams.

As the World Tour is currently structured, the only teams that really need to practice the TTT are the handful that have a serious contender for winning the GC (General Classification, i.e., the overall winner of the race) in one of the Grand Tours. The time in a TTT is taken on the fifth rider to cross the finish line. Every rider who finishes with the team (usually not all of them do) is given this time. This means that the rider who is a contender for the GC gets the time of the fifth best rider on the team. There are often large time gaps between teams in TTTs and over the years many serious contenders for the overall win have fallen too far behind to compete because their teammates were not strong enough or not practiced enough to turn in fast TTT times. Opponents of including the TTT in stage races argue that it shouldn’t be the case that riders are knocked out of contention for the overall win because of time lost by weaker teammates.

As it stands now, inclusion of a TTT in a stage race runs the risk that this single stage can have large and negative consequences for the overall GC competition. If race organizers and fans hope to see a hard fought contest for the GC among all of the top contenders, the best they can hope for is that the TTT doesn’t have any effect on the overall race. It’s no wonder that so few stage races include TTTs.

In 2015 the Giro d’Italia and the Vuelta a España addressed these problems by scheduling short TTTs as the first stage of the race. The TTT in the Giro was a short 17.6 kilometers and the Vuelta’s TTT is a very short 7.4 kilometers. The idea is that these short distances will result in smaller time gaps between teams. In addition, holding the TTT on a tour’s first day gives a team additional motivation to practice it because the winner of a tour’s first stage wear’s the overall winner’s jersey (e.g., the yellow jersey in the Tour de France) on the next day and can often keep it for several days of racing.

The problem with scheduling a short TTT on a tour’s first stage is that the TTT is too short to be much of a challenge and it ends up being more of an exhibition than a contest. The Tour de France opted to hold a longer and more challenging TTT as the 9th stage in the 2015 race. At 28 kilometers the stage was still short but it was more of a contest than the TTTs in the Giro and the Vuelta. However there was a 4:58 gap between first and last place which is more than enough to eliminate every rider on the last place team from contention for winning the yellow jersey.

What can be done to make the TTT more attractive to race organizers who want to include TTTs but don’t want to risk having the results dominate the GC competition? I will suggest an approach called the constant time model that allows for longer and more challenging TTTs and at the same time reduces the large time gaps that typically accompany longer TTTs. After examining the strengths and weaknesses of the model I will suggest a modified version that maintains the model’s strengths and mitigates it’s weaknesses.

In the constant time model every team is given the same base time for the TTT. This can be the time of the fastest team, the slowest team, the average time for all teams, or the median time. Which time is chosen as the base time makes no real difference for the overall outcome in this version of the model.

The base time for each team is adjusted by a constant amount of time based on the order in which the teams finish. The formula is,

T_T = B_T + (F-1) L_T

where T_T= time for the TTT, B_T= the base time, F = the position in which a team finishes, and L_T= the time-loss constant. For example, if L_T= 3 seconds, then the team that finishes first gets the base time, the team that finishes second gets the base time + 3 seconds, the team that finishes third gets the base time + 6 seconds, and so on. There are 22 teams in this years Tour de France which means that application of the constant time model would result in a 63 second time gap between first and last place in the TTT ((22-1) x 3 seconds = 63 seconds). This is a significant amount of lost time for a rider who wants to win the Tour but unlike the 4:58 that was lost by members of the last place team in this year’s TTT it is not enough to eliminate a rider from contention for the yellow jersey.

The organizers of the Tour de France adopted a similar scoring method for the TTT in the 2004 and 2005 tours. The maximum loss was set to 3 minutes and the loss each team suffered was based on convoluted scheme that combined the team’s finishing place with a range of possible times between one team the team that finished just ahead of them. The constant time model is much simpler.

The constant time model has both strengths and weaknesses. The main strength of the model is that it reduces the maximum amount of time that can be lost in a TTT in such a way that GC contenders on poor time trial teams face a time deficit that is significant without being insurmountable. This strength can be shown by applying the constant time model to the TTT results from the 2009 Tour de France in the table below. Astana’s winning time is shown in the first row. Subsequent rows show the amount of time lost by each team.

Application of the constant time model with Lt = 3 to the 2009 Tour de France TTT

Team	Real time	L_T= 3
Astana	46:29	46.29
Garmin – Slipstream	0:18	0.03
Saxo Bank	0.40	0.06
Liquigas	0.58	0.09
Columbia – HTC	0.59	0.12
Katusha	1.23	0.15
Caisse d’Epargne	1.29	0.18
Cervelo Test Team	1.38	0.21
AG2R La Mondiale	1.49	0.24
Euskaltel – Euskadi	2.10	0.27
Rabobank	2.21	0.30
Quick Step	2.26	0.33
Silence – Lotto	2.36	0.36
Française des Jeux	2.46	0.39
Milram	2.49	0.42
Cofidis, Le Credit en Ligne	2.59	0.45
Lampre – NGC	3.25	0.48
Agritubel	4.18	0.51
BBOX Bouygues Telecom	4.42	0.54
Skil-Shimano	5.23	0.57

As can be seen in the table, application of the constant time model insures that no rider loses all hope of winning the GC because his team did poorly in the time trial.

A weakness of the constant model can also be seen in the preceding table. Astana is unlikely to be very happy about having its 18+ second advantages over all of its important competitors reduced by such large amounts. A further weakness of the model can be seen when it is applied to the shorter TTT results from the 2015 Tour de France

Application of the constant time model the 2015 Tour de France TTT

Team	Real Time	L_T= 1	L_T= 2	L_T= 3
BMC Racing	32:15	32.15	32.15	32.15
Team Sky	0:01	0:01	0:02	0:03
Movistar Team	0:04	0:02	0:04	0:06
Tinkoff-Saxo	0:28	0:03	0:06	0:09
Astana Pro Team	0:35	0:04	0:08	0:12
IAM Cycling	0:38	0:05	0:10	0:15
Etixx-QuickStep	0:45	0:06	0:12	0:18
Lampre-Merida	0:48	0:07	0:14	0:21
Team LottoNL-Jumbo	1:14	0:08	0:16	0:24
AG2R LA Mondiale	1:24	0:09	0:18	0:27
Trek Factory Racing	1:25	0:10	0:20	0:30
Team Cannondale-Gramin	1:29	0:11	0:22	0:33
Bora-Argon 18	1:31	0:12	0:24	0:36
FDJ	1:33	0:13	0:26	0:39
Lotto Soudal	1:36	0:14	0:28	0:42
Team Giant-Alpecin	1:37	0:15	0:30	0:45
Team Europcar	1:42	0:16	0:32	0:48
Bretagne-Seche Environnement	1:46	0:17	0:34	0:51
Team Katusha	1:53	0:18	0:36	0:54
MTN-Qhubeka	1:56	0:19	0:38	0:57
Cofidis, Solutions Credits	2:32	0:20	0:40	0:60
Orica-GreenEdge	4:58	0:21	0:42	0:63

When L_T= 3, application of the model increases the time lost by Sky and Movistar who finished 1 and 4 seconds respectively behind the winner BMC. Reducing L_Tto 1 or 2 solves this problem but increases the problem of overlarge reductions in the losses suffered by competitors that did not do well in the TTT.

These problems can be solved by a modified version of the constant time model. In the modified model the base time (B_T) is not set at the stage winner’s time. Instead it is set at a time slower than the winner’s time and time adjustments are only applied to teams that lost more than the base time. For example, set the base time at 1 minute. Every team that finishes less than 1 minute behind the winner gets their real time. The first team that finishes 1 minute or more behind the winner also gets their real time and their time is set as the base time. All of the teams that finished behind the team with the base time have their time adjusted by the constant time model. The results for both the 2009 and 2015 TTTs are shown in the following table with L_T= 3.

Modified constant time model applied to 2009 and 2015 Tour de France TTTs

	2009 Tour de France TTT			2015 Tour de France TTT
Finishing position	Team	Real time	Modified time	Team	Real time	Modified time
1	Astana	46.29	46.29	BMC Racing	32:15	32:15
2	Garmin – Slipstream	0.18	0.18	Team Sky	0:01	0:01
3	Saxo Bank	0.40	0.40	Movistar Team	0:04	0:04
4	Liquigas	0.58	0.58	Tinkoff-Saxo	0:28	0:28
5	Columbia – HTC	0.59	0.59	Astana Pro Team	0:35	0:35
6	Katusha	1.23	1.23	IAM Cycling	0:38	0:38
7	Caisse d’Epargne	1.29	1:26	Etixx-QuickStep	0:45	0:45
8	Cervelo Test Team	1.38	1:29	Lampre-Merida	0:48	0:48
9	AG2R La Mondiale	1.49	1:32	Team LottoNL-Jumbo	1:14	1:14
10	Euskaltel – Euskadi	2.10	1:35	AG2R LA Mondiale	1:24	1:17
11	Rabobank	2.21	1:38	Trek Factory Racing	1:25	1:20
12	Quick Step	2.26	1:41	Team Cannondale-Gramin	1:29	1:23
13	Silence – Lotto	2.36	1:44	Bora-Argon 18	1:31	1:26
14	Française des Jeux	2.46	1:47	FDJ	1:33	1:29
15	Milram	2.49	1:50	Lotto Soudal	1:36	1:32
16	Cofidis, Le Credit en Ligne	2.59	1:53	Team Giant-Alpecin	1:37	1:35
17	Lampre – NGC	3.25	1:56	Team Europcar	1:42	1:38
18	Agritubel	4.18	1:59	Bretagne-Seche Environnement	1:46	1:41
19	BBOX Bouygues Telecom	4.42	2:02	Team Katusha	1:53	1:44
20	Skil-Shimano	5.23	2:05	MTN-Qhubeka	1:56	1:47
21				Cofidis, Solutions Credits	2:32	1:50
22				Orica-GreenEdge	4:58	1:53

Application of the modified model preserves the advantages Astana won over its nearest competitors in the 2009 TTT while at the same time eliminating the penalties suffered using the unmodified model by Sky and Movistar in the 2015 TTT. In addition, all of the teams in both TTTs that benefit from reduced losses suffer a loss of a least 1 minute which is significant, while none of the teams suffer losses greater than 2:05 which leaves every rider with at least a chance of winning the GC.

The modified constant time model insures that no team will lose so much time in the TTT that their GC contender is eliminated from contention. The modified model also insures that teams with serious GC contenders have a reason to excel at the TTT because time gaps that are less than or equal to the base time are retained. The model effectively divides the teams in a TTT into two groups. The top TTT teams in the first group are racing for real time differences. Riders on the lower quality teams in the second group face a significant time loss but are not eliminated from having a chance at winning the GC because of poor TTT performance. Race organizers can set the dividing line between these two groups by adjusting the base time value (B_T), and can fine tune the maximum amount of time lost by adjusting the time-loss constant (L_T).

Adoption of the modified constant time model for scoring TTTs has the potential to invigorate the TTT as a regular component in stage races. Organizers of stage races that are shorter than the three-week grand tours can include a TTT stage without fear that the results will dominate the entire race. Stage races can include longer and more challenging TTTs without fear that the unmodified time gaps will have a serious negative impact on the GC competition. If more race organizers include TTTs in their races, a larger proportion of racing days will be devoted to the TTT, teams will have more motivation to train for it, and they will have more success when they ride it. Instead of being a race where the best thing that can happen is that nothing of consequence happens, the TTT can join the field sprint, the mountaintop finish and the individual time trial as respected and eagerly anticipated stages in a stage race.

Chainring Shifting Techniques

Posted on May 15, 2015 by Kevin Murnane

Many people seem to think that the main reason for having different chainrings on a bike is to provide the rider with two completely different sets of gears. In an earlier article we saw that this is not the case. Most of the gears that are available on one chainring are duplicated or have a very close analog on the next chainring. The main benefit that comes from having different chainrings is that the size of the step up or down from one gear to the next differs on each ring. You get smaller and more refined steps on smaller rings. Understanding how this works can help solve some problems riders may have when shifting between rings.

A common gearing setup for a bike with a double chainring pairs 53 and 39 tooth rings on the front derailleur with a 12 – 25 tooth gear cluster or cassette on the rear derailleur. The table below shows the gears that are available for this setup expressed in meters of development (MoD).

Gears for a 53/39 double chainring and a 12 – 25 cassette in meters of development.

	12	13	14	15	16	17	19	21	23	25
39	7.0	6.5	6	5.6	5.3	4.9	4.4	4.0	3.7	3.4
53	9.5	8.8	8.2	7.6	7.1	6.7	6.0	5.4	5.0	4.6

Meters of development is way to describe bicycle gears that is more commonly used in Europe than the US. It defines gears in terms of the number of meters the bike moves forward every time the pedals make one complete revolution. For example, when you are on the 53 tooth big ring and the 17 tooth cog on the cassette, the bikes moves 6.7 meters forward every time you turn the pedals through one full revolution. MoD along with other methods of defining bicycle gears is presented in more detail in Gearing Part 1: The Basics. I’m using MoD here because it makes it very easy to understand what happens when you shift gears.

An important thing to notice about the gears shown in the table is that gear changes are nonlinear. This means that shifting up or down by the same number of teeth on the rear cassette does not usually result in the same change in MoD. For example, if you are in the big 53 tooth ring and you shift from the 17 tooth cog to the 16 tooth cog on the cassette you go from a 6.7 to a 7.1 meter gear. A shift of one tooth on the cog produces an increase in difficulty of 0.4 meters for every pedal revolution. If you take one more step and make another 1 tooth shift from the 16 tooth cog to the 15 tooth cog you get an increase of 0.5 meters per pedal revolution. It’s harder going from the 16 tooth gear to the 15 tooth gear than it is going from the 17 tooth gear to the 16 tooth gear even though both shifts are carried out by shifting down 1 tooth on the cassette.

Being aware that gear changes are nonlinear can help provide solutions for some common shifting problems.

Shifting into an easier gear on the cassette while climbing

Finding the right gear on a climb often involves a series of shifts into easier gears on the cassette until you find one that is comfortable for the gradient. If one of these downshifts is too big, you can spin too freely and lose momentum. A solution is to drop into a smaller ring early in the climb and then drop into progressively easier gears on the cassette as the climb gets harder. The reason this works is that the changes between gears are smaller and more refined on smaller rings. When you drop into an easier gear on the small ring you are not dropping as far as you would from the same position on the big ring. For example, shifting from the 17 to the 19 tooth cog on the cassette when you are in the big 53 tooth ring is a drop of 0.7 meters per pedal revolution. The same shift from the 17 to the 19 tooth cog on the cassette when you are in the small 39 tooth ring is a drop of only 0.5 meters. The more refined steps on the small ring make it less likely you will lose momentum on a climb by downshifting too far.

Shifting between rings while climbing

Wait a minute. If dropping one gear on the cassette is too big a shift when you’re in the big ring, how can shifting to the smaller ring solve the problem? Look at the table. No matter which gear you’re in on the big ring, shifting to the small ring is a larger drop in MoD than staying in the big ring and dropping down one gear on the cassette. Dropping into the small ring looks like it creates a bigger problem.

The solution is to briefly shift into a higher (harder) gear on the cassette right before dropping to the smaller ring.

There are two circumstances where this technique usually comes into play. The first is the situation described above where you drop to the small ring early in the climb because you know you will handle the climb better with smaller drops in MoD with each shift into an easier gear as the climb progresses. To accomplish this without losing momentum you have to quickly shift up through 2 or 3 cogs on the cassette before dropping to the lower ring. Pulling off this triple (2 shifts up on the cassette + 1 shift down to the small ring) or quadruple (3 shifts up + 1 shift down to the small ring) shift is not easy and is going to take some practice.

The second situation where shifting up into a harder gear on the cassette before shifting down to the small ring comes into play happens when the hill is overwhelming you and you need to get into the small ring to keep your momentum going. In this case you usually only need to do a double shift – shift up one gear on the cassette and then drop to the small ring. This is a good deal easier than the triple or quadruple shifts described above.

How do you do these shifts without losing momentum? The trick is to shift quickly with split-second timing so that you spend very little time in the harder gear. Put a surge of extra power into the pedals as you shift up into the harder gear on the cassette. As soon as the chain catches in the teeth of the gear drop down into the smaller ring. When you get the timing right you will be spending a quarter to a half of a single pedal revolution in the harder gear on a double switch.

Getting the timing right will take some practice. If you stay in the higher gear too long you’re in too big a gear for the gradient and you lose momentum. If you drop into the smaller ring before the rear derailleur shift is complete, you run the risk of dropping the chain and turning a small problem into a big one. The goal is to drop into the smaller ring a split second after the rear derailleur shift into the harder gear is complete.

When to shift into the big ring ring from the small ring

Thus far we have looked at shifting to the small ring from the big ring but there are times when doing the reverse and shifting to the big ring from the small ring can pose its own set of problems. I once fielded a query from a rider who was comfortable riding in the small ring but was starting to ride with stronger cyclists and needed the bigger gears on the big ring in order to keep up. He was shifting up into progressively more difficult gears until he reached the limit on the small ring at which point he shifted up into the big ring. When he got onto the big ring the gear was too hard for him and he had to shift into easier gears at which point he fell behind the people he was riding with.

One possible solution is to drop back into an easier gear on the small ring before you shift up to the big ring. This usually doesn’t work because you are likely to lose too much momentum while you are in the easier gear on the small ring.

Gears for a 53/39 double chainring and a 12 – 25 cassette in meters of development

	12	13	14	15	16	17	19	21	23	25
39	7.0	6.5	6	5.6	5.3	4.9	4.4	4.0	3.7	3.4
53	9.5	8.8	8.2	7.6	7.1	6.7	6.0	5.4	5.0	4.6

Fleche Wallonne Femmes - 23/04/2014 - Huy/Huy - Marianne VOS

Fleche Wallonne Women – 23/04/2014 – Huy/Huy – Marianne Vos

The solution is to shift over to the big ring earlier rather than waiting until you’ve maxed out the small ring. Take a look at the MoD values in the table and remember that the increase in difficulty as gears get harder is nonlinear. If you wait until you’re in the 13 tooth cog on the small ring to switch over to the big ring you’re getting hit with a MoD increase of 2.3 meters. This is a huge jump in difficulty. If you shift into the big ring while you’re in the 23 tooth cog on the cassette you’re looking at a MoD increase of only 1.3 meters. This is still a big jump but it’s not nearly as difficult as the 2.3 MoD increase you get if you shift near the top of the small ring. Moreover, if you work up to the 13 tooth gear from easier gears on the big ring, the final step from the 14 tooth gear is much easier (a MoD increase of 0.6 meters) than jumping to the big ring 13 from the small ring 13 (a MoD increase of 2.3 meters).

The technique for carrying out the shift into the big ring is similar to the one described for doing a double shift to get from the big ring to the small ring. Put a surge of power into the pedals and then shift up into the big ring. The jump in MoD may be too large to maintain and if it is, you can quickly shift down to an easier gear on the big ring. When carried out correctly, this will put you in a bigger gear than you were in on the small ring without losing momentum.

Switching to the big ring sooner rather than later can be useful in any situation where you expect to use the high MoD gears on the big ring. For example, when you have a downhill followed by a flat you can often pick up enough speed on the downhill to keep a large gear turning on the big ring when you get to the flat. If you do the descent in the small ring and then try to switch to the big ring when you get to the flat, the increase in MoD may be too much to handle. If you shift into the big ring early in the descent and keep shifting into harder gears as your speed increases on the downhill, you will be flying by the time you reach the bottom and you’ll be able to maintain a bigger gear for a longer time on the flat.