A Final Look at the 2022 Tour de France

The Monday after the Tour de France ends is always a day on which I have a little trouble powering down.  And I'm just a sports physicist who models the race, not one of the guys in the saddle!  I have a lot of fun modeling the Tour de France each year.  Most of the fun has to do with learning something new.  Using science to understand how athletes perform at the pinnacle of their métiers is what drives my research.  Posting predictions of stage-winning times is just fun on the side.  The table below summarizes how predictions fared this year.

Nothing like that great start in Denmark!  Thirteen of the stages (~62%) were predicted to 3% error or better, which I strive for.  Three more stages (~14%) were just outside that error range.  And five stage predictions (~24%) were simply terrible.  Stages 5, 6 (especially!), and 19 had cyclist power outputs the likes of which I didn't think they could do.  But then Stages 12 and 21 were so much slower than anticipated, though I worry less about missing the ceremonial final stage.  There is always more to learn!

I love estimating cyclist power output.  So many riders and teams want to hold that information close to their respective vests.  But it's easy to obtain what my model cyclist outputs.  Check out the graph below.

The energies in the above graph are supposed to go after the winning cyclist for each stage, not any one particular cyclist.  Stage 6 is quite the anomaly!  I have a lot of work to do to understand how cyclists could complete the longest stage in the Tour de France at an average speed that was nearly that of a time trial.  If they really could achieve those speeds within the confines of what they are supposed to ingest, they definitely needed many Calories that day!  To see more of what I have to say on the subject of cyclist energy output during the Tour de France, click here (or here for the article translated into French) for a piece I wrote for The Conversation and here for a neat video put together by Mark Langtry.

Now look at what Jonas Vingegaard was able to achieve while winning his first Tour de France general classification.

That is quite an average speed for Vingegaard!  I usually do better matching the stage-winning times than the winner's time.  My model cyclist's mass changes, depending on what type of stage I'm modeling.  I don't model a single cyclist; I want the stage-winning times.  My model wasn't supposed to be that close to Vingegaard's time!  What I've learned is that the peloton -- collectively, with all its drafting and shielding of cyclists from wind -- is generating a LOT of power.  Tadej Pogačar averaged 41.17 kph last year (3414.4 km total race length) and 39.89 kph the year before last (3484.2 km total race length).  This year's race was shorter than those two races at 3349.8 km, and that may partially explain why Vingegaard biked 2.3% - 5.6% faster than Pogačar did during the past two Tours de France.  Whatever the case, more analyses need to be performed!

It was another fun summer with the Tour de France.  I thank my University of Lynchburg research student, Michael Charecky, for helping me with terrain data acquisition.  I'm sure we'll need to tweak the model before next year's Tour de France arrives! 

Jasper Philipsen Wins Sprint on Final Stage!

Jasper Philipsen edged out all riders in a ferocious sprint to take the final stage of this year's Tour de France.

After all the super-fast stages, today's stage was molasses running up a sand pile at the start.  More champagne consumed than I had in my model!  Speeds really picked up during the laps in Paris.

Our prediction was much too fast.

• Stage 21:  2h 58' 32" (actual), 2h 45' 50" (prediction), 12' 42" fast (-7.11% error)

It's always impossible to know how things will go at the start of the last stage.  Sometimes we nail the time; other times we miss.  Today we missed.  Below is Philipsen's average speed.

• Stage 21:  10.79 m/s (38.85 kph or 24.14 mph)

That's slower than the Tour de France organizers imagined.

I will write a summary blog post tomorrow.  For now, I'll end this post with a great image I grabbed while watching on my office computer.

It was wonderful watching Jonas Vingegaard and Tadej Pogačar battle for the yellow jersey.  I'll never forget this year's Stage 11 and the final climb on Col du Granon.

Wout van Aert Dominates Time Trial!

Wout van Aert was the favorite to win today's time trial, and he didn't disappoint.  He just edged his teammate and this year's GC winner, Jonas Vingegaard, who let up a little at the end (he also nearly crashed on the final fast descent!).  Tadej Pogačar finished third, 27 seconds behind van Aert.

Van Aert's time was impressive!

• Stage 20:  47' 59.86" (actual), 46' 53" (prediction), 01' 07" fast (-2.32% error)

I'll definitely take that error!  Speeds have been so fast this year.  Check out van Aert's average speed.

• Stage 20:  14.13 m/s (50.88 kph or 31.61 mph)

Now that's cooking in the saddle!

Tomorrow's final stage will be a celebration for Jonas Vingegaard.  There will surely be some champagne imbibed early on.  The 115.6-km (71.83-mi) flat stage commences in the Paris La Défense Arena and takes riders in a big counterclockwise loop to the southwest before returning to Paris for the famed laps on the Champs-Élysées.  Our prediction is given below.

• Stage 21:  2h 45' 50" (prediction)

I never know how a mostly ceremonial stage will go, but it will be wonderful to see!

Christophe Laporte Has France Celebrating!

Christophe Laporte gave France a much-needed stage win.  He blasted past the sprinters in the final kilometer and actually won by a second over the second-place finisher.

Team Jumbo-Visma is having quite a Tour de France!  They got their fifth stage win today, and they'll have the yellow and green jerseys in Paris.

Now I come to our terrible prediction.  I sat watching today's stage much like I did on 7 July while watching Stage 6.  Speeds were through the roof today.  The breakaway and the peloton were both moving at incredible speeds.  Halfway into today's stage, I knew our prediction was headed the way of Stage 6's prediction.

• Stage 19:  3h 52' 04" (actual), 4h 15' 51" (prediction), 23' 47" slow (10.25% error)

Check out the winner's average speed.

• Stage 19:  13.52 m/s (48.68 kph or 30.25 mph)

That is close to a time-trial average speed!  Tour de France organizers figured 46 kph (29 mph) as the possible maximum speed.  They are probably scratching their heads as much as I am!  Frank Bonnamour was the last rider to finish today's stage.  He came in 139th place with a time of 4h 13' 59".  We want to model the winner, not the guy who comes in last!  I'll definitely need to devote a lot of time to analyses after this year's Tour de France is over.

Tomorrow's 40.7-km (25.3-mi) time trial begins in the French commune of Lacapelle-Marival and takes riders west to the commune of Rocamadour.  Our prediction is given below.

• Stage 20:  46' 53" (prediction)

It's a fast prediction, but the way cyclists have been taking the flat French stages, they might challenge half an hour!

Vingegaard Locks Up Tour de France!

Jonas Vingegaard dominated the final climb -- and dominated Tadej Pogačar.  Each time Pogačar attacked, Vingegaard stayed right on his wheel.  And then Vingegaard showed on the final climb that he is the strongest rider in this year's Tour de France.  He picked up more than a minute on Pogačar, thus effectively ending the competition for GC.

Vingegaard had a lot of team help, especially from Wout van Aert, who contributed to cracking Pogačar on the final climb.  Our prediction was a bit fast today.

• Stage 18:  3h 59' 50" (actual), 3h 50' 19" (prediction), 09'31" fast (-3.97% error)

I had about 2% too much power in my model, which is a big deal when it comes to mountain stages.  I wonder if the winning time would have been a tiny bit lower if Vingegaard and Pogačar had not had trouble on the final descent.  Pogačar attacked, and Vingegaard nearly crashed after he kicked his back wheel.  And then Pogačar did crash after taking a turn a bit too wide and getting his front wheel caught in gravel.  But in a classy demonstration of sportsmanship, Vingegaard held up and let Pogačar rejoin him, knowing they would battle on the final climb.  It was something to see.

Vingegaard's average speed is given below.

• Stage 18:  9.95 m/s (35.82 kph or 22.26 mph)

Tomorrow's 188.3-km (117.0-mi) flat stage begins in the French commune of Castelnau-Magnoac and takes riders north to Cahors.  Our prediction is given below.

• Stage 19:  4h 15' 51" (prediction)

Vingegaard just needs a safe ride in the peloton to keep his yellow jersey -- and his polka dot jersey.  I hope there are some good breakaways and a great sprint to the finish line.  If a few riders decide to go all-out for a stage win, our prediction could be on the slow side.

Hat Trick for Tadej Pogačar!

Jonas Vingegaard rode Tadej Pogačar's wheel up the entire final climb, never giving Pogačar the belief that an attack would work until the two battled for the finish line.  I kept wondering when Pogačar was going to attack, but it never happened.  I guess his legs weren't primed for an attack that could have left Vingegaard well behind.  Time bonuses meant that Pogačar got four seconds closer to Vingegaard.  It was fun watching them power up the final climb!

We had a great prediction for today's stage.

• Stage 17:  3h 25' 51" (actual), 3h 27' 32" (prediction), 01' 41" slow (0.82% error)

Speeds were pretty fast today, especially for the top two GC contenders.

• Stage 17:  10.50 m/s (37.80 kph or 23.49 mph)

Kudos to Pogačar's teammate, Brandon McNulty, who provided the pace for Pogačar on the final climb.  McNulty had to replace the work of Rafał Majka, and he was a true yeoman, easily earning most aggressive rider.

Tomorrow's 143.2-km (88.98-mile) mountain stage begins in the Pyrenees town of Lourdes and takes riders west in a counterclockwise loop that ends at the ski resort Hautacam.  Cyclists will contend with an hors catégorie climb to the 1709-m (5607-ft) peak of Col d'Aubisque.  A category-1 climb will precede the hors catégorie climb to the finish.  Our prediction is given below.

• Stage 18:  3h 50' 19" (prediction)

Tomorrow is Pogačar's last big opportunity to grab yellow from Vingegaard.  I'm not sure it can happen because Pogačar doesn't have enough firepower left in his team to help him with attacks.  Our prediction is a fast one.  I hope Pogačar goes all out to overtake Vingegaard!

Hugo Houle Gets Emotional Stage Win!

I learned while watching today's Stage 16 of the Tour de France that Hugo Houle lost his brother, Pierrick, ten years ago when a drunk driver stuck him as he was running.  Houle's win today was dedicated to his brother.

Our string of three straight predictions with less than 1% error ended today, but we still had a good prediction.

• Stage 16:  4h 23' 47" (actual), 4h 18' 22" (prediction), 05' 25" fast (-2.05% error)

Tadej Pogačar attacked three times, but Jonas Vingegaard never faltered.  The breakaway took the stage.  Check out Houle's average speed.

• Stage 16:  11.28 m/s (40.60  kph or 25.23 mph)

I thought the winner's average speed would be a tad faster, but I'll take a 2% error!  We actually did better modeling the GC contenders.

Tomorrow's 129.7-km (80.59-mi) mountain stage begins in the French commune of Saint-Gaudens and takes riders into the Pyrenees, culminating in an hors catégorie finish at the ski resort of Peyragudes.  Our prediction is given below.

• Stage 17:  3h 27' 32" (prediction)

Can Pogačar make a successful attack on Vingegaard?  Pogačar will need that to happen soon or he'll finish second this year!

Jasper Philipsen Wins Sprint to take Stage 15!

I was rooting hard for Benjamin Thomas to hold off the peloton and win a stage for France.  But, alas, Thomas was caught with half a kilometer left and finished 24" behind the winner.  Jasper Philipsen crossed the line first, just a tiny bit ahead of Wout van Aert.

Philipsen is on the right; van Aert is on the left in the green jersey, a jersey he'll lose only via catastrophe.  As for our prediction, I was rooting for perfection!

• Stage 15:  4h 27' 27" (actual), 4h 26' 56" (prediction), 00' 31" fast (-0.19% error)

We can't do much better than that!  Philipsen's average speed is given below.

• Stage 15:  12.62 m/s (45.43 kph or 28.23 mph)

Riders will stay in Carcassonne tonight and during tomorrow's rest day.  Tuesday's 178.5-km (110.9-mi) medium mountain stage will take riders southwest to the French commune of Foix.  Our prediction is given below.

• Stage 16:  4h 18' 22" (prediction)

I can't wait to see if the yellow jersey swaps cyclists again.  The above prediction is fast, which can happen if the top GC contenders attack the yellow jersey hard on Tuesday.

Michael Matthews Dominates Breakaway!

Michael Matthews outdueled Alberto Bettiol on the final climb of today's Tour de France stage.  It looked as if Matthews had cracked at one point, but he picked the perfect moment to attack Bettiol.  And then he had plenty of time to celebrate on the way to the finish line.

It was funny watching Tadej Pogačar and Jonas Vingegaard ride with each other on the way to the line.  Why sprint in the final 300 m?

We had another great prediction today.

• Stage 14:  4h 30' 53" (actual), 4h 32' 29" (prediction), 01' 36" slow (0.59% error)

Same error as yesterday, just in the other direction.  Check out the average speed for Matthews.

• Stage 14:  11.84 m/s (42.64 kph or 26.49 mph)

Tomorrow's 202.5-km (125.8-mi) flat stage begins in Rodez and takes riders south to Carcassonne.  Our prediction is given below.

• Stage 15:  4h 26' 56" (prediction)

If tomorrow's stage is like the Danish stages, we'll be too fast.  If it's like the first few French stages, we'll be too slow.  Will the yellow jersey have a break before Monday's rest day?  Will a breakaway group fight for the stage win?

Mads Pedersen Wins from Breakaway!

I was hoping for a great sprint today, and I wasn't disappointed.  But the sprint came from the breakaway group, not from the peloton.  I was thrilled while watching the three-rider duel in the final few kilometers between Mads Pedersen, Fred Wright, and Hugo Houle.  They danced among each other, taking turns in the front, and then let it all out with half a kilometer left.  Pedersen just edged Wright with Houle finishing third.  Pederson was pretty happy to get his first Tour de France stage win!

I was also very happy with our prediction.

• Stage 13:  4h 13' 03" (actual), 4h 11' 33" (prediction), -01' 30" fast (-0.59% error)

I'm glad to be under 1% error again!  Check out Pedersen's average speed.

• Stage 13:  12.69 m/s (45.67 kph or 28.38 mph)

The GC contenders were content to let the breakaway compete for the stage, especially after a couple of early crashes.  It was great seeing three riders, each of whom had never won a Tour de France stage, go for glory.

Tomorrow's 192.5-km (119.6-mi) medium mountain Stage 14 commences where today's stage finished, which is in Saint-Étienne.  Riders will head southwest to the French commune of Mende.  After dealing with four category-3 climbs, cyclists will face a category-2 climb near the finish.  Our prediction is given below.

• Stage 14:  4h 32' 29" (prediction)

Will the yellow jersey face an attack tomorrow?  It would be fun to see!

Tom Pidcock Devours Alpe d'Huez!

In his first Tour de France, Tom Pidcock maintained his breakaway and ate up Alpe d'Huez.  Not bad for a kid who won't be 23 for another fortnight!  Does he look happy crossing the finish line?

Today's stage was a blast to watch, but it certainly didn't have the fireworks contained in yesterday's stage.  The CG contenders were content to let the breakaway go.  Calmer cycling and very high temperatures made for much lower average speeds than I predicted, despite some speeds on descents reaching 100 kph (62 mph), and despite Tadej Pogačar attacking Jonas Vingegaard a couple of times on the final climb.

• Stage 12:  4h 55' 24" (actual), 4h 32' 56" (prediction), 22' 28" fast (-7.61% error)

A bad prediction for sure!  I was only 2.71% off in 2018 when the Tour de France last had a stage end on Alpe d'Huez.  Too much power by about 2% in my model for today.  Learning and improving are what are important!  Check out Pidcock's average speed.

• Stage 12:  9.32 m/s (33.53 kph or 20.84 mph)

Tomorrow's 192.6-km (119.7-mi) Stage 13 is mostly flat, which means a possible great sprint for the win.  Cyclists will start in the French commune of Le Bourg-d'Oisans and head due west to Saint-Étienne.  Our prediction is given below.

• Stage 13:  4h 11' 33" (prediction)

I hope we don't have too much power tomorrow.  Then again, the last flat stage -- Stage 6 -- blew my model cyclist's power output away!

Vingegaard Conquers Col du Granon as Pogačar CRACKS!

Wow ... just wow.  I will not soon forget what I witnessed during Stage 11 of the 2022 Tour de France.  The seemingly unbreakable Tadej Pogačar was the victim of a brilliant strategy by Team Jumbo-Visma.  Pogačar was attacked early and often.  And when the GC leaders began their assault on Col du Granon, Pogačar was not at his elite best.  With less than 5 km (3 mi) left, Jonas Vingegaard, last year's runner up, went for the yellow jersey.  I grabbed a photo of the moment when the yellow jersey would change riders.

Vingegaard gave a look back to Pogačar and then rode a speed to the finish line that nearly doubled Pogačar's.  Instead of responding to Vingegaard's attack, Pogačar cracked with 4 km (2.5 mi) left.

I kept waiting for Pogačar to do what he has done so often in the past couple of years, and that was to kick his cycling up a notch and rejoin his attackers.  But it never happened.  Vingegaard rode hard across the finish line, eschewing a celebration for precious seconds.

As Vingegaard said after his win, it was a team effort, and Team Jumbo-Visma now has the yellow jersey on Vingegaard.

I thought yesterday that our prediction would be a fast one, but Vingegaard's push on the final climb gave us a good prediction.

• Stage 11:  4h 18' 02" (actual), 4h 12' 20" (prediction), 05' 42" fast (-2.21% error)

Check out Vingegaard's average speed.

• Stage 11:  9.80 m/s (35.27 kph or 21.92 mph)

That is an amazing average speed on such a tough stage.  Fans watch sports to be dazzled by elite athletes, and I was certainly dazzled today!

If today's stage was tough, tomorrow's 165.1-km (102.6-mi) mountain Stage 12 could be even more grueling.  Cyclists will begin in the French commune of Briançon, situated in the Alps in southeastern France, not too far from Italy, and then head northwest.  They will need to repeat what they did today, which is make the hors catégorie climb to the 2642-m (8668-ft) peak of Col du Galibier.  They will then face another hors catégorie climb, this time to the 2067-m (6781-ft) peak of Col de la Croix de Fer.  And finally, what I have been waiting for since the start of the race, they will finish with the famous hors catégorie climb nearly to the 1860-m (6102-ft) peak of Alpe d'Huez.  By the time the first of those glorious 21 hairpin turns is reached, what will the gaps be among the GC contenders?

Our prediction is given below.

• Stage 12:  4h 32' 56" (prediction)

I have no idea what will happen tomorrow.  The above time is fast, but who knows?  Will Pogačar fight back, or will he wait until the race is in the Pyrenees?  Whatever happens, I cannot wait to see the action unfold!

Magnus Cort Wins Head-to-Head Sprint!

It was an exciting -- and bizarre -- day of racing in today's Stage 10 of the Tour de France.  Multiple attacks on the final climb culminated in Magnus Cort just barely outsprinting Nick Schultz.

Cort is on the right; Schultz is on the left.

What made today's stage bizarre was the protest concerning the environment, which happened with about 35 km (22 mi) left in the stage.  The race was paused and organizers had to determine all the gaps so that riders could be restarted with those gaps in place.

The photo I grabbed above shows the peloton waiting for the restart.  What does a paused race do to modeling?  A protest and paused race certainly were not in my model for today's stage!  Riders had a lot of time to take fluids and rest.  I worried that my prediction would be too slow.  And that is exactly what happened.

• Stage 10:  3h 18' 50" (actual), 3h 27' 04" (prediction), 08' 14" slow (4.14% error)

I did a lot better modeling the peloton.  Lennard Kämna made a strong push for the yellow jersey.  He was the in breakaway group and jumped up to second place overall, just 11 seconds back, after Tadej Pogačar led the peloton across the finish line.  Pogačar sprinted across, holding off riders who tried to sneak a few seconds on him.  Pogačar finished 08' 54" behind Cort's winning time.  We would have been nearly perfect with that time!  But we want the winning time.  Check out Cort's average speed.

• Stage 10:  12.41 m/s (44.69 kph or 27.77 mph)

Announcers noted that this year's race is the fastest to this point in the last 20 years.  Nobody wants to see a repeat of what was going on in the Tour de France 20 years ago.

Tomorrow's 151.7-km (94.26-mi) mountain stage will be a true test for the climbers.  Beginning in the 1992 Olympic city of Albertville, riders will head south into the Alps where they will tackle two hors catégorie climbs.  The first will be the climb to the 2642-m (8668-ft) peak of Col du Galibier.  The second will be the climb to the finish line at the 2413-m (7917-ft) peak of Col du Granon.  Our prediction is given below.

• Stage 11:  4h 12' 20" (prediction)

That will be a pretty fast time.  But given how this year's race has gone, "pretty fast" may not be fast enough.

Inspirational Attack and Win for Bob Jungels!

With a bit over 60 km (37 mi) left, Luxembourgish cyclist Bob Jungels decided to attack and go for glory.  And though he had some company after that attack, he eventually rode free and took today's Stage 9.  Check out Jungles looking at his competition behind him to see if he had followers.

Jungels held off all attackers and rode across the finish line by himself.  It was an inspirational ride to say the least.

He looks happy to have his first Tour de France stage win!  The GC contenders were happy to let the attackers go, though they did finish within a minute of Jungels' time.  Our prediction was a tad fast, but not too bad.

• Stage 9:  4h 46' 39" (actual), 4h 38' 03" (prediction), 08' 36" fast (-3.00%)

A prediction error of 3% has been my upper limit for what I consider good, so we were right on that cutoff.  Jungels still had an impressive average speed.

• Stage 9:  11.22 m/s (40.38 kph or 25.09 mph)

Cyclists will travel to the French commune of Morzine for tomorrow's rest day.  The 148.1-km (92.03-mi) medium mountain stage will take riders north to Lake Geneva, and then due south to what looks to be a great category-2 climb finish in Megève.  Our prediction is given below.

• Stage 10:  3h 27' 04" (prediction)

A lot of great mountain climbing awaits riders in the Alps over the next three stages!

Wout van Aert Wins Sprint for Second Stage Win!

Wout van Aert outsprinted Michael Matthews and Tadej Pogačar for his second stage win in this year's Tour de France.  Another beautiful day of racing with a great finish!

My photo cropped van Aert's head on the finish.  Oh well, I might have been more interested in the sprint!  I was also interested in the time.

• Stage 8:  4h 13' 06" (actual), 4h 11' 22" (prediction), 01' 44" fast (-0.68% error)

After the past three stages, I'll definitely take that prediction error!  Check out van Aert's average speed.

• Stage 8:  12.27 m/s (44.16 kph or 27.44 mph)

Will anyone be able to get the green jersey off van Aert?  Will anyone be able to take down Pogačar?

Tomorrow's 192.9-km (119.4-mi) mountain stage begins in the Swiss town of Aigle and takes riders in a big loop through southwest Switzerland before finishing just across the border in the French commune of Châtel.  A couple of great category-1 climbs in the Alps await the cyclists.  Our prediction is given below.

• Stage 9:  4h 38' 03" (prediction)

Monday is a rest day, so teams may go all-out.  It will be interesting to watch the strategies unfold.

Can Anyone Beat Tadej Pogačar?

For the third straight stage, speeds were through the roof, though not as unbelievable as in yesterday's stage.  But today's final kilometer on the gravel was breathtaking. Lennard Kämna was biking for stage-win glory.  Nope, he cracked inside 100 m and finished fourth.  Jonas Vingegaard blasted his way past Tadej Pogačar and Kämna.  Nope, he couldn't hold off the explosion from Pogačar in the final 5 m on the 24% grade and finished second.  Tadej Pogačar is simply better than his competition.

Elite riders came in under four hours today, which is incredibly fast.  Our prediction was once again too slow.

• Stage 7:  3h 58' 40" (actual), 4h 11' 24" (prediction), 12' 44" slow (5.34% error)

Though much better than yesterday's prediction, I still don't like having over 3% error.  Pogačar and his fellow cyclists are simply outperforming what I've seen in recent years.  It's amazing to see what human beings are capable of on a bicycle!  Check out Pogačar's winning average speed.

• Stage 7:  12.31 m/s (44.32 kph or 27.54 mph)

He was more than 2 kph faster than my model cyclist.  For a kid who's not yet turned 24 years of age, the rest of the field has to wonder how long Pogačar will dominate cycling.

Tomorrow's 186.3-km (115.8-mi) medium-mountain Stage 8 commences in the French commune of Dole and finishes to the southeast in the Swiss city of Lausanne, which sits on the north side of Lake Geneva.  Our prediction is given below.

• Stage 8:  4h 11' 22" (prediction)

More grueling stages follow tomorrow's stage.  Will cyclists hold back a little or will speeds continue to be sky high?  It will be fun to see what happens!

Pogačar Back in Yellow and Disastrous Modeling!

Tadej Pogačar showed why he is the man to beat in this year's Tour de France.  He dominated the final sprint, showing an explosive ability that had my jaw on the floor.  He was pretty excited to win today's stage and grab the yellow jersey!

My jaw was on the floor for more than just the final sprint.  For this year's longest stage, I couldn't believe the speeds the cyclists were able to maintain.  I thought yesterday's stage was the ultra-fast stage that I miss every year.  But today's stage gave me, if not my worst prediction, nearly my worst prediction (I have to check).

• Stage 6:  4h 27' 13" (actual), 5h 06' 53" (prediction), 39' 40" slow (14.84% error)

Yeesh!  Check out Pogačar's average speed for today's 219.9-km (136.6-mi) stage.

• Stage 6:  13.72 m/s (49.38 kph or 30.68 mph)

With super-fast stages, I want to learn something about what elite athletes can do.  I will need a lot more time to digest what I witnessed today.  Stage 1's 13.2-km (8.2-mi) individual time trial, during which cyclists were going all out, saw the winner with an average speed of 51.78 kph (32.17 mph).  Cyclists were going at that rate during much of today's stage -- and they already had five stages under their belts!  A quick calculation shows that I needed nearly 40% more cyclist power output (or peloton power output) on much of today's stage.  I'm as flummoxed as I've ever been in nearly two decades modeling the Tour de France.

Wout van Aert and his yellow jersey were attacked mercilessly today, and he earned the most combative rider with an admirable effort to hold onto the lead.  But he fell to 103rd place, 7' 28" behind Pogačar.  The last rider to finish today was nearly 16 minutes off the winning time, still much faster than our prediction.  The yellow jersey attacks pushed speeds to heights I'd not seen before.  Can these ridiculous speeds continue???

Tomorrow's 176.3-km (109.5-mi) Stage 7 is nearly a repeat of Stage 7 in the Tour de France ten years ago, though this year's version is a bit shorter.  Both Stage 7s have the same endpoints.  Beginning in the French commune of Tomblaine, riders will head south to La Planche des Belles Filles in the Vosges Mountains.  This year's first mountain stage will have a great category-1 climb to the finish.  Our prediction is given below.

• Stage 7:  4h 11' 24" (prediction)

After yesterday and today, I won't be surprised if we are slow again!

Simon Clarke Wins Photo Finish!

Cobblestone racing, crashes, and a photo finish made for an exciting day in the Tour de France, though Team Jumbo-Visma may not agree.  Wout van Aert crashed but then rode with gritty determination to hold on to the yellow jersey.  Simon Clarke won an amazing sprint against Taco van her Hoorn to take the stage.  Check out the photo I took.

What also made today's stage exciting was the blistering pace set by the riders.  They were practically flying, even on some of the cobblestone sections.  This is the stage I wrote about yesterday when wondering when the ultra-fast stage would be.

• Stage 5:  3h 13' 55" (actual), 3h 31' 36" (prediction), 18' 01" slow (9.31% error)

After four wonderful predictions to start this year's Tour de France, we have our first terrible prediction.  Check out Clarke's average speed.

• Stage 5:  13.52 m/s (48.66 kph or 30.24 mph)

How fast is that average speed?  It's 1.66 kph (1.03 mph) faster than the Tour de France website's estimated top time schedule speed, and it's just 3.12 kph (1.94 mph) slower than Stage 1's individual time trial, which was only 8.4% the length of today's stage.  It seems that every summer there is a Tour de France stage that blows me away with high speeds, and that stage this year is Stage 5.

Tomorrow's Stage 6 begins in the Belgian city of Binche, just across the border from France.  At 219.9 km (136.6 mi), the hilly stage is this year's longest.  Cyclists will ride southeast to the French commune of Longwy, not too far from where Belgium, France, and Luxemburg meet.  Our prediction is given below.

• Stage 6:  5h 06' 53" (prediction)

I hope we can get back on track tomorrow.  I don't think we can do any worse than we did today!

Second No More -- Van Aert BLASTS to Victory!

After three consecutive second place stage finishes, Wout van Aert blasted his way to victory in today's Stage 4.  He and his Team Jumbo Visma mates went for it with about 12 km (7.5 mi) left in the stage.  They powered their way up the final climb and van Aert took over the final 10 km (6.2 mi).

Van Aert was 8 s ahead of the peloton.  He was very happy!  I am happy, too, after watching a stage raced on what looked to be a beautiful day in northeastern France.  I got even happier when I saw how our prediction fared.

• Stage 4:  4h 01' 36" (actual), 3h 59' 04" (prediction), 02' 32" fast (-1.05% error)

I thought we could be a bit slow today, but we did well.  Check out van Aert's average speed.

• Stage 4:  11.83 m/s (42.59 kph or 26.46 mph)

Not too shabby!

Tomorrow's 157-km (97.6-mi) hilly Stage 5 begins in Lille and ends to the southeast in Trouée d'Arenberg.  Our prediction is given below.

• Stage 5:  3h 31' 36" (prediction)

Wout van Aert has been the dominant rider for the first four stages.  Will he have the yellow jersey after tomorrow?  I cannot model team strategies because I do not have access to those strategies -- obviously.  With tomorrow's stage being relatively short in length, our prediction could be too slow.  We've had four great predictions, but I keep waiting for the blisteringly-fast stage that happens every year.

Groenewegen Wins Brilliant Sprint!

The three Danish stages are in the books, and Wout van Aert earned bridesmaid distinction.  The great Belgian cyclist was second on all three stages.  In today's third stage, Dylan Groenewegen just edged van Aert in a spectacular sprint to the finish line.

Groenewegen is just right of center in my photo, in light blue.  He was across the line just a couple of centimeters ahead of van Aert, who at least retains the yellow jersey.

We had another great prediction.

• Stage 3:  4h 11' 33" (actual), 4' 08' 46" (prediction), 02' 47" fast (-1.11% error)

I though we would be a tad slow today, but it wasn't until the last 10 km that speeds went through the roof.  I loved seeing in the final few km a speed limit sign for 70 kph (43.5 mph), which the peloton was just breaking.  Check out Groenewegen's average speed.

• Stage 3:  12.06 m/s (43.41 kph or 26.97 mph)

That's quite a clip!

The Tour de France transfers to France tomorrow, giving cyclists a break from the saddle.  I'll put our prediction up today instead of waiting until tomorrow.

Tuesday's 171.5-km (106.6-mi) hilly (six tiny category-4 climbs) Stage 4 begins in Dunkirk and ends in Calais.  The route in northeastern France, not too far from Belgium, will take cyclists through a lot of French history, especially WWII history.  It will be fun to watch.  Our prediction is given below.

• Stage 4:  3h 59' 04" (prediction)

I'm still waiting for the first ultra-fast stage, and Stage 4 could be it after a day of rest.  I hope we aren't too slow!

I'll enjoy Independence Day tomorrow and get back to the Tour de France on Tuesday morning.

Jakobsen Wins Fantastic Sprint!

If you love watching cycling with crosswinds and headwinds and gorgeous bridges, today's second Tour de France stage was made for you.  How great was it watching the peloton move across the Great Belt Bridge?  Too many crashes in today's stage, though, including on the bridge and within a few kilometers of the finish line.  Fabio Jakobsen timed his sprint in great position to just edge Wout van Aert by half the width of a wheel.  Two stages, and two second-place finishes for van Aert, but he'll wear the yellow jersey tomorrow.  I once again took a photo of the finish.

We had a great prediction today.

• Stage 2:  4h 34' 35" (actual), 4h 32' 29" (prediction), 02' 06" fast (-0.76% error)

I'll take the first two stages predicted to better than 1%!  Check out Jakobsen's winning average speed.

• Stage 2:  12.27 m/s (44.18 kph or 27.45 mph)

Tomorrow's Stage 3, the final Denmark stage, commences in Vejle and ends in Sønderborg.  The 182-km (113-mi) flat stage should have another great sprint finish.  Our prediction is given below.

• Stage 3:  4h 08' 46" (prediction)

We could be a tad slow if headwinds aren't a problem.  Hard to predict weather effects!  I can't wait to see more of Denmark and more great racing!

Lampaert Wins Time Trial!

Belgian Yves Lampaert won today's first Tour de France stage, an individual time trial in Copenhagen.  My prediction was nearly perfect with fellow Belgian Wout van Aert sitting in first place, just one second off what I had predicted.  It seems there is a big push by media companies to prevent screen shots, so I had to use my lousy cell phone camera to get Lampaert crossing the finish line.

I'm a dinosaur with social media and cell phone usage.  Maybe I'll find a better way to grab an image.  Seems like the media outlet wouldn't mind me doing free advertising for it!

We started this year's Tour de France off with a great prediction.

• Stage 1:  15' 17.76" (actual), 15' 21" (prediction), 3.24" slow (0.33% error)

Not a bad way to begin!  Lampaert was really cooking on his bike, despite lots of rain and 18-kph (11-mph) winds.  Check out his average speed.

• Stage 1:  14.38 m/s (51.78 kph or 32.17 mph)

Lampaert will be in yellow tomorrow, but he and 174 other riders were put on notice when Tadej Pogačar finished third, just 7 s behind the yellow jersey.  He's still the man to beat!

Tomorrow's flat second stage begins in Roskilde and ends after 202.2 km (125.6 mi) of cycling, in Nyborg.  It will be fun seeing more of Denmark.  I'm not sure we can hit tomorrow's winning time as well as today's, but we'll try.

• Stage 2:  4h 32' 29" (prediction)

Early on in each Tour de France, I wonder if predictions will be too fast, too slow, or about right.  It seems there are usually a quarter to a third of the stages that we can't predict to better than 3% error.  We'll learn a lot during tomorrow's long stage!

Time for the 109th Tour de France!

For the first time, the Tour de France will begin in Denmark.  Stage 1 will be an individual time trial of just 13.2 km (8.2 mi) in Copenhagen.  I will once again be modeling the world's most famous bicycle race.  My research student this summer is Michael Charecky, a rising junior physics major here at the University of Lynchburg.  We are excited for the start of the race!

Our prediction for Stage 1 is given below.

• Stage 1:  15' 21" (prediction)

Whoever wins the short time trial will get to don the famed yellow jersey for Saturday's second stage.  The man to beat this year is the winner of the past two Tours de France, Tadej Pogačar.  Who can knock PoGo off his pedestal?!?

When Empathy is Impossible

The slaughter continues.

My wonderful wife, Sally, stopped me dead in my tracks yesterday when she informed me that elementary school children were killed in Texas.  Robb Elementary School in Uvalde, Texas is now likely known to most Americans.  That is where 19 children and two adults were murdered.  I've tried to explain reasons for mass shootings to my overseas colleagues who are just as perplexed as I am for why killings continue with little to no action taken to prevent future killings.  I wrote a blog piece after Sandy Hook in late 2012.  I wrote another blog piece in early 2018 after Stoneman Douglas.  I doubt the words I write in this blog piece will add much to what I've already written, but I'll attempt a slightly different angle.

Webster's second definition for "empathy" is:  the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another of either the past or present without having the feelings, thoughts, and experience fully communicated in an objectively explicit manner.  As a parent of two incredible daughters, it takes no effort for me to empathize with the parents who lost their children yesterday.  It also takes zero effort for me to empathize with those who regret that yesterday's perpetrator had been killed, only so that something worse -- more painful -- could happen to that evil individual.  But I predict that it is impossible for me to empathize with yesterday's shooter, even though I know next to nothing about him.  I am not wired for "vicariously experiencing the feelings, thoughts, ..." of someone who enters a school and opens fire.

I suspect that nothing in my previous paragraph is especially disagreeable.  Let me change that.  I struggle mightily to empathize with those who love guns.  I've held various opinions on that topic during more than half a century of life.  The empathy I feel for a parent whose child was murdered is effortless for me to experience.  Most of the time, though, empathy is hard.  Empathy requires effort and, sometimes, a lot of work.

I own a .30-06 Savage rifle that sits in a gun cabinet about 200 miles (as the crow flies) from my home.  I hunted with my family for a few years, mostly in an effort to understand hunting culture.  I enjoyed it.  My family loved deer meat, and I felt better about eating deer I killed than I did eating meat that came from factory farms.  I've been a vegetarian for over five years, but the reason for that choice has nothing to do with guns.  I've no interest in hunting because of my diet choice.  But I also have no interest in the rifle I own.  And here is where empathy is hard for me.  Regardless of conversations with hundreds of gun enthusiasts over several decades, much study on the history of guns in America, and my own experience of owning a gun, I've been incapable of empathizing with those who adore guns.  Facebook friends have recently posted the need to arm teachers, and despite my best efforts, I cannot get my mind in a place where I could ever imagine the efficaciousness of such a strategy.  I wouldn't bat an eye if I had to give up my gun as part of a national effort to eliminate gun use.  I understand that there are those who will read that previous sentence and be unable to empathize with me.

Far from being the first to point this out, people are tribal.  Social media, with it's headlines-only approach to disseminating news, is but part of the reason why diametric sides of an issue are on opposite sides of a vast chasm that used to be filled with nuance.  Like empathy, nuance requires a lot of work.  Reading long articles and books, talking to people from all walks of life, and spending serious time cogitating in a sans-cell-phone environment are just some of the ways people begin to develop nuanced views.

Consider the following 10 questions.

1. Do you believe in a god?
2. Should abortion be legal?
3. Should capital punishment be legal?
4. Should research be performed on stem cells?
5. Do you think animals should be killed for food if non-animal food options are readily available?
6. Do you support Donald Trump?
7. Should torture ever be used during an interrogation?
8. Should private citizens of adult age be allowed to own guns?
9. Should marijuana use by private citizens of adult age be legal?
10. Do you support government-funded, universal healthcare?

Perhaps my biases have been partially revealed by the way I asked each question even though I tried to pose questions that did not suggest a preferred answer.  Does asking "Should abortion be legal?" imply something different about me compared to asking "Should abortion be illegal?"  I've no idea.  Each of the above questions is meant to evoke an immediate "yes" or "no" answer.  But I can imagine objections to insisting on binary responses.  Those objections would be founded in desires for nuance.  Any one of my questions could occupy classroom discussions during a semester-long course, and entire books could be, and have been, devoted to addressing my questions.  If you had to answer "yes" or "no" to my questions, could you do so?  My guess is that most people could, even though they would be yearning to offer slews of caveats.

Now for a simple math question.  What is the number 2 raised to the 10th power?  It won't be hard to come up with 1024.  Because each of my 10 questions sought only a "yes" or "no" answer, there are 1024 distinct ways of answering those questions.  That means if you and a thousand people answer my questions, there is a chance, albeit vanishingly small, that each one of you could have a unique set of answers.  And if you feel passionate about each of your 10 responses, you could look upon the answers given by the other thousand people -- and want nothing to do with each and every one of those people.

Yesterday was 24 May 2022, the 144th day of the year.  The massacre in Texas was the 27th school shooting this year.  That's one school shooting per 5 days and 8 hours.  How does this problem get solved when tribalism reigns supreme, nuance is all but gone, and empathy is hard to come by?  I know people who would have nothing to do with me if they were aware that my answer to a particular question on my list differs from theirs.  How does someone in the pro-gun culture talk to a person who wants to eliminate guns?  Sure, they likely agree that shooting children is evil, but neither might be able to empathize with the other on what to do with guns.  The traditional political spectrum has been replaced with a Möbius strip; left and right meet at a twisted point behind the part of the spectrum where nuance used to sit.

While people shout at each other, try to cancel each other, and refuse to do the hard work of empathizing with each other, the slaughter continues.