Sumo Glory in 5.5 Seconds!

Ever since I began researching Chapter 9 of my first book, I have been fascinated by the sport of sumo.  I discussed the great Taihō Kōki in that chapter while discussing lovely physics topics like linear momentum.  Though Taihō died three years after my book was published, I still check in on sumo when I can.  I'm glad I watched the final match of the Autumn Grand Sumo Tournament that took place in Tokyo on 22 September (click here for an article in English).  Several top-ranked rikishi, including two yokozuna, were absent from the final of the top division.  But that didn't stop Mitakeumi Hisashi from attaining sumo glory after defeating Takakeishō Mitsunobu in just 5.5 seconds.

Check out the start of the match (click on image for a larger view).

The ring (dohyō) has a diameter of 4.55 m (14.9 ft).  The rikishi are behind the starting lines (shikiri-sen), which are 70 cm (2.3 ft) apart.  The referee (gyōji) is ready for the start of the action, which happens only by mutual consent of the rikishi.  Mitakeumi with a mass of 177 kg (a weight of 390 lb) is on the left and Takakeishō with a mass of 169 kg (a weight of 373 lb) is on the right.  The two rikishi combined for a mass of 346 kg (a weight of 763 lb), which is the weight of a good-sized grand piano or over a quarter of the weight of my Honda Civic.  A lot of mass was about to collide!

The initial charge (tachi-ai) saw Takakeishō opting to stay low and Mitakeumi looking to defend high (click on image for a larger view).

You can see Mitakeumi's hands are out, preparing to keep Takakeishō from getting too low.  Check out the initial collision (click on image for a larger view).

Even though rikishi seldom are able to get to a speed of more than 2 m/s (4.5 mph) or so due to the short distance they travel prior to collision, the combined kinetic energy can be large.  I calculated a combined kinetic energy at the collision to be about 850 J.  If that amount of energy could be turned into work, I could be lifted about a meter off the ground!  A baseball would have to be moving 108 m/s (242 mph) to have that much kinetic energy!  But the only work that kinetic energy was turned into was the work needed to depress and move fat around.  If ever there was an inelastic collision, it's what you see in the above image.  Most of that kinetic energy was gone after the collision.  Before you think of 850 J as being a huge amount of energy, and nobody wants to be hit by a baseball moving over 100 m/s, consider that 850 J is the same amount of energy as 0.2 Calories.  That's only 10% of a Tic Tac!  The next time you pop a single Tic Tac in your mouth, think about how much chemical energy is stored in food.

Okay, back to the action.  Mitakeumi's opening strategy worked; he kept Takakeishō from staying low (click on image for a larger view).

Note that the center of mass of the two rikishi hasn't moved much from the initial collision.  Because both rikishi were pushing back on the floor with roughly the same force, the floor pushed back on them with the same force (Newton's Third Law).  With those external forces nearly canceling, the system of the two rikishi felt no net, external force.  That meant that the system's linear momentum was conserved during the collision.  That's why the center of mass didn't move much after the initial collision.  But now we come to the key point in the action where Mitakeumi took advantage of physics and made sure the system of the two rikishi had a net, external force (click on image for a larger view).

You can see Mitakeumi on the left driving forward while Takakeishō got caught standing still.  The above image is just 1.3 s after the initial charge.  Because Mitakeumi has a little speed to the right, the system linear momentum isn't zero as it was during the initial hit.  The system linear momentum is to the right, which means the two rikishi will likely move to the right after the next big collision.  A split second later and Takakeishō is still stuck (click on image for a larger view).

Takakeishō is essentially at rest in the above instant, and Mitakeumi is heading toward victory.  Check out the next collision (click on image for a larger view).

The system linear momentum is to the right!  Mitakeumi is charging and you can see that Takakeishō is reeling by the fact that his left foot has come off the ground.  Mitakeumi's next big step with his left leg drove Takakeishō right where Mitakeumi wanted him (click on image for a larger view).

Takakeishō doesn't have much room to back up, which was Mitakeumi's intended goal.  Mitakeumi then opted for stability and went low (click on image for a larger view).

By keeping low, Mitakeumi avoided Takakeishō getting the advantage by pushing off the raised ring and offsetting Mitakeumi's balance.  In the image below, you see Mitakeumi low and ready to deliver the winning punishment (click on image for a larger view).

When Mitakeumi next drove into Takakeishō, Mitakeumi had his center of mass dropped and his right leg back for added stability (click on image for a larger view).

You can see that Takakeishō had his feet against the raised ring.  That was his last effort to keep from being pushed out of the ring.  Takakeishō tried to sneak out to his right, but the position Mitakeumi had achieved in the above image prevented that from happening (click on image for a larger view).

All that remained of the match was great technique, strength, and using physics in the way it's supposed to be used.  Mitakeumi next helped with leverage by grabbing Takakeishō's mawashi (click on image for a larger view).

You can just spot Mitakeumi's right hand under Takakeishō's mawashi.  And look at the wonderful stance Mitakeumi had!  His wide base with left foot slightly back prevented Takakeishō from driving off the raised ring.  Now comes the lift (click on image for a larger view).

Mitakeumi had Takakeishō's mawashi fulled gripped with both hands, and Mitakeumi was prepared to lift and push (click on image for a larger view).

Mitakeumi had raised himself and Takakeishō up and driven Takakeishō almost out of the ring.  A lot of chanko-nabe has to be consumed to get that massive and strong!  Takakeishō was done for at this point.  A look from behind shows the precarious situation Takakeishō was in (click on image for a larger view).

Takakeishō was out a split second later (click on image for a larger view).

You can see on Takakeishō's face what second place looks like.  The above image is just 5.5 s after the initial charge began.  That's all the time Mitakeumi needed to take full advantage of the laws of physics and secure a tournament win.  He got a pretty nice trophy, too (click on image for a larger view).

He can put a lot of Asahi Super Dry in that thing!

Albert Pujols and Lifetime 0.300 Hitter

With the Astros win over the Rays last night, the two American League heavyweights will be squaring off against each other for the pennant.  Game 1 of the Astros/Yankees series begins on Saturday.  Both of the National League heavyweights, the Braves and Dodgers, were ousted from the playoffs by the Cardinals and Nationals, respectively.  The Cardinals host the Nationals this evening in the first game for the National League pennant.  The silliness of partially deciding the champion a 162-game Major League Baseball season with a single game in the wild-card round and a best-of-five in the division-series round will have to be discussed in a future blog post.  The topic of this blog post is Albert Pujols.

(image credit:  https://www.flickr.com/photos/dherholz/246301261/)

Pujols hasn't played for the Cards since helping them win the 2011 World Series.  His Los Angeles Angles finished this past season 35 games behind the Astros.  But his old team being in the hunt for this year's World Series title got me thinking about Pujols.  His 11 seasons in St. Louis were not only some of the best seasons any player has had to open a career, they punched his ticket to the Hall of Fame.  He finished top-5 in MVP voting in 10 of those 11 seasons (and 9th in his "off" year!), winning the award three times.  Two of his second-place MVP finishes were to Barry Bonds (make of that what you will).  His career numbers after those 11 seasons in St. Louis already had him ranked among the game's best.  He had over 2000 hits, nearly 1300 runs, nearly 450 home runs, nearly 1000 walks, over 1300 RBI, an OBP of 0.420, a SLG of 0.617, and a batting average of 0.328.

We've known for many years now that batting average isn't nearly as valuable a statistic as, say, on-base percentage or slugging percentage.  But batting average still resonates with many baseball fans, even scientists like me (who should know better!).  I'm 49 years old and I have vivid memories of collecting baseball cards when I was very young.  The stats on the backs of those cards became numbers that my brain couldn't shake.  Batting titles, 200 hits in a season, getting over 0.300 batting average, and sluggers who could top 100 RBI became the baseball benchmarks of my youth.  Finishing one's time in baseball as a "lifetime 0.300 hitter" had the cachet of a great career.  When Pujols left the Cards after the 2011 season with his 0.328 lifetime batting average, that number caused names to pop up in my head at the time.  I was lucky enough to have watched Rod Carew and Wade Boggs on television during their prime years.  Those two names represent a combined 12 American League batting titles, two players who each topped 3000 career hits, and two players who have lifetime 0.328 batting averages.  You know who else hit 0.328 for his career?  Honus Wagner.  Setting aside disputes over 9 hits and 10 at-bats in his career, Wagner's name is known to any baseball fan, and certainly to anyone who collects baseball cards.  He was in the inaugural Hall of Fame class and regarded by many as the greatest shortstop, though comparing dead-ball-era players to the athletes of today is next to impossible.  The point I'm making here is that when Pujols left the Cards after their championship season in 2011, he had the career average of great hitters like Carew, Boggs, and Wagner.  But his power numbers blew those greats away.  Those of us who watched Pujols in his prime were privileged to see one of baseball's elites.

Despite finishing 5th in the 2011 MVP race, Pujols had his worst year with the Cards.  Though he had a year that essentially every baseball player would love to have, it wasn't the elite year that Pujols was used to in his first decade in the league.  It was the first year that he didn't top 100 RBI (he had 99) or hit over 0.300 (he finished at 0.299).  His OBP and SLG were down, and he continued his penchant for grounding into double plays, leading the majors with 29.  He was nearly 32 years old and, if he was like most players throughout baseball's history, was getting ready to enter the decline phase of his career.  Maybe the Cardinals could see all that, though they did offer him a lot of money to come back.  Pujols was traded to the Angels prior to the start of the 2012 season.  The Angels signed Pujols to a 10-year deal worth approximately $254 million, which was about $44 million more than what the Cards were willing to pay.  Much has been written about how financially crazy that was for the Angels, though hindsight does aid in the complaining about the contract.

The Angels surely thought they could get four or five seasons of Pujols nearly at the level of his best seasons with the Cards.  He walloped 50 doubles and 30 home runs in his first season with the Angels.  But the 0.285 batting average he had that first year with the Angels was, by far, his best batting average season with the Angels.  He made just one All-Star team in the past 8 seasons as an Angel, and that was in 2015 when he finished the year with 40 home runs.  But as impressive as that was, he hit just 0.244 with a paltry 0.307 OBP.  Over the past 3 seasons, Pujols collectively hit less than 0.245, had an OBP under 0.300, and had a -1.0 WAR.  That last number is almost hard to believe for a player like Albert Pujols.

Though he's hit over 200 home runs in his 8 seasons with the Angels, no one can argue that Albert Pujols has been anything close to the player he was for the Cardinals.  He did finish the 2019 season, his 19th in the big leagues, with a career batting average of 0.300, which means his years with the Angels knocked 0.028 off his career batting average.  But though the record books have Pujols as a 0.300 hitter, that's rounded.  He actually has a 0.2996 career batting average.  If he retired today, Pujols would indeed be able to wear the "lifetime 0.300 hitter" moniker.  But there is a trace of Ted Williams in me that wants to see Pujols come back for his 20th season and get his lifetime average over the exact 0.300 number.  Albert Pujols has come to the plate 12231 times in his career.  He needed just five outs he made in his career to have been hits for his lifetime average to be over the 0.300 line.  Five outs.  In 19 years.  Fans of Pujols can surely recall a couple of great defensive plays made against him, or a couple of blown umpire calls that cost him hits.

What would you do?  If you were Pujols and about to turn 40, would you retire and have the magic 0.300 in the record books?  Would you bust your tail over the off-season, get in the best shape of your life, and come back with a mission to get over .300?  Pujols hasn't reached 500 at bats in the previous two seasons, but let's give him exactly 500 at bats for the 2020 season.  Pujols would need 155 hits in those 500 at bats to have a lifetime average of 0.30008 (154 hits would have him at 0.299991).  Getting 155 hits in 500 at bats means Pujols would have to hit 0.310 next year, something he's not done since 2010, i.e. half his career ago.  So that seems very unlikely.  But what if Pujols got hot to start the season?  He could go 6 for 6 and sneak over the 0.300 line (0.300009 to be closer to exact).  Now that would be almost like Ted Williams going 6 for 8 in the double header to end the 1941 season and finish comfortably over 0.400.  Starting the season 6 for 6 is unlikely for Pujols, but not nearly as improbable as hitting 0.310 over the course of a full season.

So, again, what would you do?  The elephant in the room, of course, is what Pujols will earn next year.  Pujols has already made over $285 million in his baseball career (not including endorsements!).  He's set to earn $29 million next season, and then $30 million the following season.  He'll make over $179k per game next season, which is nearly $20k per inning (assuming each game has 9 innings, which won't be true).  He could be the DH and only play four or five innings per game.  Just a select few people can even comprehend the money that Pujols could make next year.  If Pujols comes back and plays one game, he'll earn more from that one game than I will in all of 2020.  So I would do what I suspect most everyone else would do, and that's come back and earn an incredible salary doing something that I love to do.  Even if he plays the next two seasons, and he plays well below his former self, he'll still finish his career with a first-ballot Hall of Fame ticket.  He'll also give fans like me, who have never seen Pujols play in person, the chance to cross off one item on our bucket lists.  I'm rooting for Albert Pujols to come back strong next season -- and hit at least 0.310!