Hitting a baseball is all about momentum. Momentum is a vector describing a "quantity of motion" or in mathematical terms p (momentum) = mass * velocity. In a closed system, momentum is conserved. Conservation of momentum means that the harder you throw the ball, the harder the ball will bounce back. Think in the case of throwing a ball against a solid wall. The harder you throw the ball, the harder it bounces back. This is easy to see in the case that fast balls tend to be hit harder and further than curve balls. What this also means is that the bat transfers momentum to the ball. This is why it can be better to use a heavier bat if you can swing it just as fast. The momentum is a product of the mass and velocity, so a heavier bat swung with the same speed as a lighter bat will have more momentum.
But real life is not a closed system, so in the process of hitting a baseball you will lose some momentum. Part of this momentum is lost in the deformation of the ball and to a lesser extent the bat.
A number to determine what this compression does to the ball is called the Coefficient of Restitution (COR). The COR rating for a baseball is 0.555, which means a ball will return 55.5% as fast as it came in. When I used this number with another known my numbers didn’t come out correct and I think this is due to the COR of a bat. I was able to get the numbers to work if I use a COR for ball + bat of .37.
The formula for the balls exit speed will be:
Where:
va is the final velocity of the first object after impact (ball)
vb is the final velocity of the second object after impact (bat)
ua is the initial velocity of the first object before impact (ball)
ub is the initial velocity of the second object before impact (bat)
ma is the mass of the first object (ball)
mb is the mass of the second object (bat)
Cr is the coefficient of restitution
What we can assume is that Alfonso Soriano isn’t swinging the bat as fast due to his aging. He just can’t swing the bat as fast he can when he was younger. Let’s say 6 years ago in 2006 when he had 46 home runs his bat speed was 81 mph*. We know the weight of his bat was 33 oz. So his momentum is 81 mph * 33 oz = 2673 mph*oz (this is a made up unit, but it will work). Let’s say that over the years his bat speed has dropped 3% to 78.55 mph while still swinging the same bat. The new bat speed momentum is 78.55 mph * 33 oz = 2592 mph*oz. This is going to relate to less momentum being transferred to the ball which means the balls aren’t going fly as far. Soriano may still hit a 95 mph fastball** out of the park if he makes contact with it, but an 85 mph curveball may not have enough momentum to make it out of the park.
*I am using 81 mph because I read that Albert Pujols’ bat speed was 86.99 mph with a 31.5 oz bat. This gives us a momentum of 2740 mph * oz. I’m just going to assume Soriano is his prime was a little worse than that. For reference, it is said that Babe Ruth had a 54 oz bat and swung at an estimated 75 mph.
**A baseball has a weight between 5 oz and 5 ¼ oz. This gives an average weight of 5.125. At 95 mph, the ball has a momentum of 486.9 mph*oz. At 85 mph, the ball has a momentum of 435.6 mph*oz.
Sveum has asked Soriano to drop his bat weight down an ounce, from 33 ounces to 32 ounces. This is to increase his bat speed. In our previous example I assumed that Soriano had a bat speed of 81 mph. If he returns to this bat speed with the loss of an ounce, his new momentum will be 81 mph * 32 oz = 2592 mph*oz which is where it was with a larger bat at a slower speed. What it looks like though is that the exit speed of the ball will be more, even if he uses a lighter bat, so it should pay off.
Another thing to consider is that the change in bat speed will effect where the ball will make contact with the bat. He may be late with the swing or quicker with swing so that will effect where the ball goes.
Comments
Nice work, WaLi!
Mercurial OutfielderQuote Reply
The longer LaHair continues this streak, the more afraid I become of a drastic and precipitous regression. That 30% K-rate, outlandish BABiP and Pujols-esque ISO haunt me.
Mercurial OutfielderQuote Reply
Despite all the random numbers, this actually made sense. Kudos to Wali.
Rice CubeQuote Reply
Aisle424Quote Reply
@ Aisle424:
FLAGGED
Mercurial OutfielderQuote Reply
This is why you don’t give Dempster runs.
ACTQuote Reply
Whoops. If you saw the pitch location on Gameday…
I’m surprised that wasn’t a grand slam, that ball had “KILL ME” written all over it.
Rice CubeQuote Reply
Good throw and execution from Campana and the rest of the defense
BerseliusQuote Reply
I guess Dempster decided he didn’t want to wait for the bullpen to fuck it up.
Mercurial OutfielderQuote Reply
ACT wrote:
Mercurial OutfielderQuote Reply
Gameday says Dempster has lost the handle on his 4-seamer.
Mercurial OutfielderQuote Reply
Dempster can’t win.
ACTQuote Reply
BABiP regression happening all in one inning for Dempster.
Mercurial OutfielderQuote Reply
This is pretty good Wali, but I think mine was a little more thorough.
GBTSQuote Reply
LaHair stole a base!
ACTQuote Reply
LaHair is going to win the Triple Crown this year and lead the league in SB%. Superstar.
Mercurial OutfielderQuote Reply
Was that pitch as meaty as it looked on Gameday? Because to me, it looks like Soriano just turned a hanging slider into a fucking WAG.
Mercurial OutfielderQuote Reply
@ Mercurial Outfielder:
Productive out!
ACTQuote Reply
@ ACT:
Two years ago, that’s a productive HR.
Mercurial OutfielderQuote Reply
Ugh, Soto. Terrible AB.
Mercurial OutfielderQuote Reply
I like this IBB…they’re basically forcing Dempster out of the game even though he’s had a bad inning and should be out anyway.
Rice CubeQuote Reply
@ Mercurial Outfielder:
It was a check swing from Soriano, must have thought it was a fb or something
BerseliusQuote Reply
Clown shoes on those sliders
BerseliusQuote Reply
At this time last year, Reed Johnson had an 1.078 OPS.
Mercurial OutfielderQuote Reply
@ Rice Cube:
It was a bad call by the Cards (though I’m less concerned about the bad inning than I am about the fact that Demp has been through the order 3 times already).
ACTQuote Reply
@ Berselius:
Ugh. on Gameday that looked like a pitch he should have airmailed.
Mercurial OutfielderQuote Reply
I wonder if Sveum wanted to save Cardenas for another AB or something. I guess he figured Matheny would switch in a LOOGY.
Rice CubeQuote Reply
Helluva AB from DeJesus.
Mercurial OutfielderQuote Reply
Yadi is having a bad day.
ACTQuote Reply
Starlin bunting?!?!
ACTQuote Reply
Way to go, Dale.
ACTQuote Reply
Only the Cubs
BerseliusQuote Reply
BerseliusQuote Reply
What the Fuck.
WaLi22Quote Reply
dammit
GWQuote Reply
goddamit, if a bunch of idiots on computers in living rooms drinking beers know that a sac bunt is a moronic move, why is it so hard for an MLB manager
Recalcitrant Blogger NateQuote Reply
Against all odds (dying laughing)
BerseliusQuote Reply
ACTQuote Reply
Lighter bat! (dying laughing)
WaLi22Quote Reply
if brett boone and rick sutcliffe know that Lahair is gonna get walked if Castro bunts, why the fuck don’t dale swayme? Time for him to get a chat from Theo the same way he gave to Campana earlier in the game
Recalcitrant Blogger NateQuote Reply
@ Recalcitrant Blogger Nate:
I got nothin’…
Rice CubeQuote Reply
Sveum is a fucking idiot.
Mercurial OutfielderQuote Reply
That Castro sac bunt was the dumbest thing I’ve seen since Neifi’s two outs in the bottom of the ninth bunt.
Mercurial OutfielderQuote Reply
Even Carrie Muskat was scratching her head at Castro bunting
BerseliusQuote Reply
@ Berselius:
I don’t think even Sveum knows why he did that.
Mercurial OutfielderQuote Reply
Hey guys, i was curious what your opinion was on having one of the best hitters on the team bunt with runners on first and second and the fastest guy on the team on first. I was curious if you guys thought that was a good idea and a bad idea.
joshQuote Reply
Soto getting hit is about the best chance he has of getting on base these days. Epic slumpage!
joshQuote Reply
@ josh:
There’s a lot of debate in the scientific community on this one
/Global Warming
BerseliusQuote Reply
(dying laughing)maker
BerseliusQuote Reply
More bunting, gents! Sure do love a gaming bunt!
joshQuote Reply
Sveum pulled a homer!
ACTQuote Reply
So many bunts
BerseliusQuote Reply
This sucks. All this does is justify, in Sveum’s mind, the bunt.
joshQuote Reply
These positive results are only supporting his negative actions
WaLi22Quote Reply
Miracle! 😀
Rice CubeQuote Reply
Hey WaLi, are you able to write a similar piece re: the corked bat and its effect on a batted ball?
Rice CubeQuote Reply
I didn’t even know Campana was allowed to swing. And now I know why it’s so rare to see.
joshQuote Reply
@ Rice Cube: I don’t think it will be a full post but I’ll put together a detailed comment tomorrow
WaLi22Quote Reply
@ josh:
If anything, HE should have bunted to squeeze that run in (dying laughing) (dying laughing) (dying laughing)
Rice CubeQuote Reply
@ Rice Cube:
Exactly, prime bunting situation right there.
joshQuote Reply
Dale Sveum is a unmitigated disaster. I want him gone. Like, yesterday.
Mercurial OutfielderQuote Reply
I like the double punch strikeout maneuver by the umpire. That’s my favorite way to see that called.
joshQuote Reply
Wow, Dolis actually looked pretty good today
BerseliusQuote Reply
Well I’ll just be double god damned. 1-2-3 inning by Dolis.
joshQuote Reply
That inning was just managing FAIL after managing FAIL and it all worked out.
If by “working out” one means “getting two runs when you could have gotten at least double that amount.”
Even when this team succeeds it fails, because they are managed by a fucking myopic moron.
Mercurial OutfielderQuote Reply
2 strikeouts looking for Dolis (the only kind of strikeouts he is capable of getting).
ACTQuote Reply
Sveum’s postgame PC will be like watching a puppy who’s caught its tail and thinks it’s an achievement.
Mercurial OutfielderQuote Reply
@ ACT:
The umpire seemed to be calling any borderline pitch tonight. Which is fine. Works well for guys like Dolis who hang out right at the bottom of the zone.
joshQuote Reply
Man, Dolis sat ’em down.
Mercurial OutfielderQuote Reply
@ josh:
He was probably anxious to get back to the umpires room so they could all have a good laugh about the festival of bad they just saw.
Mercurial OutfielderQuote Reply
@ Mercurial Outfielder:
Yeah, the stubborn refusal to let his hitters hit is frustrating. We might have walked out of Milwaukee with at least one win if he just lets anyone not named Tony Campana swing away. At least this was a win. I mean, we’re not going to win the World Series, but I still like to see them beat the damn cards.
joshQuote Reply
Cubs ————> 4th place
Cubs ————-> Still in last place
BerseliusQuote Reply
I do like the defensive shifts Sveum has been employing and there does seem to be some improved defense but the AGGRESSIVE BASERUNNING and the buntfest need to be cut down. I guess the front office is still secretly hoping for a top 5 pick which is why they haven’t had the Billy Beane talk with Sveum yet.
Rice CubeQuote Reply
@ josh:
I like a win any time. But the sheer amount of mental mistakes in the 8th and 9th innings, taken in concert with his auto-bunt and AGGRESSIVE BASERUNNING strategies, makes me think that once you get ol’ Dale away from his precious spray charts, he’s just a stick-in-the-mud baseball guy like most managers.
Mercurial OutfielderQuote Reply
@ Rice Cube:
The shifts are nice, but any moron who can read a spray chart can set that up. He was fucking up basic shit for two straight innings. That was like watching Mike Martz try to manage the clock.
Mercurial OutfielderQuote Reply
This is why I sorta hate the draft going in reverse order of winning percentage: it creates a perverse incentive for losing (or at least not putting much effort into winning). I like it when they win (even when they suck), but I also want the rebuilding project to work. I hate being deeply torn like this (as I’m sure the FO is also torn).
ACTQuote Reply
@ Mercurial Outfielder:
No, I agree. I’m glad the Cards found it in their heart to make some shitty plays and the Cubs thereby found some way to win. I’m not happy with what I’ve seen from Sveum at all. I didn’t really get it at the time of the signing, and I don’t get it now.
joshQuote Reply
Wait, Nate McLouth is a Pirate again? That’s kind of funny.
joshQuote Reply
WaLi, I know I said this in an email, but should also be said here. This is a fantastic article and thanks a lot for writing it.
mb21Quote Reply
@ ACT:
Agreed. I hate having to wash the taste of shitty baseball and stupid managing out of my mouth with elixir of draft position.
Mercurial OutfielderQuote Reply
@ Mercurial Outfielder:
I heard this draft class was kind of meh so it might not be a bad idea to win as many games as possible even if they don’t make the playoffs and feed the Hope Monster a bit.
Rice CubeQuote Reply
Aisle424Quote Reply
Why do you guys hate the baserunning. We’ve actually been a very good team running the bases. Sure, we’ve made more outs doing it too, but overall it’s been positive and we’ve been mostly good doing it.
Doug etetectdsaagaQuote Reply
@ Doug etetectdsaaga:
I know the baserunning numbers are positive overall but the number of facepalms we’ve had this season make me think that the metric is broken (dying laughing)
Rice CubeQuote Reply
@ Doug etetectdsaaga:
They lead the league in CS and they’re 14th (out of 16 NL teams) in total bases, and they have contributed 2 base runs. The only person who thinks this team is anything but mediocre, at best, on the bases is Dale Sveum.
Mercurial OutfielderQuote Reply
One interesting stat that I enjoyed tonight…
In six plate appearances, David DeJesus saw 39 pitches. He did strike out three times, but they had to work for them, dammit.
Rice CubeQuote Reply
@ Rice Cube:
Yeah, he had a couple great ABs tonight.
Mercurial OutfielderQuote Reply
@ Aisle424:
That is outstanding.
Mercurial OutfielderQuote Reply
Jed and Theo need to give Swayme a limit or quota of bunts per game that he can’t go over. I’ll suggest 0, but I’m guessing 1-2 is more realistic.
Recalcitrant Blogger NateQuote Reply
@ Doug etetectdsaaga:
I’m not as ashamed of the baserunning as I feared I might be. But the stubborn insistence on bunting with a runner on first no matter what is annoying.
joshQuote Reply
@ Mercurial Outfielder:
I think that’s what he used to be known for, back when he was a Royal or whatever he was.
joshQuote Reply
There are very few players who I think are too shitty of people to be allowed to play their respective sport. Ron Artest (I refuse to call him meta world peace) is one of them.
Recalcitrant Blogger NateQuote Reply
@ josh:
He was always a good hitter with the Royals, but he’s gotten into some bad habits the last 2-3 seasons. Couple that with age-based decline, and you see games like tonight less and less often. It was good to see him look like his old self at the plate, though.
Mercurial OutfielderQuote Reply
@ Recalcitrant Blogger Nate:
Yes. And Joey Barton.
Mercurial OutfielderQuote Reply
@ Recalcitrant Blogger Nate:
But he supports world peace!
joshQuote Reply
OMFG, even Sullivan called this fucking stooge out, and fucking Sveum sutkc by his choice. Fucking dumbass cracker:
Mercurial OutfielderQuote Reply
http://mickopedia.org/mickify.py?topic=chicago+cubs
Suburban kidQuote Reply
Hey guys, thanks for all the kind words for the article. I hope it made sense as I put it together pretty quick. I also had this table I forgot to attach that shows the ball exit speed based on the COR equation above.
Weight (oz) Speed (mph) Momentum Exit Speed 95 mph Ball Exit Speed 85 mph
2006 Pujols 31.50 86.99 2740.19 119.44 117.65
2006 Soriano 33.00 81.00 2673.00 113.71 111.85
2012 Soriano 33.00 78.55 2592.00 110.80 108.94
2012 Soriano 32.00 81.00 2592.00 112.83 111.03
Baseball 5.13 -95.00 -486.88
Baseball 5.13 -85.00 -435.63
Also I forgot to mention that this is simplified quite a bit. It doesn’t take into account the spin of the ball or where on the bat the ball makes contact or when in the swing the ball makes contact to determine whether the ball is hit to left field or right field. This is just one dimensional momentum.
WaLiQuote Reply
Rice Cube wrote:
The advantages of having a corked bat would depend on how much faster you can swing it. Let’s say you have a 31.5 oz bat and you cork it. By corking it you can reduce the weight 1.5 oz. So if you can swing it fast enough to make up for that 1.5 oz in loss of mass then you come out to an advantage. Also if you can swing it faster, you can wait on the ball more so there is an advantage there. This was a problem I had with the calculations above though. I wasn’t sure how much faster Soriano’s bat would get by reducing the weight an ounce.
Weight //Speed //Momentum //Exit Speed 95 mph Pitch//Exit Speed 85 mph pitch
Corked 31.50 80.00 2520.00 111.20 109.42
Uncorked 30.00 84.00 2520.00 114.45 112.75
WaLiQuote Reply
http://www.hardballtimes.com/main/article/bryan-lahair-is-cubs-silver-lining-so-far/
MishQuote Reply
@ WaLi:
I got the part where the bat would be lighter but since the bat is now sort of hollow instead of one solid chunk of wood I thought that would change the way the ball would bounce off the bat due to the difference in material or energy transfer or whatever. That was probably what the MythBusters guys were trying to do (not very well).
Rice CubeQuote Reply
@ Rice Cube:
If you fill it with the proper cork, the COR is surprisingling similar to a solid bat.
This means it should perform the same as far as energy transfer.
However, I read that with Sosa’s bat he didn’t cork his bat the traditional way (drilling out the center from one end and filling with cork). He had his bat corked in the taper closer to the handle. This allowed the moment of inertia to be greater at the end of the bat where you would want it (think swinging a sledge hammer compared to a bat) so he had some advantage since it wasn’t a uniform loss of weight. This disadvantage with this is that the bat is weaker around the tapered area, so when he got jammed with a pitch inside (as he did) the bat was more likely to break. This actually lends credence to his explanation of having a Batting Practice bat, as during BP the pitcher isn’t going to jam you.
WaLiQuote Reply
WaLi wrote:
Interesting. I’ve never cared one way or the other, but it would seem silly to use a bat corked in the area his bat was corked in seeing as it’s much more likely to shatter.
mb21Quote Reply
Then again, athletes aren’t known for being intelligent.
mb21Quote Reply
@ mb21:
This is true (dying laughing) If it gave him more of an advantage maybe he was willing to take the risk.
WaLiQuote Reply
I think we’d be shocked if we knew how prevalent bat alterations were. Hell, Bob Brenly said once that the Giants kept a cabinetmaker on staff when he played there.
Mercurial OutfielderQuote Reply
Huge tits anal physics
GBTSQuote Reply
Just trying to draw the right crowd in. (dying laughing)
GBTSQuote Reply
@ WaLi:
So I guess in Sosa’s case he’d want all his force focused in the sweet spot (end of the bat or thereabouts) and that would more efficiently transfer the force to the baseball to make it go further. Interesting.
I’d do a Star Wars segue since we’re talking about the force here, but this physics stuff is very cool.
Rice CubeQuote Reply
I’m going to the I-Cubs game Saturday night, so expect Rizzo and B-Jax to be called up on Friday.
GBTSQuote Reply
new shit: http://obstructedview.net/commentary-and-analysis/whats-wrong-with-carlos-marmol.html
mb21Quote Reply