## FanPost Friday: The Mariners Home Run Problem is by Design

Lindsey Wasson-USA TODAY Sports

Hello and welcome back to FanPost Friday! This week we've got an absolutely scorching guest post from poster flygutifly (excellent username) that I'm sharing in full because fgf here has a VERY INTERESTING theory regarding the relationship of drag, backspin, and the dinger-prone Mariners rotation and bullpen. As fgf states, this is an unproven theory at this point. But, if it can be proven eventually, the ramifications could be pretty massive. Enjoy! - Eric

Theory: the redesigned baseball has harmed Mariners pitchers in particular due to the Mariners’ prototypical pitch type, location, and design. This has led to the Mariners leading the majors in home runs allowed (at time of writing). I believe the main culprit in this widespread bout of dingeritis is the increased drag on the new baseball.

(Content Warning: this post will include some technical discussion of fluid dynamics and some math, reader beware)

The Fangraphs article I linked below as (1), discusses how the ball in 2022 is seeing a lower than expected carry when compared to the ball over the last couple seasons. This finding might seem surprising if for some reason you have only been tuning in to the Mariners bullpen this year (which, yuck) and decidedly less surprising if you have also watched Jesse Winker. This leads to the main point of this piece: for flying baseballs, sometimes an increased coefficient of drag is a bad thing and sometimes it’s a good thing.

First, to help visualize drag force:

If you can picture a baseball in a wind tunnel with a slipstream going around it, the drag force is applied in the same direction that wind is moving (opposite the flight direction of the ball).

On the surface, the results of the Fangraphs post are unsurprising. The equation for drag coefficient (from Wikipedia) is

Now, rearranging the above equation a bit:

For this conversation, imagine two exactly similar hits in the same ballpark at the same instant, but with two slightly different balls. So basically, we are going to assume the balls exhibit a very similar area, are moving at the same velocity through the air, and that that air is at the same density. That leaves the only two changing variables as drag force and drag coefficient, where a seemingly clear relationship exists: higher drag coefficient results in more drag force. This increased drag force applies a stronger negative acceleration (F= ma) to the ball, slowing it down more quickly and reducing its overall carry distance. If spin didn’t exist, this would blissfully be the end of the conversation.

However, in fluid dynamics (and life), things are never that simple. Where this gets more interesting (read, complicated) was foreshadowed in the picture above: Fm or as it is more commonly known, the Magnus Effect. This is an additional force applied to a spinning projectile in flight which can have a major effect. This effect is so prominent in baseball, that one physics study of theoretical hit balls found that an optimally hit curveball will actually travel further than an optimally hit fastball due to the added backspin when hitting a curveball. (These results have valid criticism aimed at them which mostly boils down to which experimental data you rely on for calculating Magnus Force. I have linked the research paper below, so you can read for yourself if you are interested.) Now to be clear, this is just modeling: actually hitting the ball over the fence is another story.

The Magnus Effect is modeled as:

Where everything in the equation is the same as above and the new variable, cl is the lift coefficient. So in the same hypothetical as above, more lift coefficient means more magnus force. Lift coefficient is considered to vary closely with spin at low speeds (and less closely with another variable called an object’s Reynold’s number), but at high speeds this gets complicated very quickly. In the range we care about for baseball home runs, where velocity is over 90 mph and spin is on the order of 2000-4000 rpm, lift coefficient and drag coefficient are not directly related to each other. However, both are related to inherent properties of the baseball, which show up in the object’s Reynold’s Number and that relationship can be used to at least show a general direction of change. If we assume MLB changed some property of the ball which affected its drag coefficient (assumed generally from what I have seen to be a change in seam height), there is a high likelihood that it also affected the baseball’s Reynold’s Number. This is due to an effect known as the "drag crisis region".

See that grey box? That’s the drag crisis region. For small changes in Re (Reynold’s Number), there can be dramatic changes in drag coefficient and vice versa. For context, a baseball at 90 mph at sea level has a Re = 1.85 105. Referencing the above chart, we are smack dab in the middle of the region where rough spheres will be dramatically affected by most property changes. So assuming that MLB changed something about the ball which affected its coefficient of drag, there was likely an (outsized) impact on Reynold’s number, which is then related to the coefficient of lift. This change in lift coefficient could have a significant impact on the ball’s susceptibility to Magnus Effects and make carry more dependent on backspin.

The change in magnitude of this force could more heavily impact the travel distance of a hit ball based on the amount of spin. If my theory is correct, pitchers whose repertoires induce lots of backspin will be particularly hurt by this development. On the flip side, hitters who have flat swing planes and generate less backspin will have their batted ball distance drop because of the increased drag. Unfortunately, spin rate and spin axis data for batted balls is not publicly available. Additionally, teams have a trove of swing plane data that would go a long way in answering some of these suppositions. If such data existed for public consumption, it would be interesting to see if higher backspin hitters are producing better results than in the past.

Now to link this back to the Mariners, what I am going to attempt to prove is that the way our pitchers pitch is naturally going to produce hits with more backspin and that the impacts of backspin have become more pronounced due to the changed coefficient of drag on the baseball. To paint with broad strokes: the Mariners have the highest average launch angle allowed in the league, they are 4th in flyball rate, and third in Under %. The process is justifiable, as pop outs are one of the best possible outcomes for a pitcher. However, with the new spin-susceptible baseball, the near misses are going to produce hard hits with more backspin.

We also know the Mariners have sought out at least one pitcher for their vertical approach angle (VAA): Paul Sewald. As a short explainer if you are not familiar with VAA, it is how much a fastball actually drops compared to how much it should drop with no additional forces. Paul Sewald is particularly good at this, which is why so many big league hitters struggle to make contact with his 94 mph gas right down the heart of the plate (I still can’t believe it every time I watch). This coupled with a well tunneled slider has been a recipe for consistent success for him. He’s not the only one. The Mariners coach their guys to throw their fastballs up in the zone, which again is good process! It is really hard to hit high fastballs (if you aren’t Byron Buxton I guess). However, when these fastballs miss low and bleed down in to the zone, they are getting crushed. Here is a graphic of home runs by zone by pitcher–notice the general tendency for middle to upper zones, with Robbie Ray being an outlier.

So essentially my theory–that we don’t have the data to prove–is that the Mariners are trying to get teams to swing under their pitches, particularly their fastballs up in the zone. When these pitches run a little low or hitters actually do catch up to it, the resulting contact has more backspin because of the ball being up in the zone and "flat". This increased backspin is particularly important to getting the new ball out of the yard, and this development has been especially bad for the Mariners pitch design. This theory also might explain why certain hitters are struggling with the new ball more than other hitters. It is possible that Jesse Winker’s swing doesn’t naturally create a lot of backspin. Maybe Taylor Ward’s swing does. Again, it would be really interesting to have access to that batted ball spin data.

All that being said, I think it is possible the high rate of home runs we are giving up is not just a fluke or bad luck. The baseball operates in a very interesting region of fluid dynamics and so seemingly small changes can have outsized impact on the way that baseballs fly through the air. In this particular iteration, I believe the change they made affected the lift coefficient which has made the ball more susceptible to having its flight path altered by the Magnus Effect. This change may have had an outsized effect on some of our pitchers because of the way the Mariners design pitches and coach the guys. Hopefully, the overall good process trends back toward good results and this home run problem isn’t here to stay.

Sources for further reading:

1. Fangraphs Blog Post investigating effect of drag on carry: https://blogs.fangraphs.com/home-runs-and-drag-an-early-look-at-the-2022-season/

2. General discussion of Magnus Effect on baseballs: https://diamondkinetics.com/the-magnus-effect-and-baseball/

3. Research on calculating baseball lift coefficient at actual game speed (pdf warning): http://baseball.physics.illinois.edu/AJPFeb08.pdf

4. Explainer on baseballs living in the "drag crisis region": https://www.baseballaero.com/2019/05/03/baseball-drag-crisis/#:~:text=Engineers%20and%20Physicists%20talk%20funny,in%20drag%20coefficient%20with%20speed

5. Relationship between coefficient of lift and Reynold’s number for a rough sphere https://www.researchgate.net/figure/The-lift-coefficient-as-a-function-of-the-Reynolds-number-for-a-ball-with-90_fig8_228655071