## 10.20.2008

### Is all this really necessary?

"Here are Excel formulas using the pitch/fx fields, which are in [brackets]

Left Strike location:

=IF([px]<0, 10 + 12*[px]+MAX(0,([vx0]*(85/176/[end_speed])+0.5*[ax]*((85/176/[end_speed])^2+2*(85/176/[end_speed])*((-SQRT([vy0]^2-2*[ay]*([y0]-17/12))-[vy0])/[ay])))*12),"")

Right Strike Location:

=IF([px]>0, 10 - 12*[px]+MIN(0,([vx0]*(85/176/[end_speed])+0.5*[ax]*((85/176/[end_speed])^2+2*(85/176/[end_speed])*((-SQRT([vy0]^2-2*[ay]*([y0]-17/12))-[vy0])/[ay])))*12),"")

These formulas yields a null value if the pitch is on the other side of the strike zone, and give you a positive number if the pitch was a strike and a negative number if it was a ball, according to the rulebook rather than any de facto average strike zone. The formula after the MAX or MIN calculates the additional horizontal movement while the pitch passes over the strike zone, based on the horizontal velocity and acceleration parameters (the part that looks like a quadratic equation is figuring out the average velocity and hence time to home plate; it turns out that this is only infinitesimally more accurate than using the average of [start_speed] and [end_speed]).

Low Strike Location:

=([pz]-[sz_bot])*12-1.5

According to the rules, the - 1.5 should be +1.5. Saying -1.5 is saying that the umps in practice require all of the ball rather than any part of the ball to be above the bottom of the kneecaps. After looking at the data, it seems just as likely that they're requiring any part of the ball to above the top of the kneecaps; if you went with that, you would use -2 instead of -1.5. There is no need for an extra clause because the pitch always drops further as it passes over the plate.

Approximate High Strike Location:

=([sz_top]-[pz])*12+1.5+192*((82.5/([start_speed]+[end_speed])+((17-MIN(8.5,12*ABS(ax)))/12)/([end_speed]*22/15))^2-((82.5/([start_speed]+[end_speed]))^2))-(17-MIN(8.5,12*ABS([ax])))/600*[pfx_z]" 