Tuesday, June 7, 2011

Discussions: Ending the Game with Science

Ending the game with a called third strike is always exciting, especially if it's a called third strike to clinch the pennant, as called by Tom Hallion, who was credited with the best third strike mechanic in baseball. It can also be a little more common. Anonymous wrote today:
Michael Cuddyer had a heated argument over a close strike 3 call to end the Indians-Twins game with Adrian Johnson. He may have bumped him. Was not sure where to post this.
This is a reference to the 2-2 pitch which ended the Twins-Indians game, in which Cuddyer was called out on strikes on a fastball from Indians pitcher Chris Perez by HP Umpire Adrian Johnson. The call clinched the game for the Indians as a one run victory, and Cuddyer vehemently argued the call with Johnson (of course, to no avail).

The play is an exciting way to end the game, but most importantly, was the call right? With regard for the UEFL Rulesbook regarding strike zone Quality of Correctness, we first consider the Pitch f/x chart, courtesy of Brooks Baseball.

Pitch f/x courtesy Brooks Baseball

Pitch #5 looks outside and therefore a ball, right? Not quite. As shown in Ejections: Ron Kulpa (1, 2), looks can be deceiving. In responding to an overturned challenge of Quality of Correctness ("Incorrect" ==>"Correct"), I wrote
In using pitch f/x to determine QoC, parameters to be judged include horizontal location, vertical location (coordinates of pitch), normalized zone variability or quotient (amount of vertical "stretch" or "shrink" applied to vertical parameters so that the strike zone ranges from 1.5 to 3.5 vertical feet, movement of pitch (known as pfx, and specifically pfx_x and pfx_z), and type of pitch. In regards to pitches which only depend on the horizontal constraints of the strike zone (as is the case here), we specifically consider horizontal location, px. In this plate appearance (Nolasco against Kemp), we see pitch (1) with a horizontal location of 0.895 ft; pitch (2) has a location of -0.946 ft. Considering the working strike zone is 22.880 inches (17" plate + 2*2.944")*, we see that 11.440 inches correspond to 0.953 feet on either side of the plate. Since both 0.895 ft and -0.946 ft have an absolute value less than the working strike zone value of 0.953 feet, we must conclude that the call was correct.
*To calculate the working diameter of the strike zone, we use the formula of plate diameter + 2 times ball diameter (one for each side of the plate). The plate is 17" in diameter as defined by OBRule 1.05. The ball is a sphere with a maximum circumference of 9.25 inches as defined by OBRule 1.09. Circumference = pi * diameter; therefore, diameter = circumference / pi; diameter = 9.25 / 3.14159... = 2.944". Adding these figures together yields a working strike zone of 22.880 inches.

Therefore, we can say that definitively, any "px" value less than 0.953 feet from the center of home plate shall be correctly ruled a strike, making any px between -.953 and +.953 a strike... Back to Johnson's strike call to end the game. Johnson's called third strike had a px value of 0.918. Considering the science behind pitch f/x, it is a numerical fact that Johnson made the correct call.


Anonymous said...

Johnson has always had a bad strike zone,IMO,but given your explanation of the Kulpa ejection,I would agree with your position.

Is it me or does it seem like Johnson has a chip on his shoulder and an attitude on the field?

Mike said...

Is there a reason why Brook's box on the horizontal bounds don't match up with home plate?

Also, did anybody see this:


I had no idea what happened here. Is that even a proper mechanic?

Anonymous said...

I'm not sure I agree with anonymous. I think Johnson has improved tremendously since his hiring. This is clearly a strike watching the replay in real time and I just think Johnson is a confident Umpire. I don't really think he has an attitude problem he jsut will argue back if he is argued with. Can we possibly see a game plot of Johnson to see what his accuracy was during this game?

Lindsay said...

As called by Adrian Johnson, Normalized Strikezone Plot 06/07/2011 MIN-CLE.

87 Called Balls (4 Incorrect) => 95.4% Accuracy
46 Called Strikes (1 Incorrect, 3 Inconclusive) => (91.3, 97.8) => 94.6% Accuracy

Overall Performance: 95.2% Accuracy
Recall, the League Average is 94-95%.

Bill said...

Bad Bad job by Cuddyer here...he gets paid an awful lot of money to hit that pitch, or at least get a piece of it and foul it off. WAY too close to be looking at in that sitch.

Johnson should have given him a post game EJ to document the bump.

Jon Terry said...

I like the call. Two outs, two strikes, game on the line, and Cuddyer is staring at the close ones?

Also, I don't see any chip there. Johnson held his temper and walked away.

Anonymous said...

I agree with the strike, by definition it is a strike. As mentioned before, Cuddyer should be defending the zone on anything that close, especially on a 2-2 count with the game on his shoulders.

OTOH, Johnson did slightly expand his zone. I feel as part of his duty to keep the zone consistent. For this one to be one of his 2 widest strikes called all day, one can see Cuddyer's distaste.

In other words, I can see both sides. Judgment call goes to Johnson.

Anonymous said...

@ Mike- that was a tough one. Was that Barksdale? If so he's gotta kick someone out there! ;)

Jeremy Dircks said...


It was Dan Iassogna there on that call.

Cricket said...


Ended the game tonight. How do I get the pitch f/x data for this one?

Lindsay said...

Pitch f/x data is provided to us courtesy Brooks Baseball and is available on that website.

This is the pitch f/x chart for Linebrink-Sanchez. Pitch #5 (called strike three) appears off the plate, and has a corresponding px value of 1.008. Had we seen an ejection, original Quality of Correctness would be incorrect; and a challenge would result in upholding the original QOC.

Accounting for all variables, including margin of error, we came up with the following numerical range for px that is now UEFL precedent. As specified in the Ron Kulpa (1, 2) thread:

The following numerical range shall be established as UEFL precedent and incorporated into the UEFL Rulesbook

Abs 0.000-0.900 = Strike
Abs 0.901-1.000 = Borderline
Abs 1.000+ = Ball

Cricket said...

Final question, then: where do I find the absolute value number? I looked on the corresponding page and cannot find it? I really appreciate the response!

Lindsay said...

You find px, which is the horizontal location relative to the absolute center of the graph. If px is a negative number, just remove the minus sign.

Post a Comment