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# Refusing the Walk for an Extra Hack

Jordany Valdespin and the umpires intentionally or unintentionally ignored ball 4. How did that affect Valdespin's chances of getting doing any better on the next pitch?

Anyone watching the Mets-Marlins game on Monday night might have seen the Valdespin at bat against Jose Fernandez and were either amused or shocked.

On a 3-2 count, Valdespin took ball four. But when the ump failed to realize that a walk should have been rewarded, Valdespin hacked away, fouling off one pitch then popping up the last. However, it was difficult to tell if Valdespin was ignorant to the fact that it was ball four or if he really just wanted to stay up there and hit.

As you can see, Valdespin took 4 official balls but managed to pop up:

Here is the entire at bat, pitch by pitch, in GIF format:

Here is the infamous eighth pitch and ball 4:

So what was Valdespin's thinking if he had the intention to ignore the error and take another pitch? Did Valdespin believe he had a better chance on doing more on the next pitch rather than taking his deserved walk in the first place? If so, was he warranted to do so because he was likely to do better on the next pitch?

What were the actual chances that he would achieve something better than a walk on the ninth pitch?

Let's find out:

Let's check out the frequency of some simple counting stats on the 8th pitch and the 9th pitch since 2002:

Pitch count = 8 1B 2B 3B HR BB IBB HBP ROE FC Catcher INT Out K SUM
3393 1154 150 732 7184 3 140 179 48 2 10387 7407 30779

Pitch count = 8 1B 2B 3B HR BB IBB HBP ROE FC Catcher INT Out K
PROB 11% 4% <1% 2% 23% <1% <1% 1% <1% <1% 34% 24%

Pitch count = 9 1B 2B 3B HR BB IBB HBP ROE FC Catcher INT Out K SUM
1273 452 50 318 2842 2 46 68 22 0 3892 2689 11654

Pitch count = 9 1B 2B 3B HR BB IBB HBP ROE FC Catcher INT Out K
PROB 11% 4% <1% 3% 24% <1% <1% <1% <1% N/A 33% 23%

While there have been much fewer 9 pitch PA in recent years than 8 pitch ones, the probabilities remain rather constant between the one pitch discrepancy. The probability of Jordany's outcome on the ninth pitch being more valuable than a walk in expected run value terms would have to be a single, a double, a triple, a homerun, a hit by pitch, a fielder's choice and a reach base on error.

The combined probability of these events being mutually exclusive -- meaning one or the other or simply the probability of a single and a double is zero, because they both can't occur at once -- would be around 19%.

So, Valdespin had a better chance of walking than actually doing anything better on the next pitch.

Sure enough he popped up.

Other than counting statistics, how much better do hitters in this very specific situation improve in rate stats? Below is the AVG, OBP, SLG, and wOBA for a PA with a pitch count totaling 8 and 9:

Pitch count = 8 AVG OBP SLG wOBA
0.234 0.418 0.404 0.368

Pitch count = 9 AVG OBP SLG wOBA
0.239 0.431 0.412 0.382

dAVG dOBP dSLG dwOBA
0.006 0.013 0.008 0.014

The changes here are somewhat significant. A 14 point jump in wOBA is substantial and could bring upwards of a 11 more runs per season given 750 PA. So the changes in the realm of wOBA are nothing to scoff at.

James Gentile did a piece concerning a similar topic, back in October of 2012.

James goes on to introduce sample bias as when pitch counts get higher, the pitchers who are throwing are of less quality and the batters who are facing them are of greater quality.

Conceptually it makes sense. It takes a pretty bad pitcher to go 13 or 14 pitches deep to a hitter. But it takes a great hitter with a wonderful eye to go deep into the count as well.

While these biases are present with rare situations like we explored today, it is important to remember that Jordany took a gamble by staying at the plate (that is if he was familiar with the error). When you know you could have reached 1st base via a walk with a 100% probability like Valdespin had, if he had pointed out the mistake, it is probably a great idea to take the base rewarded to you.

In the end, Valdespin was playing with 19% odds and overcoming 81% of probability proved too much. The moral of the story is if a player is rewarded with an base they would be smart to not refuse it.

Thanks to Matt "GIF Master" Hunter and James Gentile.

Max Weinstein can be contacted on twitter .

All stats courtesy of Retrosheet and Fangraphs. Thanks to Brooks Baseball for the PITCHf/x data.