Why Steve Smith should keep being aggressive

When a runner is tagged out at home to make the first out
in an inning, everyone blames the third base coach.
But he might have made the right decision, and just
lost the bet.
Photo credit: Keith Allison

In the aftermath of today's loss to the Rays, Reds third base coach Steve Smith beat himself up over his decision to send Joey Votto home with no outs.  Votto was tagged out, and ultimately the team lost 1-0.  His quote:

"I can't get a guy thrown out with no outs, and I understand that," Smith said. "I tried to be too aggressive at the wrong time. I got burned. ... I've got to play the game. I got aggressive. If the ball bounces one way or the other, then everybody doesn't know about it. It's no outs. I always assume a guy makes a great throw, and he did. I take full credit for that."

I think Steve Smith isn't looking at this the right way.  The fact that Votto was thrown out does NOT mean that he made the wrong decision in that spot.  He may have just lost on what was a good bet.

A few years ago, Pizza Cutter wrote an article titled "Why All Third-Base Coaches Should Be Fired."  In it, he noted that, based on success rates, third-base coaches seem to be far too conservative.  He noted that in sacrifice fly situations, runners that attempted to run home were successful 96% of the time.  That's despite the enormous gains that a team receives when a runner scores.

Let's try to repeat Pizza's math for the situation with Votto.  Pizza didn't explain his math, but I think the following is right.  We have three possible outcomes:

1. What happened: Joey goes for it, gets thrown out.  That leaves the Reds with a runner on second (Phillips) and one out.  The average run expectancy in that case is 0.637 runs
2. Joey goes for it, but scores!  That leads to 1 run (Votto's), plus Phillips went on the throw and thus is now at second base with no outs.  That gives us an extra run expectancy of 1.0499, for a total of 2.0499 runs.
3. Joey holds at third on the single, giving the Reds 1st & 3rd with no one out.  Average run expectancy there is 1.6423 runs.

So, we want to find the break-even percentage of success at which point Votto should be sent.  That percentage, x, would make the average value of sending the runner equivalent to having him stay at third.  Therefore, any success rate over that percentage means you should send him, even if there is some chance that he is thrown out.  (warning, a little algebra ahead...you can skip if you'd prefer to do so)

I solved this equation for x: 

Runs_Hold = Runs_Success*x + Runs_Failure*(1-x) 

Which would be:
1.6423 = 2.0499*x + .637*(1-x) 

So:
1.6423 = 2.0499*x + 0.637 - 0.637x 

...simplying...
1.0053 = 1.4129x
x = 0.71

What this means is that if Steve Smith is more than 71% certain--let's say 75%--that Votto will score on that play, he should send him.  Even though there were no outs in the inning.  Yes, one out of four times, he'll get burned--just as he did tonight.  But he should be playing the percentages.  The Reds stand to gain more over the long haul by sending runners in that situation whenever the coach thinks they will succeed three out of four times.  The one in four chance might be that "great throw" that Smith cites in his statement.

It's probably worth mentioning that this play comes only days after Billy Hamilton's amazing feat of scoring from third on a pop fly barely past the second baseman's position.  Smith presumably was in on that, and looked like a genius.  This time, he got burned.  But I hope he continues to be aggressive on sending runners home in the future.