THE BOOK--Playing The Percentages In Baseball

Shouldn’t the math for Part 1 look like this?

Add it up:
0 to 4 runs: 0 wins
5 runs: .12 x .30 = .036 wins
6 runs: .09 x .70 = .063 wins
7+ runs: .25 wins

Total: .349 wins per game

And for Part 2 like this?

Add it up:
0 to 3 runs: 0 wins
4 runs: .13 x .25 = .0325 wins
5 runs: .12 x .75 = .090 wins
6+ runs: .34 wins

Total: .4625 wins per game

It doesn’t make much difference with Robot 2, but Robot is enough better you might be able to find a spot for him.

NM, your new numbers are correct for Robot 1.  Ignore mine.

I make him my closer, and bring him in with one out in the 8th.  I think I’ll call him Mo.

I like Rally’s idea of using him as a reliever, although you don’t have to restrict him to closing duties. 

You cleverly arrange for his home runs to occur in games where they don’t matter, either because your lead is bigger than the number of home runs he will allow in the remaining innings of the game or because you are behind late in the game and want to get his ever-so-predictable home run out of the way.

Mike, thanks I also corrected Part 2.

Rally: note that I said he cycles through, so that the next game, he picks up where he left off in the cycle.  There is no reset.

I would pay an extra $2 million a year if the pitcher combined the classic sensibilities of a 1950s robot with the dynamic flair of a 1970s street pimp.

Isn’t there enough disagreement out there that you should consider referring to “replacement-level theory” as “Tango’s replacement-level theory.?”

Anon/7: no, there is not enough disagreement out there for me to need to qualify it like that.

I know that this is not the point of your thought exercise, but these calculations do not factor in the fact that of the 5 strikeouts and one home run, none of these balls are in play.  You could potentially field a lineup of 8 DH/1B types + a catcher.  This would lead to a tangible increase in runs per game, and thus winning percentage.

Adam, what would you do on the other four days?
vr, Xei

Adam/9, I mentioned that in the other thread regarding BP’s hypothetical robo-pitcher.  I assumed here that Tango was excluding that possibility by specifying the run distribution.

But I couldn’t help but thinking with this one that if your pitcher is guaranteed to go 7 innings and give up exactly 4 runs every time out, why wouldn’t you fill the lineup behind him with a bunch of sluggers who can’t field?  If you don’t have to care about defense, even just once every fifth day, couldn’t you load your roster with good-hit, no-field players?

Your bullpen probably doesn’t need to be as deep with robo-pitcher in the rotation as otherwise, so maybe you could get away with 11 pitchers and have a couple extra Jason Giambi types on the bench and maybe even an Alberto Callaspo or Esteban German who can pitch hit and play back-up infielder on non-robo-pitcher days.

Interesting to me that a team averaging 4.7 runs/G scores 4 runs or less 54% of the time.  I can see how the numbers work, since your bell curve extends a lot further right from the mean than left, but I hadn’t considered that before.

Tough crowd!

Presuming you are going to your set 25-man roster, and since having the robot pitcher opens up 2 other roster spots, you can therefore have 2 all-hit no-field players take those spots.

So, yes, you can generate more value that way.

For a hypothetical team that scores ~7 r/g with a typical distribution around the mean, I think the robot pitcher would be more valuable than real pitchers will lower RAs.  The team’s winning percentage would be enhanced by avoiding those pesky 10-9 losses that would occasionally come up.  But this team probably isn’t realistic.

For the 2nd pitcher (4.5 runs/game), using the 2009 yankees offense empirical distribution of runs scored, the team would win 58% of the time-- worse than their winning percentage, but perhaps better than their worst starters.

Apparently there are two robots involved: one who pitches, and the other who is the manager and who lets the first robot throw to an opposing hitter late in a tie game with a HR “due”. 

I wonder how it looks if you let the manager pull the robot, instead of forcing him to throw a complete game (loss)…

It seems to me this bit of game theory is located precisely in the area of the “sweet spot” that is so important…

Would Robo2 be more valuable only giving up 1 run in his first four innings?  The, with a 2-run lead in the eighth, he would close out that game, and could be saved for any such occasion as it comes up.  By tinkering with its usage, one could concievably make Robo2 a much more valuable pitcher.  You just couldn’t ever bring it into a late, tied game, knowing that dinger was coming and with no guarantee that your team would score in those turns at bat.

And one more thing: any game where you get a lead that is more than the “rate” of runs allowed for the robot, you could put it in and guarantee a win.  No more coughing up big leads (or even small ones late, per Rally #3.) Is that figured in, or can this robot only pitch every 5th day?

And while we’re on the subject of performance vs. value, what does robot do to your attendance?  Do people want to see a foregone conclusion half or more of the time, where the game is already decided before they get back to their seat with their first four beers?  Or do the “guaranteed” home runs make up for it?  Maybe if the other team built their lineup so Mark Reynolds, Adam Dunn or Prince Fielder were always hitting 6th, fans might come to the park for two guaranteed long bombs by those guys.  There would probably be fights in the opposing clubhouse over who got to hit 6th (2 HR’s), 3rd (1 HR) or 9th (1 HR).  Would the pitcher still have to hit 9th, or would they rotate everyone through it?  Etc. etc…

"Rally: note that I said he cycles through, so that the next game, he picks up where he left off in the cycle.  There is no reset.”

I thought so.  In that case, he comes into the next game where I have a 2 run lead.

If we’re getting into what if scenarios, I can envision a robot being so good he strikes out every batter he faces.  I don’t think even primed steroidal Barry Bonds could hit a 250 MPH fastball with movement.  But I don’t see how you can guarantee a homer.  The pitch would have to be easier to hit than placing it on a tee, as I’ll bet even MLB hitters won’t hit a teeball out 100% of the time.  And what of a Reggie Willits, who has zero career homers?  Can you make a pitch easy enough for Reggie to hit it out?  How about my 2 year old daughter?  Or her feline brother Brian?  They have even less power than Willits, though I guess the Gaedel rule would keep them off the field in the first place.

Yowza, really tough crowd!

I liked the idea of signing Robot one and pencilling in your no-defense team on days when he pitches....until I realized that the opponent would be able to play their all-defense team on those days as well, since they’ll be scoring the same no matter who bats.  Not so good of a deal now.

Although, it would be nice to know how many runs you need to score to win a game.  A smart manager might actually be able to optimize his bench a little better, knowing that he only needs one more run, since he knows exactly how many his pitcher will give up.  That’s a lesser advantage, but it would be interesting to see it play out.

Rally, I agree that the premise is so artificial that it is odd to discuss it. Based on the HR derby, I would expect that the most meatballish of a pitch, called for, and delivered in the precise location requested would only be hit for a homerun (by a slugger) maybe 30% of the time. This means that given three pitches he (a top HR hitter not named Inge) would hit a HR 70% of the time.

Of course, the chance of a swinging strike is almost zero so he can bat as long as the ball stays out of play. And of course some of those balls will be hits so it is pretty complicated.

A “realistic” robot who can throw 200mph with movement, but maybe sketchy control seems within the realm of physical possibility. Maybe he throws unhittable strikes 66% of the time. The rest are unhittable balls (just in case Kung Fu Panda is batting).

Of course this robo-pitcher would maim and/or kill several people over the course of the season.

Crowd is getting tougher and tougher (though Craig brings up a great point regarding the opposing fielders).

A HR does not have to clear the fence.  A batter simply has to touch all four bases.  I was trying to get the fielders out of the equation, and I was trying to get the math easy for discussion purposes.

But, if you must… how about this: the sixth batter will reach base and score before the seventh batter’s PA is completed.  That means that once he gets on base, he can steal, get balked over, get wild pitches, or whatever it is that has to happen.

The robot simply needs to be readjusted after every run is scored because his mechanical parts are very sensitive, though they behave like clockwork.

Tango/8,

I’m just saying, your’s and Rally’s overly-optimistic projections that yield $3.5-4 MM figures wouldn’t work for a robot whose playing time projections are dead on. The figures using Sky’s replacement-level theory are probably more accurate than Tango’s replacement-level theory when we have complete certainty on our projections.

It hasn’t yet been shown that I’m “overly” optimistic. 

I understand Sky and Matt are going in that way, with their 6MM$ per win payouts.  Even Clay, in that very same thread, was quoting something far lower.

I will say that I didn’t introduce my forecasts blindly, even for future years.  They have some logical underpinnings.

If Sky and/or Matt keep putting our research that says 6MM$ is the correct figure, then we’re going to be in for a heckavu battle!

Robotics strikes me as a performance enhancement…

The robot always alternates a base on balls with a strikeout, with the BB always coming first.  So a typical inning is BB, K, BB, K, BB, K.

But every so often someone steals a base on the robot, and is later walked in home. 

So how often must the steal occur for the robot to have no value?  And does it matter if the robot is a starter or a reliever?

Ah, Ed, where were you when I needed you?

Ed #27:  I don’t follow: how do stolen bases result in someone walking in home, unless the catcher drops a third strike?  If they advance on a steal, then on the next walk, they don’t advance, right?  Or were you referring to steals of home?

How about this:  5 strikeouts followed by the machine going wild and walking (or hitting) the batter.  But the machine is set up to only throw home, it is incapable of throwing to first.  So the guy who walks (or the pinch runner for the deceased HBP at 250 MPH victim) can steal his way around the bases and score at will.

Rally, two problems with that:

1.  Once that pattern had been established, the robot would get a warning from the umpire on the first HBP, and the robot and manager would be tossed the second time - because clearly anything so predictable would be judged to be intentional.

2.  If the robot can throw home, no one can steal home.  So, a free ride to third base (making members of the opposing team fantasy all stars for the SB’s), but that’s the end of the line.

I was thinking that the robot takes a long time to throw home, and therefore, he’s easy to steal on.

So, if you want to make it 5 K (one ball followed by three strikes), 1 walk, and the guy who walks simply steals each base after each throw.

Ah, the Bugs Bunny windup!