THE BOOK--Playing The Percentages In Baseball

Not to mention all extra pitches the opposing pitchers would have to make and all the usage from the opposing teams worst bullpen pitchers.

I don’t think you can say being given a fourth out is the same as changing an out into a RBOE.

In a RBOE the hitter reaches base and all runners advance, for the Mariners, they would still face the obstacle of getting a runner on first and advancing him. (if they’re scoring 35% less than average, that seems to be quite the obstacle indeed!)

Yeah, getting a theoretical extra out is pretty big, but less than the advantage of an extra out plus a free baserunner.

How bad would an offense have to be for 4 outs to only get them average?

How many runs would an average offense score if allowed 4 runs to work with?

One thing about baseball is that if you get a leadoff runner and had batters who could sacrifice perfectly that baserunner still needs something extra to get him home - another hit/walk, or finding some way to advance an extra base.  With 4 outs, a leadoff baserunner could theoretically score on 3 sacrifices.

http://www.tangotiger.net/RE9902.html

Using that matrix, you can look at the 2 outs, bases empty status to find that you would expect .117 runs to be scored that inning. 0.117*9 ~ 1 extra run a game. This is assuming that every inning ends bases empty, which, of course, it doesn’t.

I guess if you could figure out how often on average a team ended an inning with each of the base states (bases loaded, runner on 2nd, etc), reset them to 2 outs and summed them up, you would find how many more runs an average team would score. It’s at least a couple though.

I think the best way to answer the question would be to extend Tango’s markov model to 4 outs.  I’ll give it a crack tonight if no one else jumps on it first.

I think the Markov chain is a good way to go.  Another would be to figure the bases occupied and run scored situation for all Mariner innings with one out, create a RE Matrix special for the Mariners; and then apply the situations on apercentage basis that they were in after one out, to the RE Matrix but with no outs to get the four out inning.

I think another good option would be to have someone with a good baseball simulator (MGL?) change the rules from three to four outs and see what happens.  But like I mentioned earlier there are other effects, which are that pitch counts are going to go quite a bit higher and the #6Org opponents will have to go deeper into their bullpens.

Hmmm… excellent point guys.  Not sure what I was thinking.

Ok, the minimum point would be to simply do runs per 3 outs and pro-rate it up by 1/3.  So, a team that scores 3 runs goes up to 4 runs.  Of course, you have runners on base that have a better chance of scoring because of the extra out.

Let me recompose my thoughts, as I obviously shouldn’t answer the first thing back from a mini-vacation.

First off, I shouldn’t blame being back from anything.  I was either lazy or sloppy.

And I agree, running a simulator is the easiest thing to do.

Doing some quick calculations using this as a framework:

http://www.insidethebook.com/ee/index.php/site/article/the_secret_recipes_of_the_run_expectancy_matrix/

I will guesstimate that runs per inning, for a 4-out inning will go up by 60% compared to 3-out innings.

Ken’s #4 is what I proposed on Twitter as an approximation.  Obviously it ignores the way the two-out RE would change (different strategic choices, double plays would now be possible with 2 outs, etc.).

The Markov/simulation approach would be preferable, though.

Run scoring would have to go up more than 1/3 - 60% might be right.  The end of an inning clears the bases.  Imagine a world where you get all your 27 outs in one shot - the bases never clear.  If you get 13 baserunners in a game, as long as you can avoid the DP or outs on base you will score a minimum of 10 runs, instead of the 4.5 or so that teams now get from 13 baserunners.

But DP frequency will go up, that is a consideration.  As is the new, though still highly improbable, concept of a quadruple play.

Sharply hit GB back to pitcher, throws quickly to catcher, then around the horn.  I suppose with quick enough fielders and a pair of Molinas at the plate and on first it could happen.

Ken/4: ah, excellent, yes.  That’s a great way to do it.

There’s about 38.7 batters per game, of which 4.7 score, and 27 are putout, leaving us with 7 runners left on base per 9 innings, or 0.78.  Given one more out, each of those runners will score an average of about 0.2 runs, or 0.16 runs left on base, plus the 0.12 runs for the batter and all future batters, or an extra 0.28 runs, or about 50% more runs than the 3-out inning.

That number is also close to the run value of the out, which we’d expect, though I’d expect it to be a bit higher.  It should be close to 0.32 or 0.33 runs or something.

So, I think I will stick with the +60% estimate.

Thanks very much, everyone. (I sent in the question)

I think you can do this without a Markov simulation.

Suppose you’re exactly average in three innings.  You score 1.5 runs, and you make 9 outs, and your Linear Weights is zero. 

Now, suppose you take away three outs, and nothing else.  How many runs will you score in those two innings worth of outs that remain?  Well, since an out is worth 0.25 runs below average, and average is 0.1666667 runs, each out is worth a bit less than 0.09 runs. 

Taking away three outs is therefore worth +0.27 runs.  That’s spread over two “new” innings, so instead of scoring 1.5 runs, you’ll score 1.77 runs.  That’s 0.88 runs per “new” inning, instead of 0.5 runs per “old” inning.

So instead of scoring 4.5 runs a game, you’ll score 8. 

Is my logic right?

Does data exist somewhere about the frequencies of runners left on base? For example, what percentage of the time does the inning end with runners on first and second, or bases empty, etc.?
If so, (or if not, and someone wants to go through Mariners play-by-play and find it), all that would have to be done is to take an average of the two out run expectancies, weighted by left on base frequencies, and this would give the additional runs scored after the third out.
Of course, this method (like all the others proposed) ignores any strategic changes that might occur, but those would be hard to predict and probably have an effect of a relatively small magnitude.

There’s a 14% chance of scoring from 1B, 22% from 2B and 26% from 3B, with 2 outs. 

Just call the average as 20%.  Regardless of the frequencies, you’ll be close, right?

The Mariners leave 6.94 batters per game on base (about average), so to estimate the frequencies of number of runners left on base, I just used a Poisson distribution with parameter 7/9 (this gives very few innings with 4 or 5 runners left on base, which I lumped into the bases loaded situation). Then, for one or two runners left on base, I used a two out run expectancy that was the average of the three possibilities. 

This method gives an additional .285 runs per inning, or about 2.5 extra runs per game.