LastÃ‚Â Sunday, upon logging into Twitter I was met with the following tweet:

For me, this was like Christmas in April!Ã‚Â And the answer to your question is Ã¢â‚¬Å“yes.Ã¢â‚¬ÂÃ‚Â I am a disturbed individual.

So, in honor of the update to the run expectancy matrices, today begins a multi-week series about decision making using the RE24 framework.Ã‚Â As such, I feel it is important to have a post about RE24 itself!Ã‚Â This is that post! (Perhaps, Ã¢â‚¬Å“this post is that?Ã¢â‚¬Â)Ã‚Â We will explore the following: what is RE24, where do the numbers come from, and how to read an RE24 chart. Then IÃ¢â‚¬â„¢ll present the path ahead!

To begin, RE24 stands for Ã¢â‚¬Å“Run Expectancy for the 24 Base-Out States.Ã¢â‚¬ÂÃ‚Â What is a base-out state (now to be referred to as BOS)?Ã‚Â It is one of the specific alignments of base runners and outs in anÃ‚Â inning.Ã‚Â For example, a runner on 1^{st} base with 2 outs is one of the states; the bases loaded with 1 out is one of the states; bases empty with 0 outs is another.Ã‚Â There are twenty-four of these states possible, hence, RE24.

As a baseball fan, a lot of RE24 will be intuitive to you. Consider the following example: a runner is on 1st with 1 out and the batter walks.Ã‚Â Now, there are runners on 1^{st} and 2^{nd} with 1 out; this is the new BOS.Ã‚Â The new BOS is more likely to score a run (and more likely to score multiple runs) than the old BOS, right?Ã‚Â Well, of course!Ã‚Â There is a man in Ã¢â‚¬Å“scoring positionÃ¢â‚¬Â now!Ã‚Â See?Ã‚Â Sabermetrics can be intuitive!

Now, however, we have to quantify that intuition.Ã‚Â Well, *we* donÃ¢â‚¬â„¢t have to quantify it because someone already did it for us. That was nice of them!Ã‚Â I donÃ¢â‚¬â„¢t know if Tom Tango and his cohorts were the first people to figure all this out, but they are the source IÃ¢â‚¬â„¢ll be using.Ã‚Â Tango publishes tables of all 24 base-out states on his blog, which are basically just excerpts from *The Book: PlayingÃ‚Â the Percentages in Baseball*.

I will present one of the tables, slightly modified for effect, and then weÃ¢â‚¬â„¢ll discuss it.Ã‚Â The below table shows the average amount of runs that scored from each base-out state until the end of the inning from 2010 to 2015:

As expected, we have an 8-by-3 grid filled with glorious numbers; one for each unique base-out state! Your eye is likely drawn to the red box at bottom-left.Ã‚Â This is the Ã¢â‚¬Å“bases loaded with no outsÃ¢â‚¬Â BOS.Ã‚Â It is red because more runs score, on average, in that situation than any other situation.

Before we go further, you may be thinking Ã¢â‚¬Å“where did these numbers come from?Ã¢â‚¬ÂÃ‚Â ItÃ¢â‚¬â„¢s a good question.Ã‚Â The answer is simple.Ã‚Â People with a lot of time and database know-how took every single plate appearanceÃ‚Â in the last 6 seasons and then figured out how many runs scored from that plate appearanceÃ‚Â until the end of the inning.Ã‚Â Since each plate appearanceÃ‚Â has to start in one of the 24 specific BOS, it becomes an easy algebra problem after that to arrive at the final run expectancy number.

[Note: from this point on I will start referring to base-out stats with the following notation: 1-3_0 means Ã¢â‚¬Å“first and third, no outs,Ã¢â‚¬Â 123_2 means Ã¢â‚¬Å“bases loaded, two outs,Ã¢â‚¬Â and —_0 means Ã¢â‚¬Å“bases empty, 0 outs.Ã¢â‚¬Â]

This is perhaps one of the most interesting things about RE24. It is based on reality; what actually happened.Ã‚Â A big gripe of the Ã¢â‚¬Å“old schoolÃ¢â‚¬Â or Ã¢â‚¬Å“traditionalÃ¢â‚¬Â fan base (from my point of view) is that sabermetrics often deal in theoretical situations, or perhaps focus on things that *might* happen rather than what has already happened.Ã‚Â Here, we have a cornerstone of modern sabermetrics based entirely on historic data. There are no estimates, no crazy formulas, and no hard-to-understand acronyms. The simplicity of RE24 is as astounding as itsÃ‚Â application. These tables are the building blocks for slightly more complicated concepts, but we will save those topics for another day.

So, why do we use this chart and how do we use this chart?Ã‚Â We (and by Ã¢â‚¬Å“weÃ¢â‚¬Â I mean Ã¢â‚¬Å“major league managersÃ¢â‚¬Â) should use this chart to aid the decision making process!Ã‚Â How do we use it?Ã‚Â Very easily!

Imagine for a moment you are leading of an inning.Ã‚Â Obviously, our BOS sits at —_0. From this point until the end of the inning, an average of 0.481 runs will score.Ã‚Â That simply wonÃ¢â‚¬â„¢t do.Ã‚Â We need more runs than 0.481.Ã‚Â LetÃ¢â‚¬â„¢s have our leadoff hitter smack a double down the line.Ã‚Â Now, at -2-_0, you can see from the chart our run expectancy has increased from 0.481 runs to 1.1 runs!Ã‚Â Outstanding!

But wait! We havenÃ¢â‚¬â„¢t actually scored a run have we?Ã‚Â No? No.Ã‚Â So what good is this?Ã‚Â Here comes the sabermetric thought process.Ã‚Â If we attempt to maximize the net change in run expectancy from one plate appearance to the next, over the long run we will also maximize our run scoring.Ã‚Â Maximizing our run scoring will maximize our winning. Winning is good.

[Note: The generalized expressionÃ‚Â for calculating the change in run expectancy (Ã¢Ë†â€ RE) is as follows: Ã¢Ë†â€ RE= RE_{f}-RE_{i} + Runs, which is final run expectancy minus initial run expectancy plus how many runs scored on the play.]

Corollaries of the first chart also exist.Ã‚Â The below chart shows not run expectancy until the end of the inning, but instead shows the odds that at least 1 run will score from that position until the end of the inning.Ã‚Â Behold!

On this chart, you will notice every box is occupied by a number between 0 and 1.Ã‚Â The odds are never 0% and never 100% that you will score a run.Ã‚Â Perhaps most interesting is the bases loaded with no outs box; there is only an 86.1% chance of scoring a run from this BOS. Ã‚Â As it turns out, strikeouts, pop outs, and double plays happen!

Also interesting are the four boxes ranging from –3_0 to 123_0; each has a value between 84.3% and 86.1%.Ã‚Â This shows us that once a man is on 3^{rd} with 0 out (or 1, for that matter) adding base runners doesnÃ¢â‚¬â„¢t have an appreciable effect on the likelihood of scoring a single run.Ã‚Â This is why many times youÃ¢â‚¬â„¢ll see managers walk the bases loaded in the 9^{th} inning of a tie game, setting up a force at any base. The total runs donÃ¢â‚¬â„¢t matter anymore; only the first one.

Notice that when going from 1–_0 to -2-_1 our run expectancy decreases from 0.416 to 0.397.Ã‚Â This is one situation in which a sacrifice bunt is oft employed, and this simple calculation is one of the methods used by certain folks to show why sacrifice bunts are generally poor decisions.Ã‚Â [The last part there is a sneak-peek into next weekÃ¢â‚¬â„¢s article entitled *How Productive are Productive Outs?*]

One final chart and this primer will be at an end.Ã‚Â The below chart shows the total percentage of at-bats beginning in each BOS.

As youÃ¢â‚¬â„¢d expect, the —_0 base-out state dominates, largely due to the fact that a minimum of 17 of these plate appearances are guaranteed in each game.Ã‚Â The most unlikely BOS is –3_0, accounting for a whopping 0.2% of all plate appearances.Ã‚Â This particular chart, when combined with the above charts and some math, help determine optimal lineup construction.

As promised, this primer is now at an end. Ã‚Â I know it was quite dry, but presenting all this information, along with some pertinent examples of how this can and should be used in a real baseball game by our beloved Redlegs, turned out to be far too long for a single post, hence the decision to make this a series. I promise next week will be more fun to read!

As alluded to above, next weekÃ¢â‚¬â„¢s post will be entitled *How Productive are Productive Outs?* Tune in next week to find out!