THE BOOK--Playing The Percentages In Baseball

Perhaps, this is due to the fact that the other players are getting partial credit for the LW runs that the player who makes no outs is generating by virtue of his extra PA’s. Tangotiger has explained this problem before in terms of absolute Runs (RC), and now I think you have explained the problem in terms of average Runs (LW).

Anyway, how many runs does he add to the lineup.  According to lwts, a walk is worth around .32 runs.  .32 times his own 4.64 (as, say a number 5 hitter, again, in an average lineup) is 1.48 runs.  An average lineup in the AL generates 4.65 rpg.  So with the guy who always walks, we expect 4.65+1.48, or 6.13 rpg.

MGL - Isn’t the guy who always walks replacing an average hitter in the lineup?  Isn’t that average hitter already generating .12 runs for every PA?  Wouldn’t that make the number of runs added to the average lineup by the guy who walks every time (.32-.12)*4.64 or .928 runs instead of 1.48 runs?

If an average pa generates .12 and a walk generates .32 then the walk generates an extra .20 runs per pa not an extra .32.  4.64 * .20 = .93.  Extra pa for other batters generates .12 * 3.0 = .36.  So you would expect 4.65 + .93 + .36 = 5.94.  That’s not as close a match as you thought. 

Similar story for HR but the answer is a lot closer to what you got because the extra pa for all (4.4) is pretty close to the pa for the one batter who changes to all homers.  So you end up adding and subtracting 4.4 pa.

Nevermind. I see my error.

So is saving a play still worth 0.8 runs?

http://www.insidethebook.com/ee/index.php/site/article/why_saving_a_play_is_worth_08_runs/

I think Peter is right.

Let’s use Markov:
http://tangotiger.net/markov.html

And so that it’s easier to manipulate the numbers, let’s multiply the batting line by 9 so that you have these inputs (the second line):
AB H 2B 3B HR BB SO
37 10 2 0 1 4 7
333 90 18 0 9 36 63

You get 4.905 runs per game (using either line, natch).

Now, MGL is asking what happens if we add an “all walker”.  So, let’s take the original first line and multiply by 8:

We get this:
AB H 2B 3B HR BB SO
37 10 2 0 1 4 7
296 80 16 0 8 32 56

The second line is simply 8 times the first line.

Now, add 41 walks to the second line (that represents our 9th hitter, as each hitter gets 41 PA).  So, we now have this line:

AB H 2B 3B HR BB SO
296 80 16 0 8 73 56

You end up with 7.213 runs per game.

So, converting an average hitter to an all-walker adds +2.31 runs.  The original lineup has 41 PA, and this lineup with the all-walker has 46.125 PA.  So, the extra 5.125 PA generated 2.31 runs, or +.45 runs per PA, above what you get from an average hitter.

A side note: because my Markov has not outs on base, the run value of the walk is higher than we’re used to.  In an all-average lineup, the run value of the walk is .37 runs. 

Second side note: MGL literally uses 8 average hitters plus the all-walker.  In my case, I use the team total of these 9 hitters, and get 9 of these hitters.  So, it’s a bit different.

Anyway, as Peter noted, this guy gets +.45 runs above the average hitter.  But the average hitter created 4.905/41 PA, or .12 runs per PA.  The +.45 is above that .12.

***

As for the all-HR, enter this:
AB H 2B 3B HR BB SO
337 121 16 0 49 32 56

And you get 12.088 runs. That +7.183 runs per game above average for the same exxtra 5.125 extra PA, or +1.40 runs per PA.  Again, above what the average hitter creates.

Rob/5: yes.

bsb/3: the walk adds +.32 runs above the average PA.  If the average PA generates .12 runs, then the walk generates .44 runs.  The walk does NOT create +.20 runs above the average PA.

MGL - I am not sure, however, how your added man scenario helps us to understand how to convert a player’s runs above average (in linear weights) to absolute runs created.  How do you propose to make that conversion?

Slight change of topic, but when I read this (player who walks in every PA), I immediately thought of Eddie Gaedel.  But then I thought that he’s always going to be pinch-run for, since he’s almost always going to be an easy out on the basepaths, and bad in the field.

So, what’s the best use for a player like Eddie Gaedel (yes, I know, he wouldn’t be allowed to play in MLB)?  Do you lead him off every game, adding a guaranteed walk and thus 162 * .32 runs = about 54 runs or 5.4 wins a season?  Or do you save him for critical moments, when you absolutely need a baserunner (high leverage situations)?

Which is the optimal situation?  Bringing him in to start the ninth against the other team’s closer in a one run game?  Could a team afford to have such a “designated walker”, or is the roster spot better used by someone who can contribute in other ways as well?

Didn’t Bill James ask something like this in his 2nd Historical Abstract, only he was using an all-time horrendous lineup and walking Babe Ruth every time?

If you leadoff an inning, a walk adds +.40 runs.  So, giving him 162 games, and then taking him out gives you +65 runs above average (which is also close to +65 runs above replacement), or +6.5 WAR. This is an MVP candidate, if not the MVP.

Now, if you want to save him for “tighter” situations, you probably have at least 50 occasions at an LI of 2.0 to bring him in for a guy who you don’t mind replacing.  Presuming +.03 wins per walk times 2 times 50 gives you 3.0 WAR.  You really have to gamble a bit.

So, I’d go for leading off the game with Gaedel.

As for depleting your bench, the difference between the 24th and 25th player is of course virtually nothing.  So, you lose the flexibility of one player.  But, I’m giving you ALBERT PUJOLS in order to lose that flexibility.

It’s a no-brainer.

"I think that the lwts runs we generate from the change in RE in an average run environment somehow already includes the extra PA.  I don’t know how or why, but it seems to. “

Is this not expected? Thinking on a innings by innings basis - for example a leadoff walk.
The run expectancy increases by ~0.4 runs and this is where we get our linear weights values from (appropriately averaged over all situations instead). The increased impact of the 0.65 PA or so is factored into the RE exactly isn’t it?

“So a player’s lwts per game seems to be exactly what he adds to a team of average players, no matter how large (or small, I assume) the lwt value is. “

I’m not sure this is quite right. Am I right in saying the player’s linear weights are calculated assuming an average distribution of base/out situations for him to hit in and average consequences following his PA. Having 8 other average players on the team will generate very close to this, but batting around will disrupt it very slightly.

FWIW, I ran this thru Base Runs. Using MGL’s avg team of 4.65 R/G as the standard, I got 6.31 R/G with the all-BB player (as opposed to the sim’s 6.13). So, BsR seems to include those extra PA.

I’m not sure how much justification there is to trust the sim over other methods. Couldn’t the sim be wrong?

Having one player that has an OBP of 1000, as opposed to having 9 equal players so that both teams are overall the same slash lines would be different.  From that standpoint, the sim would be better.

In any case, once you introduce such an extreme player as to completely modify the run environment “texture”, you are going to get some uncommon results.

David, unless the sim has a bug or two in it, the sim is prefect for these kinds of analyses.  It basically does everything that a team does using league average values for everything unless we change those values.

Using BaseRuns or any other formulaic model of run sscoring is definitely NOT the way to do this kind of analysis, especially if you are concerned about nuances.

I agree that the “batting around” changes things a little, but not much I wouldn’t think.

I think that #12 is right.  The lwt values we get from going through the historical empirical data includes the extra PA that everyone gets. It is just not thsat evident since we are actually looking at events within league average games, by definition.

About a player like Gaedel, I don’t think that he would walk anywhere near 100% of the time.  Maybe 50-75%, and make out of course the remainder of the time.  If a pitcher wants to throw a strike and knows that the batter cannot make contact no matter what (as opposed to, say, a pitcher at the plate who can actually get a hit if the pitcher throws a batting practice fastball), they can be pretty darn accurate with their pitches.

"According to lwts, a walk is worth around .32 runs.  .32 times his own 4.64 (as, say a number 5 hitter, again, in an average lineup) is 1.48 runs.  An average lineup in the AL generates 4.65 rpg.  So with the guy who always walks, we expect 4.65+1.48, or 6.13 rpg.”

LWTS is denominated in runs above average.  “Average” means average *per out*.  The average lineup in the AL generates 4.65 runs per game, which is 4.65 runs per 27 outs.

Once you convert 4.64 PA into a walk, you’re removing about 3 outs.  So now the average lineup in the AL generates 4.13 runs per 24 outs.  Add in the 1.48 to get 5.52.

NOW you can add in the PAs for the three extra outs, which gets you back to 6.13.

I think that’s right ... the problem is the “average” in terms of lwts is based on outs, and if you change the number of outs, by converting an out to a walk (or whatever), you have to adjust the total runs by subtracting the average runs per out.  You still come out ahead, of course, but you avoid double-counting.

Yes, that is what I mean by the lwts value “already includes the extra PA.”

Ah, okay.

MGL - Have you tried adding a player who makes only outs to a team of average players and run it through your sim?

Also, you never answered my question in Post #8 about what the implications of this research were on the correct method of converting from a player’s runs above average linear weights to his absolute runs contributed.  What method would you use to accomplish this conversion?