As it turns out, there is even less of an effect on a batting order than originally thought.

Using the league average RE for each of the 24 states, but applying the frequency rates, here are the latest LW by batting order (with 0 being average):
0 (0.312) 0.350 0.483 0.786 1.052 1.422
1 (0.298) 0.353 0.462 0.752 1.005 1.328
2 (0.306) 0.352 0.476 0.768 1.033 1.384
3 (0.308) 0.334 0.472 0.765 1.019 1.418
4 (0.324) 0.349 0.499 0.815 1.088 1.473
5 (0.322) 0.357 0.502 0.817 1.090 1.462
6 (0.316) 0.356 0.491 0.799 1.069 1.446
7 (0.314) 0.353 0.484 0.792 1.061 1.439
8 (0.313) 0.350 0.486 0.792 1.059 1.437
9 (0.309) 0.346 0.480 0.782 1.045 1.425

I'm always playing with my program, so these numbers may change in the future. (I will reintroduce the SB/CS if I can get their frequencies done correctly.

In any case, applying the above, and we see the most extreme player is Boggs who gains 3 runs in the leadoff spot or loses 4.4 runs in the 9th spot. That's the worst case scenario.

The optimal order can now add 9 runs above a random batting order:
1 - Boggs
2 - Evans
3 - Baylor
4 - Rice
5 - Barrett
6 - Gedman
7 - Buckner
8 - Armas
9 - Romero

Basically, after you figure out the top 4, the last 5 are simply your players in order of value. The biggest variation in the batting order is not the "profile" of the hitter, but the PA opps. There is a 20% diff in PA between the top and bottom player. If the best player created 120 runs in 600 PA, and the worst creates 60 in 600 PA, and you have 660PA for the leadoff hitter, and 540PA for the #9 hitter, how many runs will these 2 create in both combinations of batting order? At best, its 120/600*660 + 60/600*540 = 186 runs. Random its 180 runs, and at worst it's 174 runs. As you can see you have a 12 run difference simply on the PA effect.

As for the "profile" (and by that I mean, that since the value of the HR is least for the leadoff hitter because of the frequency in which the bases are empty, etc), there is a TWO run difference from best to worst. That is, if you give everyone the same number of PAs, the absolute worst lineup you can think of will result in a max loss of 18 runs for the team.

As well, as for the "9th hitter" / "2nd leadoff" theory that I always believed in, it does not appear to be valid. The difference in LW values between the 8th and 9th hitters is very tiny.

In every single offensive event, the LW value rises for the 4th, 5th, 6th hitter, and loses for the 1st, 2nd, 3rd hitter. Therefore, the question is always: does the increase in LW value for the 4th hitter overcome the loss in PA in the 4th spot?

By PA, your best hitters should hit 1-2-3. By LW, your best hitters should hit 4-5-6. Since PA has a bigger effect, almost always will your best hitters hit in the top 3 slots.

Between the #3 and #4 spots there is a huge jump in LW values, and at this point alone will it sometimes make more sense to put a better hitter #4 than #3, especially, if it's a big homerun guy. That jump in LW overcomes the loss of number of PAs much of the time.

And the leadoff hitter loses so much of his homerun value, that it will almost never happen that your best hitter, if he hits lots of homers, ends up in the #1 slot. (obvious to all of us)

Tango,

I'll have the SB/CS freq's ASAP. Do you need the SB attempts by outs for each slot, or the SB/CS percentage by outs for each slot? What EXACTLY do you need as far as SB/CS goes?

Also, I assume you are using NL and AL combined. Could you post the lwt values (by batting order) for the NL and AL separately. I assume that there would be quite a difference between the NL and AL at the end (and perhaps the top) of the BO because of the #9 hitter. Also, to assume that the subsequent batters are average would be a big error for the #7 and 8 slots in the NL, wouldn't it? I've forgotten already whether your lwt values are based on league average batters all the way through the lineup, i.e. they rely only on the bases/outs frequencies of each slot...

MGL,

SB/CS: Well, this one is interesting. If Rickey gets on base, he can steal with the #2, #3, or #4 batter coming up right? So, the first question I have is when does a runner steal AFTER getting on base? This one gets complicated because the leadoff hitter's frequency rates will differ greattly from the other players, NOT because they have different opporunities, but simply because they are different types of players.

AL/NL: I am using AL only until I can figure out what to do with that #9 NL spot.

frequency/RE values: I am using the overall RE values (same for each spot), but the frequency rates for the particular spot. This assumes the average batter is on deck. I'm trying to think of a clean way to come up with the proper RE for each spot. I can't use the true RE, since this has the value of the hitter itself. However, I'm thinking of using the RE of the NEXT batter somehow for each of the 24 base/outs, but applying the current batter's frequency. That is, assume the current batter has RE with bases empty 0 outs of .50 and an RE with runner on 1st, 0 outs of .65 (it's low because the next batter is the pitcher). The next batter, assume it's the pitcher, has an RE of .30 bases empty (it's low, because the current batter is the pitcher) and .55 with runner on 1st, 0 outs (it's alot higher because the next batter is the leadoff hitter).

So, I'm thinking of first figuring out the chance of the #8 batter scoring from 1B, 2b, 3b. Let's say that's .15 for 1B, .30 for 2B, and .50 for 3B. Apply the AVERAGE batter's frequency of offensive events (say 15% of PA are singles), and come up with ....something. Kinda like reverse-engineer the RE. I really have to mull this one over....

I've been following this thread with interest, waiting to see the final set of L Wt by BO values. But there's always something else which needs to be adjusted for; more to be done.

Is all this simply the analysis and solution of a problem being played out in real time on a thread? Or could it possibly be that L Wts are inherently incapable of solving the problem? That every 'solution' will also generate or uncover a new aspect of the problem? Perhaps the nature of the interactive lineup process simply can't be captured this way?

I'm just wondering.

David, oh it definitely can be captured. One way is by running a thousand simulations. However, you can simulate the simulation because there are a finite set of state-transitions. The key is to figure out the frequency in changes in state, and the frequency is dependent upon the current batter, and the next set of batters. It's complicated, and all we're trying to do is to simplify this, but still keep it valid.

Anyway, this is what I'm thinking:

Let's remember what MGL's RE matrix represents for each batting spot: the expected runs at the START of the at bat. The RE at the end of the at bat is not the RE matrix for that batter, but the RE for the NEXT batter.

For example, the RE for the leadoff hitter, with no one on, and no outs is .62 runs. This represents the expectation of runs scored for the team for the inning, before the leadoff hitter swings the first pitch (and is therefore a function of BOTH the current hitter, and the hitters behind him).

If he gets on base, is the RE now 1.03 (the RE for the leadoff hitter with runner on 1st, and no outs)? No, the RE is 1.07, which is the RE for the 2nd (next) batter, before he swings. This is crucial. While the typical batter will go from an RE of .56 to .95 (+.39) in such a situation, the leadoff hitter, BECAUSE OF THE BATTERS BEHIND HIM, will go from .62 to 1.07 (+.45).

The number 6 hitter, with no one on and no outs has an RE of .49, and the #7 (next) hitter with man on 1st, and no outs has an RE of .82. That difference, +.33 runs is a result of the batters AFTER the #6 hitter.

Therefore, in this situation, a single for the leadoff hitter, with the best batters coming to bat is worth .45 runs, while a single for the #6 hitter, with the worst batters coming to bat is worth .33 runs. Makes perfect sense.

By continuing in this manner, we can create the chance of scoring for each batting spot, for a single, double, and triple. This is the first-half of the LW formula.

The other half (the base-runner movement part) follows the same logic. With a runner on 1st, and no outs, before the #3 batter comes to bat, the RE is 1.05 runs. After the #3 batter gets done, and before the #4 batter is at bat, the RE for a runner on 2nd, and no outs, is 1.15 runs. Therefore, a number 3 hitter, getting a bloop single, adds a measly .10 runs to the runner on base, as opposed to the league average 1.20 - .95 = .25 runs. This makes sense, since the big boppers #4 and #5 are almost as easily be able to drive in the guy from 1st as from 2nd.

I think following this logic, we can create a perfect LW for each of the 9 spots, based on the other 8 batters being typical for their spots, and the current batter being average.

If this makes sense to you guys, I will construct what will hopefully be the final set of LW by batting order.

Tango,

I still don't know what SB/CS data you want!! Explain it to me like I'm a 7 yo child (or Tony Larussa)!

MGL, *I* still don't know!!

I think what I want is the frequency that the leadoff hitter steals 2B when the #2, #3, or #4, etc hitter is at bat, with 0, 1, or 2 outs. And then do this for every batter.

The denominator should be the "opportunities to steal".

I think this is what I want....

Based on 2 posts ago, here is part 1 of the LW formula, the chance of the runner scoring from any base. Using the RE/frequency tables provided by MGL, here they are, for each batting spot:
31.6% 31.4% 27.5% 27.7% 26.3% 24.1% 24.9% 23.6% 25.3%
52.4% 49.0% 42.5% 41.8% 43.2% 41.3% 41.4% 42.9% 44.8%
69.9% 68.2% 59.5% 60.1% 58.2% 60.0% 55.9% 57.7% 66.3%

It is based on the actual frequency for each spot, and the actual batters followign him. In reality, this table could have been figured out by looking at the play-by-play data (taking care of the fielder's choice).

I'll come up with part 2, base-runner movement, tomorrow.

MGL, Need your help if you can.

I'm racking my brains trying to do it, and I don't have the resources. You see, when it comes to the base-runner movement part, I know that if the leadoff hitter gets on base, then I can see how much extra RE the #2 hitter gets for moving him an extra base. That RE though is based on the typical #2 hitter, followed by the typical #3 hitter, etc. Then we get into the problem with the pitcher, as we well documented.

But, here's a way around it. Figure out the RE by offensive event. That is, what is the RE for the 24 base/out situations when the #2 hitter gets a single? A double? An out? etc.....

If you were to apply the "real" frequencies of these offensive events for the #2 hitter, you by definition get the famed RE table that you produced by batting order.

HOWEVER, if I were to instead apply the "league average" frequencies to these offensive events, I then get an RE table that is based on the league average for the #2 slot, but the "real" batter in the #3, #4, and #5 slot.

This will take care of the pitcher problem by "forcing" an average player into this (and every slot).

Tango,

Not sure what you mean...

If I understand the way you calculate the RE, you take the number of runs from the point a particular state exists to the end of the inning and divide that by the frequency of the state. So, if it's 1 out, and man on 1st, and this happens 5000 times and 4000 runs scored, then the RE is 0.80

However, what if you add another variable to the state, and make it: 1 out, man on 1st, and the hitter gets a sinlge. Maybe this happens 1000 times and 1100 runs score, so the RE is 1.10. For each event (each type of hit, walk, hit batter, and out) what is the RE?

My hope is that when we get to the #9 NL spot, maybe we'll only see 500 times where the above event happened (half as much as regular), and 600 runs or so score for an RE of 1.20 following a single (i'd expect a little higher because the top of the order is following).

Then, I would apply the league average frequency of 1000 times that a sinlge would occur in such a situation, multiply that by 1.2 and get 1200 runs scored with an average batter in the 9 spot, but typical batters in the regular spots. Do that for all the offensive events, and you get a batter-neutral (but batting-order specific) RE. This will take care of the #9 NL spot, and all other spots.

Part 1
The chance for the leadoff hitter in the AL, to score from 1B, with 0/1/2 outs:
44%
28%
13%
The frequency he will be on 1B with 0/1/2 outs:
6.1%
8.5%
9.3%
Multiplying the two, the chance of him scoring overall from 1B:
31.6%

Doing the same procedure for each batting spot, from 1B,2B,3B:
31.6% 30.9% 26.6% 26.7% 26.3% 24.2% 24.6% 23.9% 26.3%
52.5% 50.2% 43.3% 42.7% 43.9% 41.7% 41.2% 42.0% 46.0%
70.2% 68.4% 61.8% 61.5% 60.8% 58.6% 57.5% 57.5% 65.4%
(numbers slightly different from before, due to slightly different methodology)

And for the NL:
30.5% 31.2% 28.5% 27.5% 24.7% 23.0% 19.4% 20.6% 25.0%
49.4% 48.1% 45.0% 44.3% 42.1% 39.3% 36.9% 35.9% 41.0%
67.0% 68.1% 60.7% 60.6% 59.6% 58.1% 55.5% 51.8% 57.5%

Part 2
This is interesting. The #9 AL hitter has a 26% chance of scoring from 1B (given that the typical 1,2,3 batters are coming up). The leadoff hitter has a 52% chance of scoring from 2B (given that the typical 2,3,4 batters are coming up). This means that if the leadoff hitter gets a walk, he add .26 runs to the value of the #9 hitter. That is a big difference from the .18 league average, and completely due to the batting order.

Anyway, these are the "base-runner advancement" for each spot, 1B-2B, 2b-3B, 3B-HP, 1B-3B, 2B-HP, 1B-HP:
0.262 0.186 0.123 0.161 0.171 0.154 0.170 0.174 0.221 0.180
0.242 0.159 0.116 0.182 0.181 0.148 0.158 0.163 0.234 0.174
0.346 0.298 0.316 0.382 0.385 0.392 0.414 0.425 0.425 0.378
0.439 0.368 0.309 0.349 0.340 0.324 0.333 0.329 0.415 0.359
0.540 0.475 0.498 0.567 0.573 0.561 0.583 0.588 0.580 0.540
0.737 0.684 0.691 0.734 0.733 0.737 0.758 0.754 0.761 0.737

The chance of taking an extra base, for S (man on 1B), S (man on 2B), D (man on 3B) is pretty constant and comes in at:
33%
65%
42%

The chance of coming up with a runner on 1B, 2B, 3B is:
23.9% 29.9% 31.9% 35.4% 34.3% 34.0% 33.8% 32.9% 31.8%
17.0% 20.0% 22.0% 22.9% 23.0% 21.7% 21.4% 21.6% 21.3%
8.9% 10.2% 12.1% 13.3% 12.1% 11.9% 11.5% 11.5% 11.1%

Part 3
Working all this out for part 2, and adding in part 1,here is the LW by batting order (last column in batting order neutral:
0.497 0.485 0.440 0.497 0.488 0.450 0.462 0.457 0.499 0.474
0.783 0.777 0.728 0.787 0.790 0.755 0.756 0.763 0.809 0.770
1.000 1.014 0.986 1.055 1.037 1.006 1.003 0.999 1.067 1.014
1.299 1.330 1.368 1.441 1.430 1.419 1.429 1.424 1.413 1.392
0.402 0.384 0.322 0.354 0.355 0.324 0.334 0.325 0.368 0.352

Doing the same in the NL and we get:
0.481 0.481 0.459 0.492 0.460 0.438 0.401 0.423 0.499 0.459
0.741 0.749 0.737 0.785 0.760 0.729 0.707 0.708 0.788 0.744
0.954 1.001 0.969 1.027 1.012 0.995 0.974 0.955 1.035 0.980
1.284 1.319 1.361 1.421 1.416 1.414 1.419 1.437 1.460 1.397
0.377 0.381 0.345 0.354 0.324 0.306 0.265 0.285 0.358 0.330

I'll have to think about how to figure out the out value.

That's it for now...

You notice that the biggest difference between the AL and NL profiles is not the #9 hitter, but rather the #7 and #8 hitters. Because those batters are the players most influenced with the fact you have the "automatic out" coming up after them, the value of each of their offensive events falls drastically. The value of the #9 NL hitter however looks normal (or even better), because he's got the top of the order coming up.

These LW figures are based on an average batter at the plate, but the typical batting-spot players coming up. However!! However, if you start rebalancing a whole lineup, and put let's say Larry Walker in the 7 spot, these LW values will no longer hold. Barring such a major move like that, these LW values are pretty useful.

(There is actually a tiny thing I have not considered, which I have explained in a previous post as to what I'd need to get around it. But the effect would be very minor, and so I consider these figures to be almost perfect.)

I will tackle the outs issue in another post, and maybe base-stealing. As for base-running, I would need to know how often each player in each batting spot takes the extra base (Single Man on 1B, Single Man on 2B, and Double Man on 1B). MGL, if you have that handy, that would be great!

Good stuff.

As far as the outs, all you need to know is that, in your system, outs decrease the scoring probabilities of all runners on base and who subsequently reach base in the inning. All a CS does is decrease the scoring prob. of the runner from what it was to zero, plus decrease the scor. prob. of all other baserunners. If the average scor. prob. of the ruuner is .27, and the ave. sc. prob. of other runners, adjusted for their frequency, is .09, you'd have .36. Since the average is around .09 to .10, and there are probably fewer other BR in innings which feature a CS, this would reduce the .09 to, say, .05, in which case the CS is -.32.

Of course that's outs. If you want outs above average, that's harder to do in the system you have.

David,

First, the CS is not as easy as it seems. While .27 is the average value, the average value for the leadoff hitter is higher. However, if the leadoff hitter only steals when the #3 batter is at bat, then it's not the scoring rate for the leadoff hitter that needs to be used but the #2 hitter! That is, if a #1 hitter or #2 hitter steals when the #3 hitter is at bat, they obviously have to use the same figures. So, while all the other offensive events were easy, this one is not. What I would need to know is how often does each of the batting spots steal with the next guy, the guy after him, and the guy after him in the order. If the #1 hitter ALWAYS stole with the #2 hitter at bat, then I'd have no problem using the information I currently have.

I haven't given any serious thoughts to the out issue, but I will soon....

Tango et. al.,

I haven't forgotten about the requests for more data crunching. They are forthcoming. I am also almost finished with my min-sim, which will enable the user to test any batting order (you input a stat profile for each slot). It is a DOS .exe file.

Yes, I see. Good luck, Tango.

I was just trying to emphasize that outs are directly tied to baserunners. People like to say that on a CS you lose a BR and and out. But the out has no effect unless there is another BR. For that reason, the cost of a CS (and GDP) tends to be overestimated. And if a batter makes an out in an inning in which nobody reaches base, the out does not have negative value; it's neutral. (Of course, it still shortens the game, but that's not part of runs.) And I'm, of course, talking about runs, not runs above average.

Tangotiger, I'm trying to understand your figures.

Part 1
The chance for the leadoff hitter in the AL, to score from 1B, with 0/1/2 outs:
44%
28%
13%
The frequency he will be on 1B with 0/1/2 outs:
6.1%
8.5%
9.3%
Multiplying the two, the chance of him scoring overall from 1B:
31.6%

I don't see the relevance of "frequency he will be on 1b".
Do you mean frequency he will be at bat with 0/1/2 outs?
I assume that you are calculating the value of, say, a single as equal to the chance of scoring from 1B plus the chance of advancing a baserunner. So the value of a single with no outs would be .44 + base advancement, but only .13+ with two outs. To combine these, you would need to weight by the frequency of plate appearances with 0, 1 or 2 outs, right?

Assuming so, I can't combine those figures to get your 31.6%. Adding the frequencies, we get a total of 23.9%, so we need to divide each frequency by that to make 100%. .44*(6.1/23.9) = .112, .28*(8.5/23.9) = .100, .13*(9.3/23.9) = .051, total is .262, looks like the average chance of a leadoff hitter scoring after reaching first is only 26.2%.

Since your linear weights look reasonable, I must be missing something.

David, it took me a while to understand your assertion if a batter makes an out in an inning in which nobody reaches base, the out does not have negative value; it's neutral. I guess you mean there will always be three outs in an inning. It seems to me, however, that each out clearly denies at least one batter a chance to hit, say, a home run that inning. So there always appears to be a loss of potential; isn't that a negative value?

Beyond that, there is an effect significant at least in the National League. A good example would be the #8 hitter at bat with 2 outs and no plans to pinch-hit for the pitcher. If #8 makes an out, the next inning begins with a likely out, but if #8 reaches base and #9 ends the inning, the next one begins with the maximum-run-potential top of the order.

Tangotiger, would it be possible to calculate a LWBO for 0, 1 and 2 outs, then combine those figures for an overall? I was thinking that method might make it easier to understand the value of an out, and would certainly be interesting -- for example, how valuable is a leadoff walk to start a game?

I'm also wondering if a simulation might be easier after all. Maybe I'll try that if no one beats me to it.

lexoglan, the loss of run 'potential' relates to runs above average, not runs. In runs above average (L Wts), the inning starts with a run 'expectancy' of .56 or so. In runs, or reality, a team starts an inning with zero runs. If someone reaches base, an out will decrease their chance of scoring before the inning ends. But if noone reaches base, the out has no actual effect (other than shortening the game, which is in the realm of runs per game, not runs).

As usual, I spoke too fast.

The frequency PA for a leadoff hitter, with 0,1,2 outs:
47.2%
26.6%
26.1%

Multiplying the 2 gets you the 31.6%. I will put the spreadsheet on a website soon, so that you guys can download it, and have fun with it.

As for the simulation, it is definitely better. MGL is writing one now. I have a general one written as well, but I haven't looked at it for years. The problem with the sims is that I don't get into the meat of it, like I have this way. Right now, I am able to isolate very specific things. I prefer having BOTH of course.

As for the out, you two are both right. The out has TWO components. One is reducing the chances of the current runners from scoring, and the other is reducing the chances of FUTURE batters from coming to bat and scoring. So, if an inning always goes 1-2-3 (a perfect game), the out MUST be worth 0 runs. It must! The total runs of the game was zero, there were no positive events, and therefore the out is also worth 0. However.... however, the EXPECTATION that a team of 9 batters given 27 outs is that they should score 5.0 runs (0.56 RE at the top of each inning). Therefore, each out has a negative POTENTIAL effect of -5.0/27 = -.19 runs.

When I will present the value of the out, I will break it down into 2, so that you can figure out the actual Runs Created, and the plus/minus runs against average.

I look forward to your out analysis. The reason I started talking about the 'absolute' out value is that it seemed to be the part that is a natural part of your line of analysis. I'm not sure how you are going to incorporate the 'above average' part.

Okay, finally got some time to dedicate to this.

SB: These are the LW values by batting order
0.209 0.193 0.167 0.160 0.176 0.175 0.166 0.181 0.197

As you can see, the leadoff hitter gets the most bang for his buck. However, because the leadoff hitter gets so many more opps to steal with no outs, and with the best hitters behind him, the SB really adds some value.

CS: I broke it up into two parts. Part 1 is strictly the value of losing the runner from 1B, and that is:
-0.316 -0.309 -0.266 -0.267 -0.263 -0.242 -0.246 -0.239 -0.263

(All totals AL by the way.)

Now, the fun part, the out. The out has two run components. One component is when you get the out, everyone who is already on base has his chances reduced in scoring. So, the more outs you make with runners on base, the more your outs will cost your team. Here is that component by batting spot:
-0.104 -0.128 -0.129 -0.138 -0.131 -0.120 -0.119 -0.116 -0.128

As you can imagine, the leadoff hitter has the fewest runners on base and the cleanup hitter the most. If you only use this run component of the out, and you use the rest of the LW for the positive events, you get Runs Created (actual runs scored).

The 2nd component for the out is reducing the chances of the rest of your team from coming up to score. If you make alot of outs with no outs, you are really crushing your team. If you always make your outs with 2 outs already, well, the inning was almost over anyway. Here are those results:
-0.222 -0.198 -0.182 -0.173 -0.165 -0.163 -0.170 -0.194 -0.206

In this case, the leadoff hitter takes a big beating, while the 6th hitter's outs don't cost as much. You would apply the 2nd component for the out if you want to figure out the plus/minus LW.

Adding up the outs, and we get:
-0.326 -0.326 -0.310 -0.311 -0.296 -0.283 -0.289 -0.310 -0.334

I'll have to go through my calculations again to confirm I did everything fine.

Anyway, back to the CS, we need to add the 1st out component to get the true CS value:
-0.538 -0.507 -0.447 -0.440 -0.428 -0.405 -0.417 -0.433 -0.469

As it turns out, regardless of batting order the break-even SB% is around 70-72% for every spot.

I've tinkered a bit with my formulaes, so here are the overall LW for the AL, and then NL:
0.488 0.509 0.484 0.507 0.503 0.476 0.473 0.468 0.488
0.788 0.806 0.772 0.808 0.817 0.789 0.775 0.783 0.807
1.020 1.046 1.028 1.090 1.074 1.048 1.029 1.028 1.074
1.318 1.362 1.410 1.475 1.466 1.462 1.455 1.452 1.420
0.378 0.388 0.344 0.348 0.351 0.331 0.331 0.322 0.351
0.209 0.193 0.167 0.160 0.176 0.175 0.166 0.181 0.197
-0.538 -0.507 -0.447 -0.440 -0.428 -0.405 -0.417 -0.433 -0.469
-0.326 -0.326 -0.310 -0.311 -0.296 -0.283 -0.289 -0.310 -0.334

0.470 0.495 0.488 0.505 0.489 0.463 0.429 0.438 0.480
0.746 0.768 0.766 0.806 0.799 0.762 0.743 0.733 0.779
0.972 1.022 0.994 1.058 1.061 1.035 1.017 0.988 1.036
1.302 1.341 1.386 1.452 1.465 1.454 1.462 1.470 1.461
0.353 0.378 0.359 0.354 0.331 0.313 0.275 0.280 0.332
0.189 0.169 0.164 0.168 0.174 0.163 0.175 0.152 0.160
-0.523 -0.507 -0.447 -0.424 -0.385 -0.366 -0.347 -0.374 -0.448
-0.309 -0.309 -0.291 -0.286 -0.263 -0.249 -0.254 -0.269 -0.318

I'll post my spreadsheet soon, so you guys can have some fun with it. Much thanks to MGL for providing all the seed data.