The new modified NERP

Thanks, Marc. Looking forward to reading more. Just curious, what was your Nerp for T. Holt? Not that I've ever used him, but he's got 15-8 with a bunch of pickoff chances, so I would probably just set him to never steal. But, he does have 16 speed which should give him something.

So the formulas are

expected_SB=
=[sent*(first-12)/20*9,3*(first/20-0.13)] minus cs_d plus held_prob
expected_CS=
=[0.85*sent*(first-12)/20*9,3*(1.15-first/20)] minus cs_d/36*expected_SB
where CS is never more than SB+2.

and where
sent = chances that the runner is sent to second base
first = first steal number
second = second steal number
cs_d = chances that the runner is directly caught stealing
held_prob is the probability (based on 100%) that the runner will be held (as explained above)

running NERP =(exptected_SB*0,17-expected_SB*0,28)+(((speed-8)*0,23-0,6)+(162-sb-cs)/162*held_prob*2.57))

Holt's steal rating is (*2-8,11/9,10,12 (15-8)), which translates to
sent=27 chances
first=15
second=8
cs_d=9 chances
held_prob= 80%

expected Sb
=27*(15-12)/20*9,3*(15/20-0.13)-9+0.8
=27*3/20*9,3*(0.62)-9+0.8
=15 SB

Doing the same for cs, I get 16 CS.

So if you let Holt run free, he'll produce a worse value than if he shut him down, because 15 SB X 0.17 - 16 SB X 0.28 produce a negative value.

Instead, if Holt stays on his base, his running NERP will be of:
(((speed-8)*0,23-0,6)+(162-sb-cs)/162*held_prob*2.57
(((16-8)*0,23-0,6)+(162-0-0)/162* 80% *2.57
=3.3 NERP.

minus
regular_outs * .10 (lineouts, K)
gbC/flyA * .04
gbB/flyB * .07
gbA * .15

Marc, I'm reading through this again because I think it's pretty cool stuff. One question. You're giving a little value to gbB, above. But, doesn't gbB result in the lead runner being out, so no bases are gained? Or, is there some other advanced set of rules that I'm missing there.

Just to be clear, all the values you quote are negative values. So each chance of gb/flyB is worth -0.07 and each chance of lineouts/K are worth -0.10.

The reason why gbB is worth 0.03 more is because it can move the lead runner is some instances, for example when a gbB is hit at second base with a runner on second (he moves to third). Also, when the defense is playing back, there are multiple situations where a gbB or a G2 (on defensive chart) produce a run---in such situations, most of the times, the runner on 3rd scores and either the runner on first or the batter is out.

When defense is playing in, then gbB never produces a run, unless a gbB+ is obtained, but even then, with men on corners and defense playing in, a gbB advances the runner at first to second base.

The last part one has to do to produce the ultimate NERP is to integrate playing time in the ratings. Both for hitters and the pitchers, this part is the most difficult part.

Playing time for hitters involves three separate things:
1) the impact of injuries and the value of replacement players
2) the impact of batting order
3) the impact of platooning

Injuries
As I wrote earlier, I based my projection on a full season of 688 PA, so first part is easy, I first assume that a player with no injury will play the full 688 PA.

After that, it's a matter of properly calculating the probabilities of getting injured. For example, players that cannot be injured for more than 3 additional game are expected to play seasons of 660 PA. Per convention, in part because defensive charts are based on roughly 659 PA, I assume that 660 PA represent a full "regular" season. Hence, players with no injury play 688PA/659 PA X 100% = 104.5% (in fact, with decimals kicking in, I have it at 105%)

Number of PA expected per season for every level of injury risk:
players that cannot be injured: 688 PA, 105% of a regular season
players that cannot be injured for more than the remainder of a game: 683 PA, 104%
players that cannot be injured for more than 3 additional games: 659 PA, 100%
1-rated players that can be injured for more than 3 additional games: 639 PA, 97%
2-rated players that can be injured for more than 3 additional games: 596 PA, 90.5%
3-rated players that can be injured for more than 3 additional games: 559 PA, 85% (129 missed PA)
4-rated players that can be injured for more than 3 additional games: 526 PA, 80%
5-rated players that can be injured for more than 3 additional games: 497 PA, 75%
6-rated players that can be injured for more than 3 additional games: 471 PA, 71% (217 missed PA)

There are a few things that I have assumed to get these totals:
1) injuries happen after the at-bat has been played out. So of course, you have to include that at-bat as being played. In other words, even though a player has an injury "for the rest of the game" in his last at-bat, in fact, he played all his at-bats and thus has missed zero PA.
2) defense is not always played out when an injury occurs, and running is never played out when an injury occurs, but the difference in expected percentage of defense and running compared to offense is so small that it can be assumed to be meaningless.
3) A 6-rated player has twice the chances of looking at the injury chart compared to a 3-rated, but this does not mean that he will miss twice the amount of PA. He is not expected to miss 258 PA (129 PA X 2, which would be twice that of the 3-rated player), but 217 PA, because when this 6-rated player is on the injury list, he has no chance of getting another injury. This might seem counter-intuitive, but it's similar to electric car autonomy: If car A has an autonomy of 180 miles before necessiting a battery charge, and car B has an autonomy of 360 miles, and each car needs a full hour for the battery to be recharged, after a full day of drive, car B won't be twice far ahead of car A, because they are not rolling when the batteries are recharged.

A last but important (and controversial) issue: should we include in establishing the value of players with high injury risk that there is a baseline level that is expected from any cheap bench?

Considering catchers. In strat, we all know the rule that requires a minimum of 2 catchers in the lineup, and that other rule which specify that the last healthy catcher cannot be injured if other catchers are on the injury list. So all teams, even those with Lucroy, must spend at least 0.50M on a second catcher. Let's say that the baseline value of a not-too-bad 0.5M catcher, say J.Molina, is worth around 18 NERP over the course of a full season. We established that Wieters is expected to play 471 PA (and miss 218 PA), while Lucroy is expected to play 659 PA (and miss 29 PA).

It seems to me obvious that the right way to establish the value of Wieters and Lucroy is to incorporate the value of that baseline catcher. I integrate to Wieters' and Lucroy's value the baseline value exemplified here by J. Molina since the rules oblige my team to have at least such a baseline. So I end up adding 5.9 NERP to Wieters and 0.8 NERP to Lucroy.

The argument is similar for other positions. While the rules don't force my team to have specifically a back-up first baseman or third baseman, the rules do force me to have at minimum 4 to 5 bench players. So in my ratings, I assume that I can have bench players that cost 0.5M who cover all positions. In other words, I apply the same logic of incorporating to the value of any player during his absence the baseline value of a bench player at no extra cost.

For any position, I calculate the NERP value of roughly four to six players costing no more than 0.54M and I incorporate the average value into every player. With a few exceptions, these bench players are all worth between 15-20 NERP regardless of the positions. So to ease my ratings, I simply assume that there is a baseline of 20 NERP available at no extra cost than the 0.5M I am forced to spend for any position.

Batting order
Players at the top of the lineup will always have more PAs than players at the bottom, simply because their chances to getting an extra at-bat is higher. Assuming that a full season represents 688 PA per player, we can expect the following PAs per batting order:

1 ... 752 (almost 10% more than the fifth spot)
2 ... 736
3 ... 720
4 ... 704
5 ... 688
6 ... 672
7 ... 656
8 ... 640
9 ... 624 (10% less than the fifth spot)

Take for example Altuve and Dozier. Let's assume that Altuve is a natural lead-off hitter and that Dozier will typically be used down in the batting order. Both have similar injury risk. Of course, Altuve is the better offensive card and Dozier has the better glove. If we assume that both players has 683 PA offensively and 200 defense rolls on the X-charts, then I guarantee that our ratings will be heavily biased towards the defensive player. But in reality, Dozier might not be the better choice, because he is unlikely to have 683 PA, he's likely to have something between 656 and 624 rolls, while Altuve will have his best asset, offense, being played over 750 PAs. In other words, if you want your ratings to beat out how SOM evaluates players, you have to "guess" how REALLY players will be used offensively.

This said, considering the number of at-bats is not sufficient. As Tom Tango and al. showed in "The Book", the first hitter will have much more at-bats with bases empty than any other lineup position. In contrast, the 4th and 5th hitters are much involved, proportionally speaking, than any other hitters in high-leverage offensive situations, in "rbi situations" or "clutch" situations as traditionalists would say. When we combine the increased at-bats at the top of the lineup with the higher leverage that we have at the middle, we end up, if we simplify a bit, that the first four positions of the batting order are roughly of equal importance, with the fifth position slightly behind, while positions 6 to 9 are in descending order of importance.

I have came up with a formula that follows this logic: Players that are expected to play in the first four batting order positions, either because of their on-base and/or their slugging, should be given a playing time adjustment between 104% and 106% while the other players should be given a lower ratio playing time that depends on the quality of the offensive card, but which could be as low as 90%.

Of course, the logic has to be applied separately vs lefty and righty pitching.

To illustrate, here is a list of players who get an adjusted playing time of 104% or more
Trout,M___
Bautista,J
McCutchen,
Rizzo,A___
Martinez,V
Abreu,J___
Cabrera,Mi
Brantley,M
Freeman,F_
Harrison,J
Pearce,S__
Ortiz,D___
Posey,B___
Martinez,J
Gomez,C___
Stanton,G_
Puig,Y____
Altuve,J__
Betts,M___
Turner,J__
Martin,R__

(Tulowitski and Goldschmidt are not in this list because of their high injury risk---they would get the maximum of 105% if they were not injured).

Some players are there for their on-base (Martin, Altuve), but they are all expected within the first five spots of the batting order vs both lhp and rhp.

As I wrote, if I don't make this adjustment, then my ratings awfully undervalue the best offensive players who don't have good defense, players like Martinez or Abreu.

3) The impact of platooning

As I wrote above, the baseline I use for a bench player is a minimal value of 18 NERP at no extra-cost to the 0.5M I am forced to spend on this player. 18 NERP is roughly equivalent (assuming a 28%/72% lhp/rhp ratio) to get a baseline of 5 NERP vs lhp and 14 NERP vs rhp. So if a player has a NERP value under 5 NERP vs lhp or 14 NERP vs rhp is automatically assumed to be better used as a platoon.

Let's take Ruf as an example. His overall NERP vs lhp is 74.0 and vs rhp is -19.0 (he actually costs his team when he plays vs rhp). Of course, even if Ruf only starts vs lhp, he never only faces lhp---Hal leaves him there when right-handed relievers come, and there are a few at-bats here and there vs rhp coming from the bench. My own assumption is that a player that starts 28% of games vs lhp will end up facing 21% of his at-bats vs lhp and 7% of his at-bats vs rhp (for the 72% of starts vs rhp, I use 8.6% of at-bats vs lhp and 63.4% of at-bats vs rhp). Ruf is expected to play 80% of his games when not injured (in other words, he is expected to start 22.4% of all games started by a lhp, instead of 28%---the rest (100%-22.4%=77.6%) is expected to be played by a baseline player. So combining together:
80% X (74 * 21% + (-19) * 7% ) = 11.4 NERP when starting vs lhp

The rest is given by the baseline value:
77.6% X 20 NERP = 15.5 NERP

This said, Ruf is expected to bat in the top 5 slots of the batting order, so he should receive a primium for playing time vs lhp, while the baseline player I assume for Ruf vs rhp is roughly 93% (as if that baseline would hit in the bottom of the line-up, but not necessarily 9th):

11.4 * 106% = 12.1 NERP vs lhp
15.5 * 90% = 14.4 NERP vs rhp
For a combined of 26.5 NERP

This 26.5 NERP is good for an estimated pricetag of 1.46M (bare in mind that 18 NERP was my baseline for a 0.5M bench player).

If we had included Ruf's value strictly limited to games started vs lhp, his value would stand at 11.4 NERP, below the value of bench players like Corey Hart (NERP=20.7) or M.Choice (NERP=20.3), which would not make sense.

So if I rap my series of posts, here is how I get the new ultimate updated NERP:

offense + running - defense (that is adjusted for each position) X playing time (injury X batting order adjustment X platoons, fulfilled up to 688 PA by a baseline value of 18 NERP)

I'll use a few examples to illustrate my ratings later on.

Marc is the only player I know that prices players according to his values.

I want to ask Marc if he thinks players are priced in a neutral park, or their home park--or can you tell at all.

As players seem to vary up and down some being deals in a neutral park, and some being pricey--I always kind of wondered if Strat prices players in their home park. This would explain why some are deals in a pitchers park and some are deals in a hitters park.

It's quite obvious for the three years I have played that a player like Ortiz, who always has 8 BP HR from a 1 (L) HR park--is worth much more in a park like GAP. Instead of 30-35 HR he will hit 55-60, and Ortiz always is a deal price wise in a power park--and even in a neutral park he seems like a good priced player to me--even playing him at 1B with the poor fielding since 1B gives up the least OPS with poor fielders, also you can't get worse than a 5 range when you hold runners anyway. 4 rated 1B fielders are 5's anytime runners are held.

sorry Milleram, for the delay.

In my own ratings, I assume a neutral stadium, but I believe that Strat price their players NOT in accordance to neutral parks, but to their "best valuable parks". In other words, Strat "assumes" that the player is likely to play in a stadium that fits its best value, so Strat pushes up the price of the player relative to his "true" value in a neutral stadium.

This is the reason why players like Yelich or Altuve appear so overpriced in my own ratings---their value, relatively speaking, get a hit when you assume a neutral ballpark because they don't have the ballpark homeruns that most players have.

Another category of players that are likely overpriced by this "best valuable park" criteria are non-dh non-platoon sluggers whose value comme mostly uniquely from their slugging, players like José Abreu, Gattis, Dunn. My ratings have them almost 1M below their pricetags. These players have bad defense, and usually have bad numbers relative to clutch and gbA, so their value takes a hit when they are not playing in a power stadiums as if these players don't have much left to offer.

In contrast, players like Trout or Soler are not as likely to be overpriced because they provide value from other means than their slugging---by their defense, or direct hits, so they have good value even if they play in a neutral stadium.

Ortiz and a few other players like Carter are in another category. They seem to fit the Abreu-Gattis group of sluggers with little other assets, but in fact they are truly dh cards. I mean by that that their cards are so bad defensively than you can presume they are likely to play dh. In these cases, the cards are usually a good value because of another pattern---Strat prices the card as if they were playing in the field. What the value they seem to lose from "not fitting a neutral stadium" is gained back from "not hurting with their defense". Expressed otherwise, the worse defensively, the better the value.

So, while Ortiz is a much better value in a power stadium, he's still a good value, at least in my ratings, if he plays a neutral stadium. I have him worth at 6.62M for neutral stadium and he's priced at 6.38M.

Thanks for the reply Marc, I was offline for a couple of weeks due to moving--just got back.

I have to say that pricing players in the best park (presumed production stat wise I assume) for each individual player would probably make most players seem overpriced, unless you picked the park they would perform the best in.

I assume weak powered hitters are priced in low Homer, high Singles parks, and High HR players are priced in high Homer, high singles parks.

players like Lucroy who are a lot of Doubles (or guys with Triples too), but lowish HR with N power should be the ones least susceptible to bad/good park matches, therefor more neutrally priced I'm guessing.

If the three outfielders have an arm rating of -1, then collectively, the value of this asset can simply be computed with the same unit (0.23) X 9 (to go across the lineup) = 2.07. Then I must distribute that value (2.07 defensive NERP for each -1 arm rating) between the left fielder, the center fielder, and the right fielder. Not knowing how to do this, I took the arbitrary decision (based on my experience of playing online strat) to distribute the value the following way:
1) 2.07*arm_Rating*15% for left fielders
2) 2.07*arm_rating*50% for centerfielders
3) 2.07*arm_rating*35% for right-fielders

Close. It's actually 20% LF/45% CF/35% RF. This is per my Uncle Ross who taught math at the Air Force Academy and arrived at those figures via linear regression.

That's the extent of my contribution to this community's knowledge, because Marc's contributions were already so comprehensive and accurate. I've followed his system and finished #1 in my first Barnstormers regular season, and when I complete 50 teams in a few days I'll debut on the leaderboards with the 2nd-highest winning percentage all-time.

Here are a few more helpful links I can contribute (many of them also by Marc):
http://www.ultimatestratbaseball.com/US ... ry2016.htm
http://www.ultimatestratbaseball.com/US ... ry2016.htm
http://forum.365.strat-o-matic.com/comm ... 6&t=641226 arm value
http://forum.365.strat-o-matic.com/arch ... 1&t=567231 lots of fun simulation-derived analysis, including the "More Baserunning Decisions" setting
https://tht.fangraphs.com/why-woba-works/ such a good linear weights explainer, especially how outs are valued
http://tangotiger.com/index.php/site/ar ... foundation
https://www.baseball-reference.com/abou ... ined.shtml

edit: Pelletier on catcher defense: https://forum-365.strat-o-matic.com/com ... b1c8243ace
More recent catcher defense thread: https://forum-365.strat-o-matic.com/com ... 2e481e1c51