Offense vs. Defense article

[childsmwc]

Dean,

I took a look at your grid, and I have one very similar in evaluating the true impact of range/error mix on team runs allowed. We both computed the error % the same way. From there our methodologies differ but I look forward to walking through your analysis.

The main difference is after I compute the error probabilities, I then multiply them by the D-20 probabilities for the range factor, to come up with an actual OBP/SLG impact for each defensive combo. I then take those results and filter them through expected fielding attempts.

Again I look forward to examining the model and see if it can fine tune my approach to pricing, or validate some of the math behind my numbers.

Bbrool

[maligned]

I would make a couple comments about calculating value using your system.
First of all, I think it's a nice system to use to calculate the relative values of two players potentially playing the same position and batting with the same hand. I also think it's a nice starting point for determining some good overall value comparisons. As you said, there are some tweaks still to be made for speed, arm strength, etc. Here are some additional considerations:

1. This system is not comprehensive in its usage of calculating player card values in DH leagues until you consider a baseline "replacement" NERP value for defense so that defensive NERP works as a bonus for a baseline offensive value, not just a subtractor. Let me explain: Manny is often drafted as a DH because he has below-average defense. In fact, a normal NERP for an outfielder in an 80M league may possibly be about 3.5 NERP. Anything above 5 NERP for an outfielder might actually be considered "bad" or "replacement" level. If I were calculating outfielder values, I would probably choose a baseline "replacement" level around 5 NERP, then calculate my player's value as this: ON + (5 - DN), where ON represents offensive NERP and DN represents defensive NERP. Thus, any player that has a NERP better than my "replacement" level of 5 would receive a player value bonus. And, any player that is worse than a 5 that I'm choosing to play in the field would in fact hurt his value. This way, a player such as Manny (or someone even worse) who doesn't play the field could maintain a static value equal to his offensive value only (the "5 - DN" defensive component of the above formula would not be considered).
So, in considering Manny's overall value in relation to other offensive players, I would consider him a 30.9 NERP and not factor in his defense. For Crawford, I would of course consider his defense and label him a 25.5 NERP (20.2ON + (5 - (-0.7DN)). If I wanted to consider Manny as an outfielder, I would downgrade his value to 29.7 NERP because I would consider his 6.2 defense to be below my theoretical "replacement" or "bad" value of 5.
If you're familiar with the concept of "replacement" value, this should make sense. Again, the above point is designed so that those players with defensive ratings considered below "replacement" simply maintain a baseline value equal to their offensive value since they can function as designated hitters and not penalize a team with their bad defense.

2. The system described in the paper doesn't consider the fact that righthanded hitters and lefthanded hitters face drastically different average results from pitchers' cards. For example, a righty hitter will face much tougher righty pitching card results, on average, than lefty hitters will. To begin to compare lefthanded hitters' values with righthanded hitters' values, an expected average opponent NERP for each type of matchup (righty vs. righty, lefty vs. righty, righty vs. lefty, and lefty vs. lefty) must be established in addition to considering the frequency of righthanded and lefthanded pitching faced.

3. Finally, a "replacement" or "bad" value for hitters needs to be considered. In other words, at some point, the hitting becomes bad enough that it would be considered detrimental to a team (much like the effect of bad defense described in point #1). For example, if your theoretical "replacement" offensive NERP value is 12.5, Manny's offensive value might actually be calculated to be ON (30.9) - 12.5 = 18.4. Then, a player having below-replacement value offense has no value unless he plays above-replacement value defense. Thus a light-hitting, slick-fielding shortstop with an offensive NERP of 12.8 and a defensive NERP of -4.0 might end up with an overall value (considering 12.5 as offensive replacement and 3.0 as SS defensive replacement) of say 7.3 compared to Manny's 18.4 (which incidentally comes close to the comparative values of Manny and Alex Gonzalez in TSN's dollar values--you're definitely on the right track with your theory).

I hope some of this makes sense. Again, if you've read papers on the theory of "replacement" value, this makes more sense. A typical "replacement" zero line is considered by Baseball Prospectus to be .729 * League Average for offensive value output ratings. BP doesn't do much with defense.

Any thoughts, Dean?

[Mean Dean]

I absolutely agree with almost all of that. I don't think it's necessary to come up with "reversie" rankings for each player, but what I think I need to do is measure performance per 186 PA, where 108 of those PA come off the hitter's card, and 78 come off the pitcher's card. The pitcher's card results will tend to equalize the players -- for instance, Alex Rodriguez and Brad Eldred, who obviously have very different expected results off their own cards, are going to have identical expected results in the 78 PA off the pitcher's card, since they both bat righty and both have N power. But for switch-hitters (who will have the platoon advantage more often) and for players with W power (who are currently being treated in my system as equivalent to N power hitters with 0 ballpark HR), incorporating those pitcher's card PA will be significant.

And yes, in order to rank everyone in a league properly, the concept of replacement value does have to be introduced. I say towards the very end of the article:[quote:4f6ce64e48]The system does indeed rank great glovemen up the middle as the most valuable defensive players, and no one is going to argue with that. However, it also ranks bad glovemen up the middle as the least valuable defensive players, and at least from a “general manager” point of view, that can be argued with. It’s certainly true that a terrible SS who gets 63 chances to be terrible will cost the team more runs than a terrible 1B who gets 18 chances to be terrible; that is just a fact. But, somebody does have to play SS for you and handle those 63 chances. Ultimately, your SS’s defensive value depends on who else could be playing SS for you, and what that guy would do defensively. That in turn depends on league size and other factors. For these reasons -- although I believe this system does hold up remarkably well when comparing players who play different positions -- if you want to get into doing that with true accuracy and/or customize it for a particular league, you need to get a little more complex. I will hopefully write more about this in the future as well.[/quote:4f6ce64e48]I think that gets at the same point you are, albeit in a different way. If we knew that the replacement value SS in a given league is worth X runs defensively, then we can both know how much the other SS are worth, and by using that number as a jumping-off point for determining the replacement value at the other positions, we can know how much everyone else is worth. That's what I'd like to do, but it's easier said than done. As you mention, it is not only a question of how many runs the player saves/costs compared to other fielders at his position, it is also a question of how easy it is to fill the position (with DH being the ultimate example of this.) As bad a defensive SS as Hanley Ramirez is, is he still worth more defensively than a LF-1, when you put proper value on the fact that he can play SS at all? How about a 2, 3, 4 or 5? How many runs' difference are we talking about in each case? These are complicated questions, and it gets even more complicated when you consider play-by-mail SOM as well, where not every league is 12 teams as it is in TSN. But I do hope to chip away at this.

Thanks for the comments, and let me know if my responses address your statements, because I think they're important.

[maligned]

I completely agree that basing the offensive ratings out of 186 and considering the average expected NERP values from the pitchers' cards in the various matchups will answer my concern in point #2 from my post. Nailing down the average results of the 78 chances from the pitchers' cards isn't absolutely pertinent for a given league, but nailing down the expected average DIFFERENCES between righty v. righty and lefty v. righty (in general) is important.

I see now from your most recent post that you do get at the idea of replacement value a bit in your article. You're absolutely right, figuring out baseline replacement values is very tricky considering all the variables of different types of leagues. I would love to get inside Bernie's head and know the method TSN uses for finding baseline production that determines the .50M starting point in TSN's pricing system. Although there may be values here and there that geniuses may disagree with, his pricing system for 80M leagues is highly effective. He and whoever else works on the system must do a LOT of research and data entry from season to season to have improved the methods so significantly over the past 5 years.

[childsmwc]

While we are on the topic of factors to consider when evaluating players another factor that has an impact is the pricing for standard deviations. If a player is expected to get 730 PA's over a season, we know that on average 365 will result from his card.

The only other thing a batters card impacts is defense. If a player plays a full season in the field he can expect on average say

195 results as a SS due to his X chance rating
167 as a 2B
83 as a CF/3B
56 as a 1B/LF/RF

Now assuming you have a good expected run model for each component of the equation, compared to a replacement level player, it should be as easy as adding offense expected runs + defensive expected runs to get your answer. However, this only holds true after millions of events.

In an average league with the above results as a guide, the batters results occurring over 365 trials will have a lower standard deviation, than a SS trials of 195, than a 2B of 167, etc, etc. In fact if you determine that a RF and a 2B will both cost you 20 runs from the replacement level norm, should both be penalized the same when pricing?

The answer is no. Just like with stocks, a result with more reliability carries more weight when being valued.

Let me exemplify in the most simplest terms. If a batter with a .300 average gets 4 at bats in a game, it is not out of the realm of possibilities that he bats 1.000 or 0.000 for that game. As he plays more and more games the likelihood that he can remain on the extreme ends of the spectrum dimenishes to a point where the probability is impossible. While it might be expected that he hit .300 over 10 at bats or 10,000 at bats, over the 10 at bats the range of possible outcomes is much greater.

This was a dynamic that I could never put my finger on. Why could players get away with poor corner OF'ers, when my expected runs model showed that those players cost tons of runs. Basically when pricing the final card, results should be discounted based on their standard deviations.

Bbrool

[childsmwc]

As far as determining the average pitcher, I used to do extensive sampling in ATG to determine those results. And while yes they are different, they are not significant. Probably the most relevant piece of data that you need to know from a pitchers card is how many HR results will come from the average pitcher and how many ballpark HR's are on the average pitcher card.

These results determine how much to penalize weak batters. I will tell you that in the ATG environment, I was surprised at how few HR results are on the average pitcher cards used there.

In the end, those of us in the community that have our own RC model's to evaluate players, try to fine tune our assumptions and use more accurate assumptions than where originally used when pricing the players. These assumptions include, but not limited to:

The average pitcher
The average ballpark
The baseline hitter/defender
The value for each offensive and defensive component used in determing expected runs.
The average lefty/righty splits
Platoon values
PA assumptions based on injury expectations

I have a fairly complex model at this point, but I am always fine tuning/overhauling it as I discover new variables to deal with. Standard deviations is my current obsession. I know it should impact pricing, I just don't know the right discount factors for each expected run value yet.

Bbrool

[toshiro]

Hey DeanTSc -- I always like reading your stuff. In your defense vs offense, I have a great candidate for you -- 2005 Jorge Cantu. Love to hear what you'd say about him.

I'm wondering if some other factors, like the ballpark or the ratio of the pitchers (particularly the starting pitchers) WHIP that is comprised of hits might have some impact on determining how costly a given defense is.

So here I am, with a full blown desire to use Jorge Cantu. I love his hitters card. Never used it. I got Bonds in the draft and am prepared, even *desiring* to use Cantu in the field. I'm not quite crazy enough about him to put him at SS, so it's between 2B and 3B. My estimates put him at giving up 71 base runners at 3rd vs 80 at 2nd. My home park is the (mostly) pitcher's park of the Metrodome. My starting pitchers are Peavy, Clement, H.Ramirez, K.Wood, Bonderman. In weighing it, I think I'll put him at 3rd and not just because he has 9 less base runners given up. Let me explain why and you can tell me if it makes sense. If it does make sense, perhaps it would be another set of factors to add to the quantification of defensive liability.

Petco is notorious for crushing the ballpark homer. But that aside, it's also difficult to score because of it's low ballpark single. Compare that to the Royals park in ATGIII, where high scoring is prominant, in spite of a low BPHR. I like to think of Petco strategies in terms of permutations-- of consecutive events. And the Royals example seems to indicate to me that there is a threshhold, that at some point, the pitchers cards and defense loses it's ability to hold scoring down.

So why put Cantu at 3rd? Well, my rational is that of his 71 chances almost match the 80 at 2nd, a huge number of the 2B "giveaways" move a runner 2 bases. Since it's not uncommon to have a runner on 2nd, that means a run scores. Pound for pound, Cantu's giveaways at 2nd cost more than the giveaways at 3rd.

Here's how I break it down:

SI* SI** E1 E2
2nd 18 36 20 6
3rd 9 18 33 11

(Note: the E1/E2 numbers are guestimates)

Runner Moves
1 Base 2 Bases
2nd 38 42
3rd 42 29

Now if I were playing in a more homer like environment like US Cell, I probably wouldn't sweat the 1 Base/2 Base differential as much. But I'm in the Metrodome, where runs will have to be earned the old fashioned way. My SPs have a slightly higher WHIP that the average, perhaps, but less hits allowed than average. So I'm banking that my opponents, while they may get on a good amount, that they'll strand more runners. There are OF arms to play with as well, but I'll leave those out of this conversation.

So back to Mr. Cantu. Given my pitchers and ballparks, I think the basepads will be somewhat jammed when I'm pitching. That means 2nd base will be occupied more than average. I want to reduce the ability for my opponents to get that runner home in a single shot as much as possible-- force them to use 'two hit events' to get him in. If I can do that, based on permutations, that should reduce the chances of a score significantly. So I don't want Cantu at 2nd, where he more than 50 percent of the giveaways allow the runner to move 2 bases. This drops to about 42% at 3rd.

Now Jorge Cantu (hopefully) won't make or break my team, but this is the rationale I use to situate him as well as to make defensive decisions about the rest of my players. I try to calculate how much I can "get away with" without things getting too bad. This includes not just how many errors/hits, but the very nature of their composition. And I try to incorporate that using the SPs and ballpark to estimate the overall threshold between keeping things under control, like Petco, vs getting out of control, like Royals Stadium.

Does that possibly help explain this, bbrool:

[quote:a9953f08a6]This was a dynamic that I could never put my finger on. Why could players get away with poor corner OF'ers, when my expected runs model showed that those players cost tons of runs. Basically when pricing the final card, results should be discounted based on their standard deviations. [/quote:a9953f08a6]

[maligned]

See below post.

[maligned]

Dean,
I have to confess I've used your data recommendations extensively over the past 6 months to work on formulating rankings in a couple different ways. Ultimately, I've come to the conclusion that there is one significant change to your approach that needs to happen:

You are currently considering NERP/PA in your rankings when you should be considering NERP or RC/Out.

I realize that your theory was designed to create simplicity in compiling and evaluating rankings (raw offense minus raw defense equals value). However, what has happened as I've compiled and recompiled data is that SLG gets valued much more highly than it should and OBP gets valued much less than it should. This got me thinking about how an offense actually functions over the long haul.
In fact, what happens, for example, is this: If Player A has .390 OBP/.450 SLG and Player B has .350 OBP/.495 SLG, the two will have NERP values per 216 plate appearances of about the same. However, Player A will have accumulated almost 9 less outs for his team. This means then, obviously, that his team has 3 more innings in which to score runs, and said player's value should be higher because of his contributing to increasing team offensive opportunities.
A secondary problem that then arises is this: There's no way to calculate the value of a player without considering the environment within which his offense is produced (you can't simply use NERP/27 outs as a rating because high-OBP players will then be OVERvalued as their stats are multiplied against themselves).
What I finally did is this: I created a formula for calculating a player's offensive value within the context of an average TEAM. Thus, his stats and the average team's stats will increase the value of Player A from the above example in a realistic way.
For the current set of rankings I've compiled, I considered the average team offensive environment to be approximately (not exactly) .350obp/.450slg because I'm trying to figure out values for STAR face-to-face tournaments (essentially 200M live-draft tournaments).

Background for formula:
Each player plays on a team of 8 other players with .350obp/.450slg results (216 PA x 8 players)
Also, each player will face an average pitcher with .310obp/.390slg
I used Runs Created per out as my basis, rather than NERP/out
Also, I give a small speed bonus and SB bonus rather than consider it in my formula (based on some old Luckyman ideas). Thus, SBs/CSs are not considered.

Simplified:
((Player On Base + Team On Base) / (Team & Player plate appearances)) TIMES (Player Total Bases + Team Total Bases) DIVIDED BY (Team outs + Player outs) = RUNS CREATED/OUT

Multiply this amount by however many outs you want to consider and subtract the total expected by the rest of the team to reveal the amount contributed by the considered player. Add speed and SB bonuses as you like (in the formula or outside).

Detailed formula for 900 outs (about 20% of season)

vLEFT = verse Left-handed pitchers
vRIGHT = verse Right-handed pitchers
OB = Considered player's times on base on his card
BPHR = Player's ballpark homeruns
BPSI = Player's ballpark singles
CL = Player's clutch opportunities (these happen approximately 12% of plate appearances)
DP = Player's double play opportunities (these come in to play 18.75% of the time)
.32/.68 = Hitters face lefties about 32% and righties about 68%
633 = on-base of the rest of the average "team" (including opponent pitcher card)
TB = total bases on player's card
.26 = total base value given to walks and hit-by-pitch in runs created formula
HBP = hit by pitch
BB = walks
784 = total bases plus .26 BB/HBP bonuses for "team"
1944 = player plus team plate appearances
108 = player plate appearances
1203 = team outs
900 = outs considered for total rating (appr. 20% of season)
183 = runs created for rest of team
SPEED = speed bonus
SB = stolen base bonus

((vLEFT(OB+BPHR*.4+BPSI*.4+CL*.12-DP*.1875)*.32+vRIGHT(OB+BPHR*.4+BPSI*.4+CL*.12
-DP*.1875)*.68+633)*(vLEFT(TB+BPHR*4*.4+BPSI*.4+CL*.12+.26*(BB+HBP))*.32
+vRIGHT(TB+BPHR*4*.4+BPSI*.4+CL*.12+.26*(BB+HBP))*.68+784)/
(1944*(108-vLEFT(OB+BPHR*.4+BPSI*.4+CL*.12-DP*.1875)*.32-vRIGHT(OB+BPHR*.4
+BPSI*.4+CL*.12-DP*.1875)*.68+1203))*900-183+SPEED+SB

Total = Runs created within a league-average environment for 20% of season by a given player.

I obviously have additional thoughts on how this philosophy should cause us to reconsider defensive value, but I'll tackle that later.

[SteadyEddie33]

Many thanks to Dean, Bbrool, Maligned, et al... awesome discussion. I have to say all of you have made great points even as you continue to tweak the player value concept.

Without getting into the model details so much (i haven't the time at work ;) ), that last point by maligned brought to the fore what was going to be my comment here: the idea of an 'absolute' vs 'effective' player value, not just in the sense of variable pitching, defense, and ballparks, but the variable of lineup--which i love because as maligned notes, it brings us back a little closer to how the game actually plays out. It's not the individual ABs vs a particular pitcher in 'the void' that makes for great offense, and certainly not timely offense. It's the rallies that get extended so that the probability of Manny's double plating 2 or 3 runs as opposed to simply putting a runner in scoring position is brought to bear. Likewise, the defensive probabilities of extended rallies resulting in runs allowed--the Cantu example above includes some key hypotheses and potential tests, i think.

In a game where all it takes at times is a limited number of rallies in a handful of games, innings even, to swing a division one way or the other, I think the feedback(s) vis a vis an average, good or bad team context represents a lot of the seemingly minor differences you all see in terms of prediction vs performance...but ultimately they're only minor depending on parity among the teams of your league. The point about offense in Royals Stadium is ringing in my head. The right offenses, right lineups rather, can maximize that extra single when it comes, the wrong ones won't, or can't.

Appreciate you sharing the fruits of your crunching guys!