Thanks I appreciate it

Not sure it has an impact but you have a bigger pitcher universe (mine was 12×9=108) and it’s unclear the impact of the two extra stats. That said, the ranges seem generally in line.

I like your thinking (monte carlo pricing, etc) but i think that drafter behavior falls within smaller bounds than one might expect from game theory. Will have to check all league IP totals to see how much variation there was…

Agreed that holds adds complexity. I have never played in a holds league (i think the hold os stupid) but would virtually punt that stat given the turnover in MLB bullpens. Maybe I throw an extra dollar or two at a MR with great K rates (venters, robertson) but that’s about it.

You should join a Razzball Commenter League and try out a 130/130 strategy. Might prove interesting…

That actually surprises me a little. I thought relief pitcher value would go up as their numbers dwindled. Perhaps it has two do with the distribution of saves in your projections or perhaps a flaw in my reasoning. I still suspect the relief pitchers will get more valuable if you reduce their representation further.

I did a similar test with the data on my screen . . . except I rebalanced the $ per point numbers based on the top 140 pitchers for a 7×7 league (ERA,WHIP,K,W,SV,IP,HD) and then assigned dollar values to everyone.

Players bounced around in a range. After 8 iterations the range for some players was:

Halladay: 28.3 to 32.8
Cain: 11.9 to 13.7
Marmol: 7.7 to 9.1

The takeaway on this might be that dollar values are rather fuzzy values. (Which will remain true even with better calculations). Go the extra 15% on a player you really like.

That’s me. Nice to be immune to something I didn’t receive a shot for.

I haven’t read the whole comment thread below post #2 yet, but I did get far enough to say I am in a different camp. I would argue that when pricing players in roto the starting point (for an MxM league, closed player pool, perfect projections, no substitutions) is 50% hitting / 50% pitching and the key would be identifying how a particular league differs from that root case and what the impact of the differences are. I.e., leagues with different rules (and different player pools [including different years]) will have different batter/pitcher pricing splits. I think doing the observations is useful and may give you a better starting point than you have (and 2011 seems like a pretty typical year from memory [and I could be wrong on that] unlike 2009 and 2010 where all of the injuries seemed to be batters and pitchers stayed amazingly healthy.

Here’s a cut and paste job of a post I made over at Tango’s site, it’s an extreme example of a case where some pricing models break down and should hold up. It does highlight the 50-50 split in

“I want to start with the simple question of Tango’s post #38 which was, I believe, in reply to Sky’s posts (36 and 37) [I thought Sky's posts were on target].

Again I want to use the limit case of an auction where every participant agrees on the player stats ahead of time. We can think of this as a retroactive selection. This is just to make it clear we are assigning a value to a stat line and not to a player (and all of the uncertainty associated with that). Also, let’s start by doing pitching only. This separates the valuation phase from the auction phase [during an auction the optimal pricing of a player can change both with respect to specific teams (as their composition change) and the league in general (as the player pool completes)]. Later I will argue that the composition of the hitting pool affects the pricing of the pitchers, or, in more general terms, the composition of one player pool affects the pricing of players in other pools (I will also argue there are more than two pools).

Let’s consider a 6 team league, each taking 1 pitcher and 4 hitters (for simplicity, in case we need to get into examples). 5 pitching categories and 5 hitting categories. Further, let the pitchers have the same ordering in each category. So pitcher A is worth 6 points in every category (30 points total), Pitcher B is worth 5 in each category (25 total) down to pitcher F (5 points total, 1 per category). This is simply to make the math more straight forward.

Pitching will generate 50% of the points in the league and we already know how they will breakdown:

Pitcher A: 30 points
Pitcher B: 25 points
Pitcher C: 20 points
Pitcher D: 15 points
Pitcher E: 10 points
Pitcher F: 5 points

Also, we know Pitcher F has a value of $1. The value of the rest of the pitchers depends upon how the stats of hitters can be divided. The order, however, does not. Pitcher A must go first, followed by B and so on. If, for example, Pitcher B is

So, how much do we spend on Pitcher A if he comes up for bid first? If Team 1 spends all of its available budget ($256, assuming a $260 budget to be spent on 1 pitcher and 4 batters) to select Pitcher A then it’s safe to say Team 1 should finish last in all of the batting categories where it could finish last (odd situations can arise, theoretically, where something else may happen, either a tie in a particular category among all players in the pool or a situation where players doing well in one category do so poorly in others they are not worth taking except under extreme circumstances. Under these circumstances Pitcher A is worth more than $256!). In that case Team 1 performs at the league average of 35 points with a spending split of $256 in pitching and $4 in hitting. That’s basically the definition of a fair price.

Let’s say Team 6 purchases Pitcher F for $1 and spends $259 on hitting. Team 6 can do no better than the 35 points for league average, but should be able to come very close to that (at least); unless the categories set-up such that they come from more than one player pool (more on this later). So $1 for Pitcher F is both fair and unavoidable.

In the absence of information about the hitting player pool, the teams that select Pitchers B through E should be distributed roughly evenly through the remaining salary spectrum (e.g., if Pitcher B goes to Team 2, pitcher C to Team 3 and so on the salary breakdowns for those 4 teams could be, respectively, 205 pitching / 55 hitting, 154 / 106, 103 / 157 and 52 / 208) so the average team spends 128.5 on pitching. I think the reasoning behind the even spacing for Pitchers B through E is obvious, but if not we can go through it later.

I’ll let this sit for a bit to see if there are any objections or need for clarification before going into the cases where Pitcher A scores below 30 points (which should be also be obvious in the absence of info on the hitters) and then go into arguing that the hitting pool can impact the pitching pool.

One last thing though, because it will come up fairly often:

Batting / Pitching Split – This is a fuzzy distinction. Consider a league with three pitching categories: Saves, Holds, Wins. Those are three separate pools of players. Pitchers that get Holds rarely get Saves or Wins. Those that get Wins rarely get Holds or Saves. Those that get Saves rarely get Holds or Wins. So we are choosing from Batters and Pitchers, we are also choosing from Batters, Starters, Closers and Set-up men. Sometimes the lines on this are blurry (light-hitting SB specialists).

When players are being selected from multiple pools but competing for the same points (in the same categories) we have added complexity.
“

Here’s how $ value changes for SPs based on SP/RP ratio (66/42, 71/37, 78/30) – (i use 71/37) using 154/106 pricing.

Roy Halladay – $32.4 / $32.3 / $32.5
Matt Cain – $15.5 / $16.1 / $16.9
Jaime Garcia – $7.0 / $7.8 / $9.0
Jon Niese – $1.2 / $2.3 / $3.6
http://razzball.com/wp-admin/edit-comments.php#comments-form
Seems pretty straightforward – more SPs = more $ value per SP

The Halladay case is more difficult – I think it could be that any ERA/WHIP gains brought on by adding substandard pitchers gets balanced out by having a lower % of average team IP. Seems like K’s is the only area where the higher # of pitchers makes Halladay more valuable
(Point Shares: W/SV/ERA/WHIP/K)
66/42 – +0.9 / -0.2 / +1.2 / +2.3 / +0.6
71/37 – +0.9 / -0.2 / +1.2 / +2.2 / +0.7
78/30 – +0.9 / -0.2 / +1.1 / +2.2 / +0.8

I was speaking in the general sense. When there is a cap on IP my example fails in translation.

That’s nice stuff. The real vs projected data isn’t the path I was going down. The difference between projected and observed rate stats jumps out.

If at anytime it’s not a hassle you might try changing your model from say 72 starters and 36 relievers to 78 and 3o or 66 and 42 and see how prices change for the pitchers that are drafted in either scenario.

I am a fan of Monte Carlo pricing, but if I use a typical z-score or SGP model and use an iterative process (price X pitchers, keep the top Y and price them, keep the top Z and so on until I get the number I want) I find the prices of some pitchers will change a couple of dollars under certain league rules at the penultimate step if I recalculate distributions. I have not observed that when doing the same thing with hitters and I don’t have an explanation beyond the categories used.

” … but ERA and WHIP also change in value much more rapidly when replacing a high-inning 4.25 ERA guy with a low inning 2.70 ERA set-up guy.”

this is a tough concept for me to understand , especially since most owners in contention for league titles attempt to max out their IP limit , AND , since I’m unaware of any site carrying out their tie-breaks in these categories beyond three numbers to the right of the decimal point .

certainly , the logic is valid , but just how ‘much more rapidly’ seems inconsequential , since you’re reaching the same stopping point .

With our commenter league data, it’s possible (at least for 12-team) to look at end of year modeled results (Point Shares) and compare it vs. real behavior. Here’s the 2011 comparison:

2011 Point Share projected league average for 12-team MLB:
IP: 16,093
W: 1,044
SV: 997
ERA: 3.26
WHIP: 1.19
K: 13,740
AB: 79,308
R: 11,352
HR: 2,829
RBI: 11,031
SB: 1,932
AVG: .278

RCL Averages:
IP: 16,102
W: 986
SV: 1,091
ERA: 3.58
WHIP: 1.23
K: 14,014
AB: 84,249
R: 11,679
HR: 2,838
RBI: 11,230
SB: 1,947
AVG: .268

My net takeways:
Hitters – AB difference driven by using replacement hitters during DL stays. This has negligible impact on counting stats. AVG has notable difference vs. model – perhaps driven by replacement hitters, perhaps driven by bias towards counting stats. If comparing vs. preseason stats, differences vary per year depending on modeled hitting environment by projector(s) + counting stats likely lower due to regression + variable difference on AVG (FWIW, I have a .270 AVG for 2012 12-team)

Pitchers – The IPs nearly line up perfectly with model. The W/SV differences seem to indicate a higher % of innings given to marginal relievers (model called for 37 relievers which can include MRs). This increases SV and reduces W. ERA/WHIP difference impacted by higher % of IP to marginal relievers + potential bias towards counting stats (W/K).

I appreciate your point and it is accurate . . . pitchers and hitters contribute in five categories even when they contribute nothing.

My poorly worded point was that which bin you pick your pitcher from matters not so much because of the bin but the distribution of the stats you pool pit of it.

I don’t know exactly how you price your players, but at some point you most likely determine which players are going to be drafted. In a points league that is straight-forward, but in a roto league it’s a bit trickier . . . and it is much trickier for pitchers than for hitters. If you include too many starters than the relievers become more valuable and vice versa . . . the player list doesn’t reach a stable equilibrium. It makes sense if you think about it . . . each Save or Win takes on a little more significance as others are added to or removed from the pool, but ERA and WHIP also change in value much more rapidly when replacing a high-inning 4.25 ERA guy with a low inning 2.70 ERA set-up guy. Replacing a 500 AB .270 10 HR 0 SB player with a 500 AB 2 HR 12 SB .285 player will have less of an effect.

So I think 5 category vs. 4 category is more a fallacy than anything else…

What I was trying to convey, in not enough words, was that when we draft hitters we are drafting from one pool of players . . . they all contribute their value in the same five categories. Pitching is somewhat different in 5×5 leagues. Closers and Starters each have their (almost) exclusive categories (Wins for starters and Saves for Closers). So, in a 5×5 league, each rostered pitcher is, more or less, a 4 category player. When buying pitching you have a choice: buy Wins or buy Saves. Of course, most buy both, but in the general sense the option increases the supply side of the supply/demand balance.

An extra UTIL shouldn’t inflate hitters too much as – you have to remember – this also reduces the value of each hitter as they represent a smaller % of the team totals. I’d mark $2 for the extra UTIL and shave $1 from each of the hitter and pitcher buckets.

So basically, no real change.

So given that the dominant approach seems to be a 180-80 split, it seems to me the optimal course would be to use a slightly lower 170-90 split (or even a 175-85 split). That should guarantee that you get a really good staff because you’ll bid higher than the other owners who use the 180-80 split (which should be most of them), but you will not get caught up in destructive bidding wars with the other one or two owners who use a 160-100 or 165-95 split (if indeed you have any such owners in your league).

Rudy (and others), I’d be curious to get your take on the application of the “zig-zag” meta-strategy on other particular strategies. For example (and this is a point I have made in previous years in Comments on this site), the “Don’t Pay for Saves” strategy seems to have been originally thought of a a zig when others are zagging spproach: the other owners pay top dollar for closers, you hold off and buy cheap closers late and get them off the waiver wire. The problem is, this strategy has become so widespread that the zig has become the zag: I’d say at least half my main auction league uses this strategy, which means: (1) the “cheap” closer bargains at the auction are not so cheap anymore because you have more guys bidding on them, and (2) it’s really competitive to try to pick up a closer off the waiver wire. I’d argue that the Don’t Pay for saves strategy has become so widespread that the correct application of the zig-zag metastrategy here is to pay (judiciusly) for closers in the upper tiers (say, the top half of all closers), because (1) you can actually get some decent values in the top half, because fewer owners are bidding on them, and (2) you don’t have to use your free agent auction dollars (or use your top waiver wire spots) on waiver wire closers who may or may not pan out.

Anyway, great stuff, Rudy, even if I didn’t quite fully understand what you did with the numbers in there.