THE BOOK--Playing The Percentages In Baseball

Good to hear the z-score stuff from you.  I did my first fantasy league a year ago, and that was my initial idea:

http://www.hiremetheo.com/wordpress/?p=90

This year, I tried to start a new metric in which I translated a player’s stats into category wins.  For example, if the average team in my league last year had 125 SB by the end of the season, then theoretically a player who is forecast to get 125 SBs this year should be credited with .5 of a category win, for his SB contribution alone.  Looking at the evaluations that result from this calculation for every player and category, I see that base stealers are scored significantly better than their average concensus position in a draft.  So either that’s an undervalued player trait, or there’s a flaw in my theory.  The other cool part about this method, versus z-scores, is that it properly evaluates catchers - McCann might be 3.0 z-scores above the next best catcher, but since he doesn’t play full-time and catchers just aren’t the strongest position, his 3.0 is worth less than someone else’s 3.0.

In my head-to-head league, I also got the impression that Wins and BA were subject to a ton of variance week to week, while Ks and WHIP were subject to much less variance.  I think a model that credits low-variance stats a little more than high-variance stats is probably a better fit for a head to head league.  In other words, I feel like a team with guys like Glaus, Sexson, and Dunn, is going to win BA more often than a team with guys like Crawford, Furcal, and Ichiro are going to win RBIs.

There’s also the issue of guys who are forecast to be injured.  My plan is to come up with a way to mix in a player’s projected PAs with the average production from a replacement player in that position for all remaining PAs up to 650 or so.

The ultimate Excel file I want to make, however, has some dynamic calculators.  What I’m envisioning is a system in which I know the mean and standard deviation of each category, as well as some kind of Pythagorean exponent for each.  So when it’s my turn to draft, my file will compare the accumulated projected stats of the players I’ve picked so far, and then one-by-one add on the incremental stats of eeach player remaining in the draft, running my new team totals (were I to pick a given player) through a Pythagorean Win/Loss formula for each category, and noting the total change.  Something like this would programmatically get by any subjective analysis in determining, for example, whether to take another speedster (say, Figgins) when I already have a good team in terms of SBs and R, but am lacking in RBI.  It will calculate for me if I benefit more from the extra insurance of winning SB and R each week with more certainty, or if I benefit more from picking a power player, in order to give myself a more reasonable chance at HR and RBI.

You might be interested in this:
http://www.humbug.com/simulator/

As for your theory: forget it.  You should stick to z-scores.  The z-score on the player basis is really just an approximation to the standard deviation on the team, since that’s what we really care about.  If you had access to say a whole set of draft standings, you will find that the standard deviation on team HR and SB are probably going to be very similar, since they are for players.

If they are not, then this may show something else, like nonrandomness of drafting.  Based on my numbers above, the spread in R and RBI is a bit over twice the spread in HR and SB.  If someone wants to report their league standard deviation scores, please do so.

And here’s another:
http://www.fantasyinfocentral.com/mlbdraftsoftware/index.php

By the way, I think the split should be 50% for pitching and 50% for hitting.  Consider if you had to draft 24 hitters and 1 pitcher.  The 21 pitchers selected in the draft by the 21 teams will have an enormous influence in 5 of the 10 categories.

In this case, I’d have Santana at +11 units, 6 units for Halladay, then 3,2,1,0 for the other 19 pitchers.  The total pitching units of our 21 pitchers is 40, of which Santana, by himself has 11 units (27%).  The 21st guy, Dontrelle Willis, would have zero, since he’s tied with the 22nd through 25th pitchers.

In this case, would it make sense to only allocated 1/25th of the marginal payrolls (234x21) to pitchers, or a total of 196$?  Santana gets 27% of that, or 53$ (plus the 1$ that everyone gets).  That numbers compares to the 57$ that he would have been allocated if there were 10 pitchers.

But if everyone only has 1 pitcher, Santana’s team (i.e., himself) has a chance to win the K, ERA, W, and WHIP categories outright.

If we allocate 50% of the marginal dollars to pitchers, as opposed to 4%, then Santana is worth over 600$!

But, 600$ is way above your max payroll.

OTOH, spend the 230$ on Santana, and the rest on scrubs.  You are likely to get the bottom score in the 5 hitting categories, and saves, and the top score in 4 of the pitching categories.  That puts you just below average.

If we allocate 16.67% of the payroll to the 21 pitchers, then that’s 819$ to split among them.  Santana gets his 27%, or 221$.

That probably sounds about right.

So, how to we extrapolate that to a 10-pitcher per team league?  If the 1-pitcher per team league should allocate one-sixth of the payroll to pitching, how much should a 2-pitcher per team league allocate?  3-pitcher?  10?  24 pitcher?

Under the 24-pitcher, 1-hitter scenario, you’ve got Reyes, Pujols, and 19 others drafted.  In this case though, unlike Santana likely walking away with 4 categories, this can’t happen here.  It will be alot tighter.  Reyes might get 10-15% of the hitter payroll allocation.  And if we have Reyes and 24 scrub pitchers, there’s no way you are going to finish in the middle.  So, clearly, Reyes can’t be bought for 230$.

If we allocate 16.67% of the payroll to the 21 hitters, then that’s 819$ to split among them.  Reyes would get 10-15%, or around 100$.

So, it seems the rule works both way.  A single pitcher or single hitter league would allocate one-sixth of the payroll to that.

Shhh, you’re giving away my secrets. This is pretty much identical to what I did when I played fantasy (for the first time) last year. Our league had some extra categories, but excluding those from my formula and converting my use of BA (roughly) to your xH and dividing by a constant to get it on the same scale, I got

HR/7.8 + SB/7.8 + R/17.1 + RBI/19 + xH/12.1

It looks like I may have undervalued BA by a significant amount, but the other numbers are pretty much dead on; surprisingly so, considering that my std. deviations were very rough estimates I made from eyeballing the previous year’s MLB leaders.

Our league used a draft rather than an auction so the $ valuation didn’t apply. I also didn’t try to project playing time, but instead adjusted everyone to equal plate appearances, and then tried to take health and job status into consideration separately when I drafted. A couple other things I noticed:
1) (My estimate of) replacement level for 3B was almost identical to that for OF/1B.
2) Replacement level for catchers is very low, but this is offset somewhat by the fact that they are rested more frequently.  In a league that allows daily lineup changes it was also of some value to have a catcher whose days off were somewhat predictable.
3) The extra stat categories we used rewarded patience and power. In this context, the players with previous fantasy experience tended to overvalue the base-stealers and undervalue the sluggers, leaving me with a classically moneyballesque team.
4) On the pitching side, I don’t have my formula handy to see how it compares, but I think I set replacement level too high and ended up scrambling a bit to fill out my rotation. Fortunately, the projections I used identified some late-round steals - Mussina, Verlander, Oliver Perez. Well, two out of three ain’t bad.
5) If you have 9 pitchers ranked ahead of your top hitter, I think your replacement level methodology is wrong. Conventional wisdom is that only Santana (or equivalent) is worth an early pick, and I think my experience backed that up (though, as I said, I erred a bit in the other direction). You may need to take into account somehow (beyond the regression that is already in your projections) that projections for pitchers are less accurate than those for hitters. I haven’t thought this through completely, but it seems to me that for fantasy purposes (and maybe for real teams as well) there is some extra value in certainty.
6) The playoffs in a head-to-head league are a crapshoot. But I managed to win anyway.

You make a good point about the uncertainty in pitchers.  After all, if I had a very high uncertainty, the standard deviation of my estimates would all be close to zero, and since I divide by a number close to zero, then you might see someone that is off the charts.

Perhaps what I should do is base the standard deviations not on the forecast, but on the actual performances.  This way, the standard deviation for wins might come in as 5.5 instead of 3.5.

That may explain why I get wacky numbers.

Still, I’d like someone to think about how you would allocate payroll to pitchers and hitters if you have 20 hitters, 5 pitchers, or 15 and 10, or 10 hitters and 15 pitchers.

It’s a good thought experiment to challenge people out there as to how it works.

FYI, Here is a set of category spreads (avg. for a bunch of 10-team AL leagues, 2003, from a stat service):
HR 10
R 30
RBI 31
SB 8
BA .0021
W 4.1
S 7.3
K 34
ERA .113
WHP .019 (per IP)

I’m too lazy to figure out how the rate stats compare to your formula.  For counting stats, looks like player SDs are an OK proxy for team differences in some cases but not others.  Ks is pretty far off, probably because the demands of the game force similar roster construction in terms of starters vs relievers (your huge SD comes from mixing the two), making the category more competitive. 

Other thoughts:

It’s clear that you DON’T want to value hitting and pitching the same, and I don’t think the difference is a function of the # of players.  It’s the difference in marginal value as revealed by your totals of 3117 vs. 601 hitting units.  Now I don’t think those numbers are quite right—you’ve overvalued R and RBI, and undervalued Ks (and your estimate of replacement pitchers might be a little high)—but the gap is at least 2:1 in favor of the hitting.  And that’s what leagues spend.  It seems logical hitting and pitching would each be 50%, but what really matters is that $/point be the same in all categories (if it isn’t, money will flow to the undervalued category until they are equalized).  If different hitting categories can have varying amounts of total value—and they clearly do—then there’s no particular reason to think spending on pitching and hitting should be the same.

Pitchers’ lower reliability may contribute a little as well—I’m not sure—but I think it’s the difference in marginal value that should fundamentally drive the allocation of $$s.  (Your pitchers are coming in high because 38% is too much of the budget.)

* *

You may be better off basing the rate stats off a set replacement level for each stat (what you get from a team of $1 players) rather than the mean.  In your system, the total value for the 3 rate categories is zero, when obviously they do generate points.  (This is an old debate in fantasy circles). But either way, the total value in the rate stats will be surprisingly small.

I’m familiar with the debate, and they’re wrong.

What if instead you allocate points from +5 to -5 in each category, for an 11-team league?  It’s the exact same things as allocating +11 to +1 or +10 to zero, or +1 to -9.  But, see it from the point-of-view of +5 to -5, and things become clearer.

***

As for the pitcher/batter, I still would like to focus on what happens if yuo have 20 hitters and 5 pitchers, or 5 hitters and 20 pitchers.  What should the payroll split be?

I agree:  on the margin, a hitter with lg avg BA will help half the teams and hurt the other half.  In any case, both approaches produce very similar valuations for players.

* *

On 5/20, think in terms of categories rather than hitting/pitching split.  Each category is worth (# of players * Mean)/category increment.  So if you had 5 pitchers averaging 140 Ks, and expected 20 Ks = 1 standing point, you’d have 25 ‘units’ for Ks.  Do same for all 10 categories and then you can estimate proportion of spending for each. 

The # of hitters vs pitchers will affect this at the extremes (like 5/20), but if you went to 13 hitters and 13 pitchers I don’t think it would change the pitcher/hitter $ distribution much.  (Except in a mixed league, where the extra 3 pitchers, and three cut hitters, would have significant value.)

However, the trick is to estimate what the category spreads will be in each scenario.  Maybe you can identify a predictable relationship btwn player SD, # of players, and category increment.  However, this gets very complicated quickly by tactical adjustments players make.  With 5 pitchers, several owners will punt saves, while others might buy 5 cheap relievers, punting Ws, Ks, and S and hoping to win the other 7 categories (unless there’s an IP requirement).  This makes it very hard to estimate the category spreads without data from real leagues.  In real leagues, prices should shift until all strategies are equally successful. 

Another complication is the correlation of categories.  Players represent packages—a closer gives you saves but no wins—so you don’t have 10 independent markets.  For example, if you had traditional rotis categories (no runs) and five hitters, Reyes’ value would plummet.  It wouldn’t make sense to devote 1/5 of your offense to a player who was only strong in 1 of 4 categories.

Oops, that’s 35 units in the K category example above.

FYI, Here is a set of category spreads (avg. for a bunch of 10-team AL leagues, 2003, from a stat service):
HR 10
R 30
RBI 31
SB 8
BA .0021

Ok, this is interesting.  Let’s remember how to take a single-player standard deviation, and turn it into a team standard deviation, assuming all is random:

teamSD
= sqrt(playerSD^2 * numOfPlayers)
= playerSD * sqrt(numOfPlayers)

The playerSD for HR is 7.4, meaning we multiply by 4 to get the teamSD, giving us 30.  Guy is reporting 10, which goes to show that players are not selected randomly.  Duh, obviously.  But, what about the other categories.

random teamSD on SB implies 30 against an actual of only 8.

random teamSD on R implies 69 instead of an actual of 30.

random teamSD on RBI implies 76 instead of an actual of 31.

SB are much more valuable than I figured. 

For batting average, I’ll assume about 6000 AB, meaning the 1SD=.0021 is 12.6 in “xH” form.  I expected a random teamSD of 30.  So, BA is not as important as SB or HR, relative to the way I was figuring it.  And R and RBI are not anywhere close to as important as I thought.

***

I’ll come back and do the pitching later.

The varying relationships btwn theoretical random and actual spread is very interesting.  Two thoughts:

1) Runs and RBI are closely correlated with total AB, i.e. playing time.  Even mediocre players contribute here, if they play.  To the extent teams vary in keeping roster slots filled with guys regularly in the lineup—in addition to skill differences—this will increase category spreads and reduce value.  As teams drop out of contention over the season, they become less vigilant about effectively replacing injured/traded players, and that may increase the spread (whereas this is less true in the rate categories, or categories like HR and SB where a few players provide big % of value.)

2) There may be a distribution issue here not captured by SD alone.  Reyes or Pierre may be 7X the mean in SBs, while the top HR hitters are only 3X and top leadoff men are 2X in Runs.

Btw, regarding the batting average thing.  Suppose the fantasy league average is .277.  If you have a bunch of .270-.275 hitters, and if you set the “baseline” level to .260 or .255, and if you have double the AB of the other teams, your xH will come out better than the other teams.  But, you are still below average.

While unlikely you’ll have the AB discrepancy, it points out the reason that you must compare against the expected league mean.  The more ABs you pile up with .270-.275 hitters (in a .277 league), the more you drag down the rest of your team.

There’s a reason to use the league mean as the baseline.  There’s no reason to use any other baseline.

Tango, if you were to create a league that more closely mimiced the perceived value of players by MLB GMs would you change the statistical categories some?

If you wanted to, if that was the objective, sure.  I think Bill James attempted that with his STATS game.  I don’t know anything about it though.

Has anyone developed an assessment tool to determine how efficiently a Roto league is in extracting the value from the player pool in a given season? I’d propose that using the counting stats in particular there may be some way to calculate what percentage of HR’s, SB’s, W’s, K’s, etc. produced in the baseball player pool were captured by the GM’s in a given league.

An “expert league” such as Tout Wars should do better than your typical league in extracting the potential “value” from the player pool in a given season.  This would involve both the correct valuation of players and correct utilization.  If such a calculation were made, it might provide insight into whether GM’s tend to underexploit the value in particular performance areas.

Tango,
You’re essentially correcting for replacement level by subtracting the 43rd or 211st best player.  But thats not optimal.  Essentially your assuming that all players use the same rankings/valuation.  But they don’t, and if you trust your projections, you can leverage this fact to play money-ball.

In a draft league, if you can create probability distributions for when each player is going to be drafted (not hard; this is available online), you don’t want to compare the value of each pick to replacement level. You want to compare the value of current picks to the value of players you could pick up late in the draft. So, if you predict a breakout, and others don’t, you can get better-than-replacement value if you pick that player late.

This lets you spend early draft picks on the premier players at positions for which valuable players disappear quickly, and cheap average players aren’t available.

I suspect that somewhere in the stats/applied math literature, theres an optimal solution to this type of problem.

I’ve actually been doing something nearly identical to this for about four years now and have made various attempts at what cdm is sugesting. 

The best I have come up with, simply in terms of ease of use (key in a drafting league; I actually also color code guys’ numbers based on a rough tier system of their z-scores, just to have an easy-to-eyeball sheet if low on time), is to take the positional list and look at any of a number of sites that either have “average draft position” numbers or articles on expert drafts or draft trends. 

Compare the two and find the handful of guys the numbers say are undervalued and use some kind of notation (I, for instance, put their names in green) and voila: an easy-to-spot group of guys who can reasonably be expected to be available a round or two (or five) later than their numbers would suggest drafting them.

The amount spent on hitters vs pitchers has in a 5x5 league nothing to do with how many of each you need, but the reliability of the players.

We can predict hitting stats with about 70% accuracy.  For pitchers we’re only around 45%.  That suggest we should spend about 40% of our money on pitching and 60% on hitting, or about $100 of your $260 on pitching.

And what if you had only 5 pitchers and 20 hitters?  Or 20 pitchers and 5 hitters?  Or 1 pitcher and 24 hitters?

The number has to mean something.  I agree reliability is also included.  You need to know both.

Here’s what I want you guys to focus on:
- category split: what if you had 5 hitter categories and 3 pitcher categories?  Or 3 and 7?  8 and 1?  1 and 15?

- player split: what if you had 20 hitters and 5 pitchers, or 15 pitchers and 10 hitters?  24 and 1?  1 and 40?

- reliability of categories: K per IP is hugely reliable, while ERA is not; HR likely more reliable than RBI

So, come up with a framework that handles these as parameters.

Rally: 
If this was all about risk, then it would follow that there would be a positive correlation between a team’s % of money spent on pitching and standing points.  While there might be a huge amount of volatility, on average it would have to be true that each dollar spent on pitching would provide a better return.  However, this is not what happens—spending more on pitching does not yield more standing points.  So risk/certainty can’t be the main explanation.

The explanation is that pitchers really are less valuable, in MARGINAL terms.  For one thing, pitchers have two categories where their aggregate value is zero (ERA and WHIP), while hitters have just one.  Also, there are simply a lot more hitters than pitchers with positive value.  Because ERA and WHIP are so highly correlated, a great many pitchers have negative value in two categories, and zero in another (saves).  At least 1/3 of the pitchers drafted will have no value, or litterally negative value (when I played, my staff always had 3 or 4 $1 pitchers, who often got dropped if they didn’t pan out).  That’s why, to answer Tango’s question, going to 5 pitchers probably wouldn’t have a big impact on pitcher spending—the four dropped pitchers cost almost nothing anyway. (But going to 1 pitcher would.)

What gets called pitcher “volatility” is really just a big downside, either because of injury or poor performance.  If that downside is properly included in our forecast, the pitchers’ lesser value will be apparent.

I think one forecasting-related factor that’s important is that a non-trivial proportion of all pitcher value isn’t even drafted, because we don’t know yet the pitcher will have value (they may be on reserve rosters), while this is much more rare with hitters.  So that increases the disparity in value between drafted hitters and drafted pitchers.

Guy hits the nail on the head. If your forecast is properly regressed, the increased volatility for pitchers will already be accounted for in your numbers. Anything else would be double-counting.

W 4.1
S 7.3
K 35
ERA .113
WHP .019 (per IP)

To get the teamSD from the playerSD I provided, you multiply by the sqrt(10).  So, the teamSD for wins, if pitchers were assigned randomly, is 10, compared to the actual of 4.1. 

teamSD for SV should be 23 compared to the actual of 7.3.

I’ll assume 1300 IP, meaning the observed xERA reported by Guy would be 16.  The random teamSD for ERA should be 16.  In effect, ERA is randomly distributed.

The observed xWHIP is 25, compared to the random teamSD of 30. WHIP is almost randomly distrubuted.

teamSD for K should be 128 compared to the observed of 35.

Players are drafting for K, SV, then Wins, and hardly at all for ERA or WHIP (based on the data in Guy’s quoted league).

***

If I used Guy’s weights for both pitchers and hitters, I get a total for hitters above replacement of 1809 units, and for pitchers a total of 485 units.  Since we’ve aligned the units appropriately, then hitters should get 79% of the payroll.

The top hitter is Reyes at $39. Jimmy Rollins (!) at $34.

For pitchers, Santana is at $24, and Carpenter at $18. 

After each team has 5 pitchers, the best pitcher available is worth $5.  The equivalently-valued hitter is after every team has 13 hitters.  That is, the 14th hitter is equal to the 6th pitcher.

This is embarrassing.  Instead of using xH, I was using H, which explains why I had Rollins so high.  So, the total SD I was quoting (the 1800 units for hitters) was wrong.  The hitters get 953 units, and the pitchers get 485 units, meaning hitters get 66% of the marginal dollars.

Jose Reyes still gets 38$ to lead.  This time, he’s followed by ARod, Crawford, Pujols, Wright.

Santana also leads with 38$, followed by Carpenter at 28$.

After the first 5 pitchers for each team goes, the next best pitcher is at 7$.  The equivalent for hitters is after the first 10 hitters for each team goes.

What if we reduce hitters down to 3 categories (HR, SB, AVG)?  In this case, hitters get almost 50% of the units (435 compared to 485).

In this case, Reyes’ league-leading 7.4 units, which puts him smack between #2 and #3 pitchers (Carpenter and Zambrano).

Reyes now gets 40$, between the $43 for Carpenter and $39 for Zambrano.  Santana runs away at $59.

***

Another question then: should we differentiate between the 400-odd units spread over 3 categories and the 400-odd units spread over 5 categories?  Seems to me that it doesn’t matter, since we can create 100 categories for pitching and 2 for hitting, and if the other 90odd categories are all pretty much random, then they are really useless.

If your forecast is properly regressed, the increased volatility for pitchers will already be accounted for in your numbers.

I don’t think this is right. The regression in the forecast gives you the optimal estimate of true talent level. For real life purposes, that’s the end of the story. But in fantasy, you still have to take the volatility into account. Having an advantage in true talent in a category where performance can be accurately predicted will be (at least slightly) more valuable than an equivalent advantage in a category where performance is more volatile.

Interesting that Tango’s split matches almost perfectly what leagues actually spend.  Fantasy baseball is an extremely efficient market. 

**

Just to clarify:  the stats I posted are the average for many different leagues, collected by a stat service.  They should be a pretty good measure of what happens.  One caveat:  “keeper” leagues will have bigger spreads than “fresh start” leagues, because owners falling out of contention in keeper leagues will trade current talent for future prospects.  But I’d think that affects all categories fairly uniformly.

* *

I agree with Andy.  I’d pay a little bit extra for some security.  But I wouldn’t pay 2X for the same expected value, which is what the 70/30 hitting/pitching split we observe in most leagues would imply (if true value were equal).  However, I also believe—and I think David agrees—that a lot of what gets called “volatility” or “risk” for pitchers is really just a much higher probability of a zero (or negative) value season.  The chance that Santana has a $5 season in 2007 must be higher than for Reyes (how much, I don’t know).  But that injury risk should already be built into our forecast.  To the extent that pitchers are truly more volatile—both up and down—even when healthy, that should have a pretty small impact on prices.  If buying more good pitchers meant increasing our chance of winning, we’d do it—even if it also increased the chance of a last place finish.

Guy - good explanation.

DSG - I see what you are saying, though it isn’t double counting.  What I was doing is using the inherent risk in pitching to justify a forced $160/$100 split between pitchers and hitters.  Then I split the $100 only among pitchers, and the $160 only among hitters.

But using Z-scores, hitters get 66% of the value anyway, as Tango shows in #25.

Pretty close either way, but a simpler and more logical method to just look at the Z’s.

I get 705 pitching units if I increase the number of pitchers selected to 16 (to match the number of hitters).  Hitters were 953 units, as per post #25.  In this case, hitters get 57% of the payroll.

That moves Santana to $35 and Reyes to $32.

I’d be interested to see the results of Tout Wars and others of their ilk, where, presumably, these guys have figured out the right balance of everything.

Tango, in the baseline analysis you did (post #25), what is the number of SD “units” for each of the 10 stat categories?  If the leagues from the sample are “efficient”, I think the number of units in each category should be roughly the same for all of the hitting categories and all of the pitching categories.

BTW, from my recollection, in “expert leagues” like Tout Wars, the % of salary allocated to hitters has varied between about 67%-71%.

Tango,

How would you suggest rating ratio stats like K/BB and K/9.  The ERA and AVG ones work easily with # of IP/AB, but would you multiply these ratio stats by the total number of strikeouts?? 

That kind of makes sense, but somehow that doesn’t quite feel right either. 

Thanks!

K/BB is a ratio, and needs to be converted to a percentage: K / (K+BB).  So, if Santana has a 4:1 ratio, he’s at .800 percentage-wise.  You follow the same process as with batting average to figure out how many units each extra K is worth.

K/IP is almost a rate, and K/(3*IP) would make it a rate: percentage of outs as srikeouts.  Once you have it in percentage form, you can follow the batting average process.

(Note that in this last case, it wasn’t really necessary to go to 3*IP, since it’ll end up cancelling itself out.  But, always a good idea to put things in percentage form.

***

mul: I don’t know how to answer you.

Sorry, tango, I should have been more clear. 

In post #25 you wrote:  “The hitters get 953 units, and the pitchers get 485 units.” My question is whether each hitting category had about 190 units and each pitching category had about 95 units, or if the units were distributed unequally among categories.

I’ve used a similar process for years in my roto league, but have always had to resort to forcing an allocation of 67% hitting vs. 33% pitching.  This is intellectually dissatisfying, but produces prices which seem to maximize value in a “real life” draft environment.

It likely is the same.  It’s hard to figure, really, because the 953 units are the number of SD above the replacement level, but after the 5 categories of each player are added up.

The net/net is that each category is equally represented, as it should.

#35: I’m yet to be convinced that each category is equally represented by this style valuation model.

One way to look at it is the hitting/pitching split.  If you KNOW the numbers exactly (say, a retro-draft), then why would you not spend the same on hitting as pitching?  A hitting point is worth the same as a pitching point.

If you want to look at the individual categories individually, then couldn’t you add up the SDs above replacement for each category?  I remember doing this for the hitting categories a couple years ago and finding out that there are many more points associated with the HR, RUN, RBI categories than the AVG and especially SB categories.  Should be able to test with your numbers, Tango, no?

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Regarding the discussion of variability… Proper regression is not the end of the issue.  Because pitching is more variable (as per the roto categories in this discussion), it’s more likely that pitching value will be found from players not in the draft-worthy pool.  I believe it’s something around 70% of end-of-season pitching value is drafted, while it’s more like 90% for hitters.  This difference explains the drift from a 50/50 hitting/pitching split to a 70/30 split.  Why would you spend equal amounts on hitting and pitching when your investment in hitting is expected to yield a higher return?

I’ve been doing a little more thinking, trying to convince myself why the SD is correct to value categories differently.  Here are my thoghts:

Obviously, taking SDs is an attempt to measure the spread of a category.  The more tightly packed a category, the more of a difference one typical player can make in the standings.  So while it would seem that buying one SD in SB and HR should have the same value, the spread-out nature of SB makes it so that the 1 SD is likely more inefficient.  You’ve got 50 SB players, 30SB players, and a lot of 10-15 SB players.  Why pay for 30 SB when it’s likely that only 20 SB would be needed to catch the next team?  On the other hand, it’s probably typical that 25 of the 30 HRs a player provides might turn out to help you catch the next team.  If you give money to all categories equally, spending $10 less on SBs might lose you 2 points, but spending $10 more on HRs might earn you 3 more points—a good trade.

If you have 24 hitters and 1 pitcher, and you have 5 hitter and 5 pitcher categories, would the average pitcher be paid 130$ each?

No, that wouldn’t happen.

I’ve been in a head-to-head, category-by-category, league, and here’s what I’ve come up with, in regards to what to use for a denominator instead of the SD of the applicable players.

What I care about in a category-by-category head-to-head league is winning each category, each week.  My chance of doing that is going to be based on how far above the league average I am in that category, and what the standard deviation is for “the difference between my score and my opponents score.”

I can estimate the correct standard deviation by combining my team’s standard deviation and the standard deviations of all my opponents.  Last year, for Runs for example, my weekly SD was 4.5, and my opponents’ weekly SD was 6.9.  (Mine is always much lower, because the quality of the other teams varies.) Combine those by taking the square root of (4.5^2 + 6.9^2) = 8.2.  So for my league (at least last year), the correct SD to use is 8.2.

During the season, I actually convert that to a “win increment” (how many runs will it take to get me one extra win on the season) by figuring how many SDs it will take me to get one more win, based on how far above or below the league average I am in that category.  I just use the inverse normal distribution for an estimate (most stats are fairly normally distributed).  It can make a difference for some categories where I’m way ahead—it could take a lot more Runs, for instance, to get one more win than if I’m right at the league average.

I think that for head-to-head leagues like ours, the SD of the differences in weekly scores is the way to go.  I’ve still never really figured out exactly what to use for the draft, though.  Should I just use last year’s results?  What if my team just happened to have a very low SD in some category?  I worry about this every year.

I’ll also note that in my experience, for some positions, setting the replacement level at the n+1 player is much too low.  This is mostly true for pitchers and outfielders (the positions where there are a lot of players taken). 

This is because many outfielders and pitchers who are below my (n+1)th player will be taken by other teams.  So at the end of the draft, the “de facto” replacement level is much higher, somewhere around 3/4 of the nth player. 

That has really messed me up in the past as I took all my outfielders way too early (something like 5 in the first 6 rounds), and a bunch of good ones were still left at the end of the draft.

I think the problem with your numbers is using VORP as your baseline.  A players positional scarcity value isn’t based on the best guy to not make a team, its based on how good he is compared to the other players who did make a team. 

An example would be if you had only 4 players and your 2B were worth $39, $25, $15, $15 and the 5th was $15.  Then you had SS worth $35, $34, $33, $25 and the 5th was a huge slide to $10.  Using a VORP system that $35 top SS is actually worth more than the $39 2B, even though SS has more depth and the top one had less value.

VORP is not how you want to adjust for positional scarcity, it just cannot account for how top heavy a position is at all so it doesnt’ really measure depth of the position. You need to come up with a good SD system for handling positional scarcity.

Let’s make it even more extreme: you have 4 teams, and their values, in “quatlus” are:
2B: 100, 30, 30, 30, 30
SS: 90, 90, 90, 10, 10

You need to knock off 30 quatlus off each 2B, and 10 off each SS, to give you:
2B: 70, 0, 0, 0
SS: 80, 80, 80, 0

What will matter however is how to optimally spend the money. Just because you valued the 2B at 70 “quatlus above last player at position” (QALPAP), and you have three SS valued at 80 QALPAP, it may be worthwhile to pay more for the 2B because of how you think you can balance it out.

I’m not necessarily disagreeing with you, but the kind of skewness you are talking about simply does not exist in reality.  You’ve got at least 8 teams in a draft, and there’s no dropoff like you are talking about. 

***

Don’t call it VORP, since that’s something used by BP for other purposes.  QALPAP sounds good to me.

It doesn’t exist to that extreme but it does exist with 2B and SS this year.  2B has a top tier guy and then a few mid tier guys and then a whole bunch of low tier guys.  SS has like 7 top tier guys, a few mid tier guys and then it drops off to where its no better than the 2B.  On my sheets Utley isn’t as valuable as the 5th best SS but I certainly would take him over any of them except Reyes and using QALPAP he wouldn’t be going over them.

My problem with QALPAP is you are basing positional scarcity on players who didn’t make the team.  When someone asks you how deep SS is in baseball do you answer them by looking at guys sitting on the bench or do you answer them by looking at SS’s who actually play?  The QALPAP system ignores the players who made fantasy teams, that just doesn’t make much sense to me.

Even if there is a dropoff at a particular position, there isn’t a dropoff when you consider all players.

In terms of drafting, I can see you valuing Utley ahead of some SS.  But in terms of auction, I don’t see it.

Drafting *may* (even then I’m not sure) be more concerned with positional distribution (i.e., players expected to be drafted).  So, this goes to what you are saying.

Auctions would be concerned with positional scarcity (QALPAP).  Whoever is the last 2B selected, that’s who Utley needs to be compared to, regardless of the guys in-between.

True, good point.  I’m a drafter so I can see where it would be a bit different in an auction setup.

Someone from Yahoo Sports asked for my opinion on the HR/SB issue:

http://fantasysports.yahoo.com/analysis/news?slug=ab-sb_vs_hr_031307&prov=yhoo&type=lgns&league=fantasy/mlb

I just looked at Pujols and Reyes here:
http://www.baseballprospectus.com/unfiltered/?p=264

BP’s has Pujols right, with a dollar value of 30$.  I think I had him at 29$.  Reyes though I have leading the league in the mid-30s I think.  BP has him at only $26. I don’t know what categories BP uses, but it sure looks wrong.

More interesting is the “average auction values” from what looks like actual leagues.  Players are paying $47 for Pujols $41 for Reyes!

It’s these leagues that you guys should be competing in.  These guys blow their whole load on top-end talent, and the only way to lose in these leagues is for you to pay the equally ridiculous prices.

It all depends on your league.  In a mixed league, such as one that uses players from both leagues but has only 10-12 fantasy teams, you can always find decent players on the waiver wire.

In that league I can blow $47 on Santana like I did last year, patch cheap pitchers around him and still take the pitching categories.

The guys who overpay a little for top talent seem to do better there than someone trying to pay reasonable prices for a balanced team.  Starting the season with holes in some spots is to your benefit if you can quickly identify breakout candidates.  Last year I spent $1 on my backup catcher, somebody useless like John Buck.  A week later I had Brian McCann.  The guy who spends $18 on Posada and $7 on Paul LoDuca doesn’t have the same motivation to look for a possible up and comer.

I guess there is a certain “keep up with the Joneses”.  You certainly don’t want to be in a position where you have left-over money.  You can even overpay for Santana, forcing everyone to overpay for all pitchers (each taking two or three overpaid pitchers instead of 1), while you sit back and wait for the rest of the pitchers.

I have a question.

My H2H, autodraft league has the same 5 pitching categories, but different batting categories. We have RBI, SB, OBP, SLG, and Strikeouts. My question is this: How do you account for a negative counting category like Strikeouts? Right now I have my batters’ formula as:

RBI/(lgRBI SD)+ SB/(lgSB SD) + xOB/(lgxOB SD) + xTB/(lgxTB) - SO/(lgSO SD)

where:
xOB = (H+BB+HBP) - AB*(lg(H+BB+HBP))
and
xTB = TB - AB*(lgTB)

I thought it was working fine, but when I combine the pitchers (after subtracting the 43rd and 211th player) with the batters, the pitchers are ranked WAAAYYY above most of the hitters. I’m sure it is because I was subtracting out the SO from the batters, however, I’m not sure what I should do instead.

Thanks for any guidance!

When you say this:
xTB = TB - AB*(lgTB)

Do you really mean:
xTB = TB - AB*lgSLG

(Same applies for your OBP).

You are correct that you simply reverse the sign for the batter strikeouts.

***

Is your worst batter and pitcher in your pool set so that it’s equal to zero?

You are correct about the xTB = TB - AB*lgSLG

***

When you say the worst batter and pitcher set equal to zero, do you mean I need to subtract their total rank from everyone’s rank? Or that I need to play with the formula so that when the lowest ranked players totals add up, they equal zero?

Subtract the replacement player’s result from everyone else’s.

@Rally:

Then yes, I have done this. Maybe what I need to do is just subtract more from the pitchers?

You want the player’s QALPAP (quality above last player at position).  So, what is Santana’s score, and what is the last pitcher’s score?  The difference is Santana’s QALPAP.  That last pitcher’s score will be zero.  Also give a complete step-by-step for Santana.

Do the same for all positions.  Report on the leaders at each position.

Santana-
1. Put him through the formula below using ZiPS prediction and the full list of players to get the standard deviation. My SD are included below.
W/3.2 + SV/3.66 + SO/33.8 + xER/11.307 + xWHIP/17.686
Some of the deviations differ quite a bit from your SD’s.
For Santana: 18/3.2 + 0/33.8 + 49.971/11.307 + 90.96/17.686 = 22.11 (numbers are rounded for convenience, excel has the full number)

2. Next, to get the adjusted rank, I subtract Santana’s rank from the lowest pitcher’s rank, which in this case is poor John Barnes whose rank is only -4.708. Therefore, Santana’s Adj. Rank is 26.82 = 22.11 - (-4.708) = 22.11 + 4.708

3. I repeat this for all the other positions and these are the leaders: (POS, NAME, Unadjusted rank, Adjusted Rank)
c Mauer 8.978 11.266
1b Pujols 16.091 19.536
2b Utley 7.449 9.304
3b Cabrera 11.288 13.711
ss Reyes 9.859 14.581
of Crawford 11.497 15.105
of Vlad 11.352 14.961
of Beltran 9.575 13.184

Comparing the pitchers and the position players, there are 20 (!) ranked ahead of Pujols.

I realize you all are pretty busy, so thank you for any help you can provide.

In post #7, the SD that Guy posted are much different than the 5000 Yahoo leagues in post #46.  In fact, the SD for the SB and HR in those Yahoo leagues look remarkably like what I posted in my initial blog entry.

I would suggest you reverting back to the coefficients I have in my original blog entry.

Doing so, I get the following:
total nonpitcher QALPAP: 1459
total pitcher QALPAP: 619

That gives us 70% of the units to nonpitchers.

These are my top 10 nonpitchers:
player $
Pujols 34.6
Rodriguez 34.6
Cabrera 34.5
Reyes 34.2
Guerrero 32.7
Wright 32.6
Crawford 30.1
Jeter 29.9
Tejada 29.0
Utley 28.9

And these are my top 10 pitchers:
Santana 42.0
Carpenter 30.2
Halladay 25.1
Peavy 25.1
Zambrano 24.8
Oswalt 23.9
Webb 21.1
Smoltz 20.8
Nathan 20.8
Martinez 20.5

***

Maybe I went too fast this time… Reyes was usually ahead of Pujols by a few dollars, but that may have been based on Guy’s coefficients.

Who is John Barnes?  Is he the lowest ranked pitcher that ZIPS projects or the lowest pitcher that is expected to be drafted in your league?

Just checked Barnes, Zips projects an 8.77 ERA for him.  He’s not going to pitch in the majors and is irrelevant to your draft.

If your league has 10 teams, and 9 pitchers per team, then the 91st ranked pitcher is your replacement level.

Right, when I said “210th pitcher”, that was based on a 21-team league out of 30 MLB teams, with 10 pitchers per team.

If you play in an AL or NL only league (or even a combined league, with only 10 teams in the draft), then you need to look at the 100th best pitcher, or whatever, as Rally is saying.

Ok, this is my final list (hitters, then pitchers). 

The basic formula for hitters is:
HR/10 + SB/10 + xH/10 + R/30 + RBI/30

And for pitchers, it’s:
W/5 + SV/10 + SO/50 + xER/10 + xWHIP/15

I decided to create coefficients based on actual data, not on forecasted data.  If a category, like Wins, is based on alot of luck, and I’ve got everyone forecasted for say 11 wins, well, I shouldn’t use a low SD now, should I.  It’s a very high SD.

Anyway, here are the dollar values for everyone worth at least 10$.  If you disagree, it’s because of the following reasons:

1 - You are not using the same league rules as I am (5x5, 2 players per position, 10 pitchers)

2 - You get to put someone at a different position

3 - You are doing a draft league, not auction

4 - You are more aware of rookies than Marcel is (i.e., Dice-K, Pedroia, etc)

5 - You are more aware of changing roles and playing time of players (i.e., Papelbon, Matsui)

6 - Your forecast for a player is different

7 - You are wrong

Hopefully, your list is different from my list because of the first 6 reasons.

68.4% of the payroll goes to hitters, and 31.6% to pitchers.

$ Prim nameLast
36 SS Reyes
35 1B Pujols
35 3B Cabrera
35 3B Rodriguez
33 RF Guerrero
33 3B Wright
32 LF Crawford
30 SS Jeter
29 SS Tejada
29 SS Rollins
29 2B Utley
28 LF Soriano
28 SS Furcal
28 SS Young
28 3B Ramirez
28 SS Ramirez
28 RF Suzuki
27 LF Holliday
27 CF Sizemore
27 1B Ortiz
27 RF Abreu
27 3B Atkins
27 1B Howard
25 LF Bay
25 CF Beltran
25 LF Lee
24 1B Teixeira
24 C Mauer
24 CF Figgins
24 SS Guillen
24 LF Ramirez
24 CF Pierre
24 SS Lopez
24 CF Damon
23 3B Beltre
23 CF Jones
22 RF Dye
22 1B Hafner
22 1B Berkman
22 CF Wells
22 3B Mora
21 3B Zimmerman
21 SS Hall
21 1B Konerko
21 3B Glaus
20 C Martinez
20 C McCann
20 3B Rolen
20 CF Hunter
20 2B Roberts
19 3B Jones
19 1B Morneau
19 3B Tracy
19 LF Dunn
18 SS Renteria
18 2B Cano
18 RF Francoeur
18 LF Ibanez
17 1B Helton
17 3B Sanchez
17 CF Matthews
17 SS Lugo
17 RF Drew
17 CF Cameron
16 3B Blalock
16 C Rodriguez
16 SS Peralta
16 2B Uggla
16 LF Roberts
16 1B Delgado
16 LF Podsednik
16 SS Cabrera
15 3B Chavez
15 CF Taveras
15 RF Ordonez
15 3B Crede
15 2B Iguchi
15 2B Giles
15 2B Durham
15 RF Rios
15 RF Cuddyer
14 CF Patterson
14 CF Crisp
14 3B Huff
14 3B Ensberg
14 CF Lofton
14 RF Giles
14 SS Vizquel
14 1B Sexson
14 3B Teahen
14 3B Inge
14 C Hernandez
14 LF Monroe
14 CF Freel
14 LF Burrell
14 2B Kent
14 RF Winn
14 C Posada
14 CF Byrnes
14 CF Edmonds
13 1B Overbay
13 RF Jones
13 LF Bonds
13 LF Rivera
13 C Martin
13 2B Phillips
13 LF Brown
13 CF Griffey
13 3B Encarnacion
13 3B Feliz
13 RF Alou
13 2B Castillo
13 1B Johnson
13 3B Lowell
12 RF Kearns
12 2B Barfield
12 1B Thome
12 SS Uribe
12 2B Hudson
12 CF Baldelli
12 CF Rowand
12 C Johjima
12 RF Hawpe
12 RF Green
12 3B Aurilia
12 1B Fielder
12 LF Murton
11 2B Weeks
11 C Pierzynski
11 RF Jenkins
11 SS Betancourt
11 1B LaRoche
11 C Lo Duca
11 2B Polanco
11 C Barrett
11 RF Encarnacion
11 C Molina
11 1B Gonzalez
11 1B Swisher
11 CF Granderson
11 LF DeJesus
11 LF Anderson
11 2B Cantu
11 RF Markakis
11 2B Kinsler
11 1B Thomas
11 SS Eckstein
11 C Kendall
11 1B Giambi
10 2B Loretta
10 CF Kotsay
10 2B Lopez
10 SS Greene
10 1B Hillenbrand
10 1B Garciaparra
10 LF Johnson
10 SS Wilson
10 C Varitek
10 1B Lee
10 3B Betemit
10 RF Bradley

$ nameLast
42 Santana
30 Carpenter
26 Peavy
25 Zambrano
25 Halladay
24 Oswalt
22 Smoltz
22 Webb
21 Martinez
20 Nathan
20 Sabathia
19 Clemens
19 Rodriguez
19 Liriano
19 Rivera
19 Young
19 Willis
18 Cain
18 Arroyo
18 Haren
18 Hernandez
18 Johnson
17 Sheets
17 Beckett
17 Wagner
17 Weaver
17 Bonderman
17 Lackey
16 Pettitte
16 Harang
16 Schmidt
16 Santana
16 Ryan
16 Cordero
15 Bush
15 Street
15 Kazmir
15 Myers
15 Hoffman
14 Olsen
14 Mussina
14 Garcia
13 Wang
13 Escobar
13 Papelbon
13 Capuano
13 Johnson
13 Lidge
13 Sanchez
13 Zito
13 Verlander
13 Schilling
12 Millwood
12 Hamels
12 Burnett
12 Garland
12 Cordero
12 Lowe
11 Putz
11 Maddux
11 Saito
11 Hensley
11 Bedard
11 Penny
11 Isringhausen
10 Harden
10 Contreras
10 Vazquez
10 Buehrle
10 Lee

The average $ per position:
$13: 3B
$12: SS
$11: LF, CF, 1B,
$10: RF
$9: 2B
$8: P
$7: C

If you think the mean should all be exactly the same ($10) for whatever reason, then knock off 3$ to each 3B, add 3$ for each C, etc.

"In post #7, the SD that Guy posted are much different than the 5000 Yahoo leagues in post #46.”

Tango, just to be clear:  the numbers I posted was the approximate category differential (what it takes to gain one point in the standings), not the SD in each category.  It was based on the average of quite a few leagues, though the data was a number of years old.  And of course, the distribution in a league will also be impacted by whether there are “keepers,” single league vs. AL/NL, etc.

While I think the marginal standings impact is generally the right way to go, it may not tell the whole story.  After all, in order to start earning marginal points, a team first has to have enough HRs, SBs, etc. to pass the last place team.  Reyes may theoretically be worth 7 places in the standings, but if Reyes is my only SB guy I won’t in fact earn 7 points in steals.

Let’s take an extreme case:  suppose we found that the SD for RBIs in an average league was just 8 RBIs—incredibly competitive.  Would all the owners really devote a huge % of their budget to chasing RBIs, when the final RBI standings would probably be determined by luck?  In that case, some owners would decide to dump RBIs and spend their money elsewhere, and some new equilibrium would be reached:  larger SD, cheaper RBIs.

Guy/62: ok, now I understand.  I should have remembered that.

Guy/63: no question about it.  After all, jumping 1 SD when you are in the middle of the pack will let you jump over more teams than jumping 1 SD if you are already in 2nd place.  However, this affects all categories.  And, to the extent that all team totals do follow a normalish distribution, all categories are in the same boat.

So, you definitely want to build up your categories so your mean in each category is at least in the -0.5 SD level (or, just punt a category altogether), and you don’t want to be higher than say the +1.5 SD level.  It wouldn’t make sense to get Reyes, Crawford and Pierre.

This post/thread is great. This is exactly the sort of thing I have been looking for to give me an edge in my fantasy league. Thanks to all of you.

However, my specific league is a points-based league with a somewhat complicated scoring system. It is a 12-team auction mixed league with 10 offensive players (c,1b,2b,3b,ss,of,of,of,of,ut) and 7 pitchers. To further muddy the waters you are limited to 162 pitching starts and 140 relief appearances.

My opponents mostly use magazines/print outs to determine value on draft day. As you well know those are geared to 5x5 drafts with 23-man rosters and different positions.

This should be fairly simple, but math is not my forte. If I have a projection set of how many total points a players is going to be worth, how can I use that number to determine an appropriate dollar value?

1. Figure out the points for every player

2. Figure out the last player to be selected at each position, and get his points.

3. Subtract 2 from 1.  That’s your player’s QALPAP (quatlus above last player at position).

4. Add up the QALPAP of the 120 nonpitchers and 84 pitchers.  That’s the league-wide total QALPAP.

5. Take the maximum payroll per team x 12 teams.  That’s the total league payroll.

6. Take the figure in 6, and subtract out 204$ (that’s the minimum 1$ x 204 players… if your minimum is 500,000$… then use that.) This is your marginal dollars.

7. Take the figure in 6, and divide by the figure in 4.  This is the dollar per QALPAP.

8. Take each player’s QALPAP (from step 3) and multiply by step 7, and add the minimum salary ($1 or 500,000$ or whatever it is).

That’s it.

Your extra wrinkles of 162 starts, utility players, etc, is extra work for you.

As a long time Roto player with a system very similar to the one that Tango described, I have one suggested change to Step 7.  In my experience, the QALPAP split between pitchers and hitters is not necessarily the best way to divide your $ between those two categories of players.  I would take Steps 7&8 and do them separately for hitters and pitchers, based on either a generally accepted fantasy split (like 65:35 or 70:30) or a split based on the history of salaries in your league.

I don’t necessarily disagree, but I’d be surprised if the split didn’t come out to around 2:1 anyway.

One more thought on the above discussion of coefficients.  I have found that stat categories are not in general normally distributed.  Typically, there tend to be clusters of teams at different (seemingly random) breakpoints, with an occasion outlier (typically for someone deciding to dump a category or just give up in the middle of the year).

My approach has been to build prices that work for me, and since my approach is to try to compete in every category, I can ignore the issue of the extra gap of going from 1 point to 2 points in a category, since I’ll be shooting for at least 5.  My coefficients are the average category differences, excluding what I judge to be any extreme outliers.  The results are pretty close to the #’s in post 7.  This seems logical to me and the results seem to work quite well.

5 x 5 roto is traditional and easy to score by hand. But, now that computers do most of the work, I’m curious: why would anyone want to play in a 5 x 5 league instead of a points league? The points can be set up to mimic real baseball much closer than the 5 x 5 scoring does. Your team will look more like real teams. Player value is closer to real baseball, etc. I always play in points leagues. However, since you guys are more than casual fans and seem to be into traditional 5 x 5 maybe you could tell me what the attraction is.

Great discussion.  When determining the last player selected in step 2 above, would it be better to use the last player that should be selected according to your projections or the last player that is likely to be selected based on average draft position?

Re: #70, some of it is probably switching costs and “if it ain’t broke, don’t fix it”.  All of the magazines are geared for traditional roto, so for more causal fans in leagues, that keeps it simple.  Also, when you’ve been in a keeper league for many years, changing scoring formats means convincing 9 other owners who are having a lot of fun and don’t care that SB’s have much less value in real baseball.  For me, 1/3 of the fun of Roto is the enjoyment I get from paying more attention to real baseball, 1/3 is the competition aspect, and 1/3 is enjoying the company of a bunch of guys I’ve played with for year.

On #71, I think it should be the last player to be selected according to the projections.  At worst, that will be your option for a $1 player.

#70 - Its tradition at this point.  People are used to the 5x5 leagues and don’t want to change.

If I were starting a fantasy league from scratch I’d look into other options, but I’d rather keep the people I draft with and the fun of a live draft night than worry about flaws of the system.

I’m also in a 7x7 league this year.  The added stats are OPS and K for hitters, and walks and holds for pitchers.  It really puts a high power contact guy like Pujols ahead of 5x5 king Reyes.

On the pitching side, Ben Sheets gains against a Carlos Zambrano, and you really don’t care if Scott Linebrink stays as a setup man or wins a closer job.  In fact, you may need him to keep that setup job.

Should there be any difference to how you split the money between pitchers and hitters if you are looking at setting up a draft board for a straight draft instead?  My first instinct is know, that you are merely “spending” picks instead of dollars.

Great posts everyone.

For Post 50 and 51, why is the formula for xOBP = (1) and not (2)?

(1) xOBP = (H+BB+HBP) - (AB * (lg OBP))

(2) xOBP = (H+BB+HBP) - ((AB+BB+HBP+SF) * (lg OBP))

Should be #2.

Protrade’s scoring system:
http://www.protrade.com/HelpScoring.html

Hitting Stats
Hit 1.00
Out -0.38
Run 0.74
RBI 0.68
HR 1.67
SB 1.75

In post 60, I said you guys should be using this:
HR/10 + SB/10 + xH/10 + R/30 + RBI/30
where, xH = H - AB*.277

If we multiply my numbers by a constant (18), this is what we get:
1.8*HR
1.8*SB
0.6*R
0.6*RBI

xH/10
= (H - AB*.277)/10, which is the same as
= (H - (H+outs)*.277)/10
= (.723*H - .277*outs)/10
So, multiply all that by 18, and you get:
1.3*H
-.5*outs

I understand why Protrade handles the batting average as they do (lower break-even point).  They seem to give R, RBI a little more credit than they deserve.  All-in-all, they must have done the same thing I did to come up with those numbers.

For pitching

Pitching Stats
Win 4.68
Strikeout 0.45
Save 2.15
Earned Run -0.98
Hit or Walk -0.53
Out 0.38

And I did this:
W/5 + SV/10 + SO/50 + xER/10 + xWHIP/15
where:
xER = (4.10-ERA) / 9*IP
xWHIP = IP*1.32 - H - BB

Again, let’s multiply by 18 allround, and we get this for me:
W 3.6 (protrade gives too much credit)
SV 1.8 (PT gives a bit too much credit)
K 0.36 (PT gives too much credit)

For ER, my formula boils down to:
(ER/IP*9) / 9 * IP / 10 = ER/10, which multiplied by 18 means
ER -1.8 (PT gives only half the value)

For H, BB:
H -1.2
BB -1.2
Again, PT gives only half the value

For IP, it’s a little messier.  I’ve got it in two places, which means, 4.10/9*IP/10+1.32*IP/15=1.8*IP, or 0.045*outs, which multiplied by 18 means
outs +0.8 (again, PT gives only half the value)

So, Protrade has decided to give extra value to W, SV, and K, and far less value to ERA and WHIP.  I don’t really see the justification for doing that, from a “realistic” standpoint.

But, since everyone knows the rules to begin with, it’s no big deal.  Wouldn’t it be a little cleaner though to simply say:
W, 4
SV, 2
K, 0.5
R, -1
ER, -1
BB, -1
H, -1
outs, +1 (or whatever to make it all scale to the hitters numbers)

By the same token, you can give the hitters:
HR, 2
SB, 2
R, 0.5
RBI, 0.5
H, 1
outs, 1/3

Kind of a mess, no, to give out 2.15 here, and 1.67 there?

When I was doing my Marcel forecasts for 2008, I was wondering why I had “Pos” (position) SQL functions in my programs. Now that I found this thread, I realized that I did Fantasy dollars for all the Marcel players in 2007. 

I will do so again, and am bumping this thread as a reminder.  I just need to import the fielding data, which is a snap, but on a different computer.

If this thread falls out prior to my releasing fantasy dollars, just bump this thread up as a reminder.  And if someone has some really early time constraint, let me know.

I have a couple questions.  I’m trying to come up with dollar values, even though this is a straight draft league.  This league has 10 teams, (1 hitter at each position plus an extra OF and a DH) so 10 hitters and 8 pitchers (5 SP, 2 RP, 1 P).

I found each player’s z-score.

1.  So should I determine a player’s QALPAP by subtracting the last draft-able player’s z-score or the replacement player (for example, the #10 catcher or the #11 catcher)?

2.  With a dollar split of 180/80, would it make sense for my league, with my league setup, to have 16 hitters valued higher than Johan Santana?

I would subtract from the replacement player, though I would find it virtually impossible to believe that subtracting from the last draftable player would make even 25 cents of a difference. 

***

As for your other question, what is the range of your top 16 hitters, and how much is Santana?  I mean, it’s possible, but it doesn’t sound right.

Post 60 gives you the numbers from last year, if that can help you.

Okay, I changed to using replacement player but, more importantly, I changed the hitting/pitching dollar value split from 18/8 to 16/10 because it looks like that’s what you used above.  I guess that’s a preference, depending on the owner.  Using BP’s PFM, the default setting is 18/8 (180/80).  With a 16/10 split, the dollar values for my top-10 look like this (using my projections for 2008):

1.  A. Rodriguez $51
2.  D. Wright $43
3.  A. Pujols $42
4.  D. Ortiz $41
5.  R. Howard $39
6.  M. Holliday $39
7.  J. Santana $38
8.  M. Cabrera $36
9.  J. Reyes $33
10. J. Peavy $31

EDIT:  I accidentally left out Hanley Ramirez.

Okay, I changed to using replacement player but, more importantly, I changed the hitting/pitching dollar value split from 18/8 to 16/10 because it looks like that’s what you used above.  I guess that’s a preference, depending on the owner.  Using BP’s PFM, the default setting is 18/8 (180/80).  With a 16/10 split, the dollar values for my top-10 look like this (using my projections for 2008):

1.  A. Rodriguez $51
2.  D. Wright $43
3.  A. Pujols $42
4.  D. Ortiz $41
5.  H. Ramirez $41
6.  R. Howard $39
7.  M. Holliday $39
8.  J. Santana $38
9.  M. Cabrera $36
10. J. Reyes $33

Actually, my split was not determined before the fact, but after the fact.  I simply have the number of QALPAP for hitters and pitchers, and that’s it.  Each unit is worth the same. 

In any case, I think I had more than twice the dollars for hitters than pitchers.  The 18/8 seems just about right.

I play in a 12 team h2h cbssportsline league. I would like to know if someone can help me incorporate standard deviation into the preparation/evaluation process. I have only been playing fantasy for 2 yrs now. I will copy and paste the league scoring format.

Roster Limits
9 starting hitters(1 is a dh)
9 reserve hitters

5 starting pitchers
2 starting RP

1 Reserve SP
2 Reserve SP

2 DL spots

now for the scoring:
1B - Singles 1 point
2B - Doubles 2 points
3B - Triples 3 points
BB - Walks (Batters) 1 point
CS - Caught Stealing -1 point
CSC - Caught Stealing by Catcher 1 point
CYC - Hitting for the Cycle 8 points
E - Errors -1 point
GDP - Ground Into Double Plays -1 point
GSHR - Grand Slam Home Runs 5 points
HP - Hit by Pitch 1 point
HR - Home Runs 4 points
IB - Intentional Walks 1 point
KO - Strikeouts (Batter) -1 point
OFAST - OF Assists 2 points
R - Runs 1 point
RBI - Runs Batted In 1 point
SB - Stolen Bases 2 points
SF - Sacrifice Flies 0.50 points
TB - Total Bases 0.25 points

Scoring for Pitching Categories
B - Balks -2 points
BBI - Walks Issued (Pitchers) -.50 points
BS - Blown Saves -3 points
CG - Complete Games 8 points
ER - Earned Runs -1 point
HB - Hit Batsmen -1 point
HD - Holds 3 points
HRA - Home Runs Allowed -.50 points
INN - Innings 1 point
K - Strikeouts (Pitcher) 1 point
L - Losses -5 points
NH - No-Hitters 20 points
PG - Perfect Games 30 points
PKO - Pick Offs 2 points
S - Saves 6 points
SO - Shutouts 8 points
W - Wins 10 points
WP - Wild Pitches -.50 points

not sure what info you need in regards to points and roster requirements so I posted all of it.

I would really appreciate it if someone can guide me on how to go about incorporating standard deviation into my draft evaluation based on my league....using excel.....

thank you for the help!

In your case, you don’t need standard deviation (SD) at all.  You need the SD to “scale” the HR and SB and RBI and Wins, etc. 

In your case, you are assigned points for each category.

So, all you need is the Marcel forecasts, and apply the points to that.

Your only concern is the position.  That’s what QALPAP is for (quatlu above last player at position).  So, figure out the points for each player at each position, figure out how many points the last player at each position is worth, and adjust each player at each position downward by that number of points.

And you’re done.

Thanks for the response.

Im still a little confused though.

lets say I want to do the top 20 for 1b-3b. When you say figure out how many pts the last player at each position is worth....do you mean #20 on that list or do I go beyond that?

heres a list of the top 20 2b that CBS projects along with the projected point totals. How would I go about QALPAP using this info? thanks again for the help...I appreciate it

Utley, Chase 658.5
Cano, Robinson 579.8
Phillips, Brandon 546.5
Roberts, Brian 538.0
Uggla, Dan 515.8
Johnson, Kelly 506.0
Kinsler, Ian 495.5
Upton, B.J.  474.0
Polanco, Placido 468.2
Pedroia, Dustin 467.0
Weeks, Rickie 456.2
Hill, Aaron 456.0
Hudson, Orlando 449.2
Sanchez, Freddy 441.8
Kent, Jeff 2B 423.8
Lopez, Felipe 414.2
Escobar, Yunel 410.2
Lopez, Jose 2B 403.8
Ellis, Mark 395.8
Castillo, Luis 389.2

If you can show me what to do I can then apply it to the rest of the positions.

Subtract 389 from each 2B.  Your last player at each position will equal 0. 

Think of it this way: the last round should ideally be players all worth 0 points (the “gimmes”, as in “gimme whoever is left").

So, in your last Utley is worth 269 points.  That is, he will give you 269 points above your gimme at that position.  You are, basically, “guaranteed” 389 points at 2B…

ok. i think i understand it now....

so just to be clear....utley is projected to be 270 pts better than the next 2b?

cano is projected to be 191 pts better than the next? etc

and if i want to make a list of overall projections of all the possitions(including sp/rp) how do I do it so it is equally valued?

thanks again my friend

270 points better than the LAST 2b, not next 2b.

And doing it this way, for each position, ALREADY makes them equally valued.  Remember, you want the LAST player selected, at each position, to be worth exactly the same (0 points).  In this case, Castillo will be worth 0.

It’s as simple as it sounds.

ok i think i got it now....

you have any other tips or suggestions I could use?

You should be good to go.

if im combining positions dont I still need the last guy to be the same last guy at other positions?

ex.

if i want to use the top 25 at each infield pos. but lets say the top 65 for of and top x for sp and rp...\

dont i have to subtract a designated amount of points from each guy?

holliday= 671 and the last OF on the list(#65) lets say is 360.

so i subtract and get 311.

now i look at utley who is at 659 and the last 2b on the list(#30) is 309.

so i subtract and get 350.

now i can just combine the 2 into an overall ranking?

how do i interpret those 2 numbers in context of an overall ranking

or dont i have to subtract a designated amt of pts from each player in each position...lets say i use 350pts is the cutoff....

No, that’s it.  Holliday has 360 QALPAP and Utley has 350 QALPAP.  You don’t need to do anything else.

The common baseline is the last player selected at his position (the “LPAP” part).  The #65 OF and the #30 2b will both be exactly 0 points.

Just make sure that the “#65” implies that you expect 65 OF to be chosen and “#30” implies you expect 30 2B to be chosen.

ok now i got it....so what i should do is multiply 12 by the #of players we need for each position.

so we need 2 players for every infield spot.
6 total of
6 sp
4rp
2dh(any position except pitching)

so im going to do
24 players per infield pos.
72 outfielders
72 SP
48 Relievers

now what do i do with the dh scenario...each team has to draft 2 and they can play any position except SP and RP obiviously

After you have your initial list of 24 1b, 24 2b.... etc, etc, put those aside.  Those are all the guys with positive QALPAP numbers.  That’s your MAIN pool.

Everybody else is considered a “wildcard” player.  In THEIR case, you simply select the top 24 by Quatlu points (no comparing to position).  It’ll be mostly OF and 1B of course.

Now, here’s the tricky part.  Now, you take those 24 wildcard players and put them BACK into the MAIN pool.  You now need to recompute the QALPAP points of every player, since you’ve now introduced a lower baseline for some of the positions.  If you don’t do this, you’ll end up with negative numbers for players.

Hope that’s clear…

ok so after i do all the positions.

1)I take the top 24 players that are not included on the previously compiled list

2)put those 24 in the main pool

3)then use the pts from the last player on the list(which would be #24 of the wildcard pool that was added in)as the number to subtract from the other players....

So lets say the last player(that now includes the wildcards) pts total is 200.

The top players original pts projection is 600

So I do 600 -200 for my final total?

is all of that correct?

if so Thanks again for all the help

By position.

Yes.

ok now..last thing:

QALPAP:
Pujols=339
Rollins=322
Holliday=317
Arod=315
Utley=290
Vmart=239

I arrived at those numbers by subtracting the playrs 08 projected pts by the #24th player of that pos.(#72 for the outfielders)

then I compiled the list of the 24 next best 08 projected pts and put them in order of pts not position.
It went from 1) Dan Johnson 366
to
24)Brendan Harris 329

those are the raw projected ‘08 pts

now do I plug them into the overal list of players?
so would I be doing
Pujols 730-329=401=Pujols QALPAP for the overall rankings

or

do I take the list of 24 wild card players and arrange them by position. and do their QALPAP score:
so lets say for 2b of the wild card players:
Derosa 360
Cabrera 357
Durham 344
Harris 329

now would I take each of those totals and subtract them from 329 to get the QALPAP score?

if so, then what would I do to incorporate all of these players into 1 list given all the info

thanks again bro.

In your case, because of the DH, you don’t need to figure the QALPAP prior to the wildcard.  Here are the steps:
1. Figure out the top 24 and 72 and whatever for each position.  Just straight gross points.  Put all those guys in the MAIN group.

2. Of all the players remaining, select the top 24 in gross points.  Those are your wildcard players. 

3. Merge the MAIN and WILDCARD groups.

4. Figure the lowest score for each position.  In this case, you might have 25 2B, 31 1B, etc. 

5. For each player, subtract out the lowest score at his position.  That’s every player’s QALPAP score.

6. That’s it.

If we were going to include OPS in our league, how would you convert that into xOPS, similarly to the other rate stats (i.e. AVG, ERA, WHIP)? 

Would you just do xOPS = (OPS_i * PA) - (OPS_lgavg * PA)? 

Thanks.

Probably, but with OPS, it’s a litle more weird because of the different denominators.

In any case, your equation simply becomes:
xOPS = PA * (OPS - lgOPS)

With lgOPS being the weighted OPS of the players drafted.

What player pool would you use for a league with benches, but no specific requirements as to what position those bench players play?  For example, say a 14-team league with 13 active hitters, 9 active pitchers, and a 7-man bench?  So each team has 22 active players and 7 bench players.  Should the player pool be 308 (14x22) or 406 (14x29)?  I’d guess it would be 406, so the owner would have to roughly estimate what the teams’ benches would look like.  Is this correct?