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DownloadAssorted Rants, Rumblings and Ruminations from the Mind of a “So-Called” Expert
This piece was originally posted in 2010 for Platinum subscribers and has been archived there since. It's the first essay associated with Valuation Theory being brought out from behind the firewall. Please feel free to ask questions in the comments, or preferably on the newly upgraded site forum.
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Much of my preseason presentation will involve discussing a player’s value. The signature element of the system is the way we set the pool size by assigning value only to useful statistics. A useful statistic is designated as production over and above that which can be had for free. That which can be had for free is specified by the replacement level player. Since this concept is so integral to our system, it is worthwhile to spend a little time focusing on replacement player theory and understanding its application and ramifications.
When I first embarked on the journey to fully comprehend the science of player valuation, the most difficult hurdle was grasping why some valuation processes gave negative value to players with positive counting stats. A player hits a home run, drives in a run or steals a base and he helps your fantasy team. How could that be worth a negative dollar amount? The answer lies in replacement player theory.
Let us begin by pretending the available player pool is just sufficient enough to provide each team with ample players at every position. Not all the statistics in that pool are useful. A certain amount of each statistic is shared by every team in the league. These shared statistics are not useful, that is they do not help you to achieve rotisserie points. Think about a typical weekly football pool where you pick the winners of all the games. If everyone picks the same team, that game does not matter. All the participants get a win or a loss.
Because a standard rotisserie roster requires players to occupy a roster spot defined by their positional eligibility, it is necessary to compare useful statistics position by position. If the useful statistics contributed by one position are different than another, the value earned by these two players is different. They may both contribute the same number of raw statistics, but they provide a dissimilar amount of useful statistics. Remember, value is only awarded to useful statistics.
A simple way to illustrate this principle is to envision a home run derby league with four available players, two catchers and two outfielders. We both need one of each. One catcher hit 30 homers, the other 10. One outfielder hit 30 homers, the other 20. You have first pick, who do you choose?
Of course, you opted for the 30-homer catcher. Of his 30 dingers, 20 would be useful as I will be stuck with the 10 from the other catcher. I’d then take the better outfielder, but he nets me a paltry 10 home run advantage over the lesser one. So, we each drafted a player that knocked 30 out of the yard, but you win as your catcher’s production as compared to my catcher surpassed the advantage my outfielder gained over yours.
Now pretend the above example is for an auction league and you have $260 from which to bid. You throw out the first name and bid $259 for the better catcher. Not that it matters, but I’ll take the superior outfielder for $2 and the lesser catcher for $1, leaving you with the $1 outfielder.
This brings us to the concept of a replacement level player. In theory, the inferior catcher and outfielder in the above scenario have no value as they supply no useful home runs. The caveat is we are forced to spend $1, even though their value is $0, thus the introduction of the replacement level player. Instead of subtracting out the statistics shared by the positively valued player pool, we subtract away the statistics of an imaginary replacement player whose estimated performance is dictated by the best remaining non-drafted players. As suggested, each position has its corresponding replacement level player.
One of the most commonly debated topics in fantasy baseball is positional scarcity. There are a couple of different types of positional scarcity. One focuses on the perception that a player pool does not contain sufficient positively Replacement Player Theory valued players at each position. The second concentrates upon the overall talent of a position or perhaps the large drop-off of talent after the top few players. The former is a facet of player valuation and can be broached using replacement player theory. The latter is really a strategy-oriented entity.
The term perception was carefully chosen to suggest some player pools lack enough draft-worthy players at the so-called scarce positions. By applying replacement player theory, this perception is more properly labeled a myth. One of the principle rules of our valuation system is that a player pool is composed in such a manner that there are exactly enough players at each position for every participant in the league to field a legal lineup. In short, there is no player scarcity—everyone has a player of positive value at each position in their lineup. This should make some obvious sense – a player has positive value if he can be rostered and does not if he cannot, regardless of what their raw stats are.
The best way to convince yourself this must be a condition of a viable valuation process is to think about how you would assign value if there were no excess players at all available. That is, every Major Leaguer had to be on an active fantasy roster. The worst players at each position would be valued at $1 and everyone else would be scaled upward. The possibility exists that $1 players at different positions would be of varying quality.
Now think about how the setup really is with extra players in the pool. The best non-drafted players at each position comprise the replacement player pool and can be valued at $0. As just illustrated, depending on the depth of the player pool, it is quite possible for there to be different levels of replacement players by position. Here’s the key. After you take away the production of the replacement level player at each position, you should be left with a similar number of useful stats at each position for the $1 player. That is, $1 players may have different raw stats by position, but they have the same amount of useful stats. The thing is we don’t just score the useful stats, we score all the stats. We just don’t assign value to all the stats.
Taking one more opportunity here, one could say that a player’s value is determined not by the raw value of their statistics but by the opportunity cost given up acquiring that player. That is, if instead of drafting player A, I instead waited until replacement to fill that slot, how much extra am I buying?
Putting this all together, it is now possible to understand why a home run from a catcher is worth more than a home run from an outfielder. For simplicity, let us again think of things in terms of a home run derby league. The replacement level for catchers is far inferior to that of outfielders; therefore, fewer homers are taken away from the raw total per catcher than per outfielder. It was just explained that the number of useful homers of a catcher and outfielder of the same value is the same. When the number of homers taken away due to the replacement level player is added back, it follows that outfielders and catchers of the same value hit a different number of home runs. Specifically, since the replacement level for catchers is less than that for outfielders, the raw total is also less. This means that a catcher earning the exact same amount as the outfielder needed to hit fewer homers to attain that value. If the dollar value is expressed as dollar per homer, a home run from a catcher is worth more than a home run from an outfielder which was the original premise we set out to prove.
Let’s use some real numbers. Pretend the number of useful homers a $20 ballplayer hits is 20. Let’s say the catcher replacement level is 2 and the outfielder level is 6. A $20 catcher hits 22 homers while a $20 outfielder hits 26. Dividing $20 by 22 yields each catcher homer being worth 91 cents. Dividing $20 by 26 means each outfielder’s homer is worth only 77 cents, 14 cents less than that from a catcher.
One could fairly say that a player’s value cannot be determined by their relation to replacement alone, that there are other factors implicit in the value determination. They would be correct. However, as a baseline for setting value, we need a process which values players against each other on a fixed level. Adjustments thereafter can and should be made to take other factors into account, but they are strategic in nature.
In summary, a proper valuation system will account for the myth of position scarcity and set the player pool to render ample players at every position. The repercussions of this are that players of the same value produce at varying levels according to position.
About a week ago, I detailed my process for generating hitting projections. Now it’s time to do the same for the pitchers.
Like with hitting, skills are expressed as a rate stat. Hitting used plate appearances, as does pitching, though I’ll express it as per innings.
Using strikeout and walks as the example, K% and BB% are better than K/9 and BB/9 to get the true skill level. For those unaware, K% and BB% use batters faced (essentially plate appearances) as the denominator. It’s subtle, but K% is a better indicator than K/9. A pitcher allowing more runners faces more hitters, availing more chances to punch them out. Think of it this way. Two pitchers carry an identical 8.1 K/9, whiffing 180 in 200 innings. One faced 800 batters, akin to about a 1.10 WHIP while the other faced 844 hitters, equating to about a 1.30 WHIP. The first posted a 22.5 K% while the second registered a 21.3 K% mark. This is like two batters each garnering 160 hits, but one needing 550 AB (.291 average) while the other required 580 AB (.276 average). Which is the better hitter? Of course, the former. Well, the difference between .291 and .276 is the same as 22.5% and 21.3%.
The engine projects K% and BB%, but I also project batters faced per inning. K% and BB% can easily be converted to K/9 and BB/9. It’s easier for me to project innings when doing pitching playing time, so while technically I use K% and BB% in the projections, the final projection takes K/9 and BB/9 out to K and BB using innings.
Pitching projections utilize the same three-year stat spread and weighted average as hitting. Similarly, MLEs are used to fill in the blanks for prospects. Finally, composite park factors and aging adjustments are incorporated in the same manner.
A common theme with pitching will be regression, even more so than with hitters. The sample size of the different events associated with throwing a baseball is small, even for a workhorse starter. Outcomes don’t always sync with skills. Thus, almost all the components require regression to best frame what’s likely to happen.
Please keep in mind I’m a bit of a obstinate stickler with respect to the term regression. It’s come to mean “play worse” in the fantasy lexicon. In my Utopia, regression would have the specific meaning of correcting for outcomes out of the pitcher’s control. Admittedly, with improvement in data collection and analysis, we’re learning more and more about the proverbial luck versus skill delineation, but we can only go by what we know at the current time. My default level of regression is 50 percent. That is, the projected number is the average of expected and actual. I’ll then massage as appropriate, but always with a reason.
With that as a backdrop, let’s go through the four basal skills intrinsic to a pitcher’s projection: home runs, strikeouts, walks and hits. From there we’ll move onto the standard roto categories then hit some of the stats used in points-leagues scoring.
Home Runs
While hitters set their own home run per fly ball baseline (HR/FB), pitchers cluster around the league average. As you know, this is on the rise:
Season | HR/FB |
2015 | 11.40% |
2016 | 12.80% |
2017 | 13.70% |
As an aside, hit types are still determined subjectively. Soon, they should be designated via objective criteria. Until then, some number, like HR/FB may differ between data sources. The key for analysis is using the same source for the research, of in this case, projections.
Based on the number of fly balls a pitcher allows, an expected number of homers can be determined. After some park neutralization, the actual and expected number of long balls are averaged. After being divided by batters faced, the park-neutral HR% is calculated. This will eventually be converted to HR/9 for the final projection.
Strikeouts
Some elegant studies show strikeouts are proportional to Swinging Strike Rate (SwStr) with an influence of First Pitch Strike Rate (FpK). I have a formula using this data to generate an expected K%. Again, a park neutral K% is computed then regressed with actual K%.
Walks
The great research team at Baseball HQ demonstrated a similar relationship between the number of balls thrown and BB%. I have developed an expected BB%. You know the rest.
Hits
There’s a reason hits are discussed last. Similar to how I project hits for batter, I use batting average on balls in play (BABIP) for pitchers. As you can likely surmise, more specifically, expected BABIP. As discussed in the hitting essay, I have data breaking batted balls into multiple classifications: groundball, infield line drive, outfield line drive, fly ball, bunt and popup. All but bunt and popup are broken into soft, medium and hard hit. The league average for each subset is determined and they employed to calculate an expected BABIP. After the usual park neutralization, a park-neutral BABIP is determined and plugged into this formula to derive hits.
Hits = (AB – HR – K + SF) x BABIP + HR
There’s a couple of components needed not discussed yet, namely hit by pitch (HBP) and sacrifice fly (SF). They’re just a three-year weighted average like what was done with hitting.
So, now I have expected hits and actual hits, all that’s left is to regress, blah, blah, blah.
WHIP
The neutral H/9 and BB/9 are treated with the aging and park adjustments to get projected hit and walk rates. This is a bit circular, but based on the projected innings, projected hits and walks are determined, which are then summed and divided by projected innings to generate projected WHIP.
ERA
I use a modified expected ERA formula, using the aforementioned described skills to derive expected runs. This is regressed to actual neutralized earned runs to land on projected earned runs which gets the aging and park alteration for the final numbers. Using projected innings, the projected ERA follows.
Wins
This isn’t perfect, but I’ve been using it for over a decade and it works as well as any other method I’ve seen. Many years ago, Bill James came up with a manner to estimate team wins using what’s now knows as Bill James Pythagorean Theorem. It incorporates runs allowed and runs scored to calculate an expected winning percentage. To get wins, the winning percentage is multiplied by the number of decisions.
Let’s start with runs allowed. Above, earned runs are projected. Using a team defense factor, I generate the number of runs. Next is estimating a bullpen component. The number of runs allowed while the pitcher in question is in the game Is added to the bullpen projection. I now have total runs allowed.
Runs scored is simply an estimation, based on previous season’s numbers and how the team has improved or declined.
Decisions are proportional to the number of projected innings, using 9 x 162 in the denominator. It’s not perfect, but correlation studies show it’s reasonable.
Calculating wins for starting pitchers plugs all this into the standard Bill James formula. Relievers are tricky, since set up men and closers have a greater chance to lose games than win them, based on their usage. As such, I flag all relievers projected for holds and saves and apply a modified Bill James formula.
Saves
Based on some research I’ll present in an upcoming Z Files, available for Platinum subscribers, there’s some science involved with projecting saves. The short version is percentage of wins that are saved correlate best with team ERA. Using this, I generate a projected team saves total. A percentage of saves projection is made for relievers, which is multiplied by projected team saves to yield the saves projection.
Holds
Currently, I haven’t found any relationship between team wins or saves and holds. It looks to be a matter of how each manage deploys his bullpen. Some use more lefty specialists, some rely on their best setup reliever to work more than an inning. As such, holds are projected manually, on a player-by-player basis.
Quality Starts
There’s a couple of formulas available on the web to derive quality starts (QS). Each year, I look to see which did the best job of back-projecting the previous season’s number of QS and I’ll use that. I’ll be interested to see how well these hold up with the current trend of pitchers throwing fewer innings. There are coefficients in each that could need tweaking with the changing landscape. With many leagues incorporating QS into their scoring, I want to make sure I provide a usable number.
Compete Games, Shut Outs, No hitters
Yes, some leagues give points for no hitters. No, I don’t project anyone to toss a no-no. I will project CG and SO using historical data, but it’s more a guess than scientific.
Singles, Doubles and Triples
Some points leagues score this so I need to project it. Homers are done as discussed while singles are hits minus extra base hits. That leaves doubles and triples. These are park-neutralized then adjusted via BABIP before the usual aging and park changes to yield the final projection.
Innings Pitched
All that’s left are innings. For starters, I use the past three seasons to derive an innings pitched per start number. It’s not always the three-year weighted, but that’s the starting point. I’ll tweak as I do each pitcher’s projected games started. Relievers are done on a pitcher-by-basis, based on past and expected usage.
As with hitter’s plate appearances, I try to keep each team reasonable, but I no doubt over-project some staffs. Most of the time, there’s a sixth and seventh starter pushing the total team starts over 162. They’re very likely to pick up starts as in injury replacement, I just don’t know who will get hurt. All I can do is give an honest appraisal.
That should do it for the Mastersball projection process. It’s a fluid process, constantly undergoing changes as more data is available to refine regressions. I’ve been asked on several occasions over the years how well it stacks up against other models, as well as wondering if I back-test against the previous season. The answers are I don’t know, and no. This usually disappoints the person asking, but it’s the truth. The primary reason is I have yet to see a grading system that adequately scores the components of projections. Some use rate stats, but that ignores the diligence of playing time estimations. Some use raw numbers, which are also influenced by playing time as well as luck. I suppose the obvious follow-up is why don’t I devise a system that scores playing time and basal skills. It’s a fair question. The answer is I know intuitively if there’s a deficiency in a specific area; I don’t need to quantify it. Early on, I could sense where the projections were faulty. Over the years, I’ve refined the process to the point my time is best spend boning up on the new research and incorporating the results into the engine, usually to further refine regressions.
Next up is bringing the valuation methodology out from behind the firewall.
Questions? Concerns? Criticisms? Hit me up in the comments, or preferably on the newly renovated site forum.
Last week, I posed the question if Shohei Ohtani should be pitcher eligible, despite serving as designated hitter 65 times last season, compared to just five appearances on the mound. For those concerned I’ve lost my mind, of course he should. That said, unless your commissioner is extremely prescient, I bet your rules don’t define pitcher eligibility. Further, I promise you, there’s a jealous owner in a dynasty league causing a ruckus, trying to screw over the Ohtani owner.
Obviously, pitchers are pitcher-eligible because they’re pitchers. There hasn’t been a need until now, and some may argue there still isn’t a need. Here’s why all rules could now include specific pitching eligibility. What happens if Ohtani suffers an odd injury that prevents him from taking the mound this season, but he’s able to hit, and is expected to pitch again in 2019? Is he not eligible as a pitcher since he didn’t pitch in 2018?
My proposal is defining a Hitting Class and Pitching Class. The eligibility within the Hitting Class is exactly as it is in your current rules. The Pitching Class is anyone taking the hill at all the previous season, provided your scoring service is set up to score their pitching stats along with a common-sense clause permitting eligibility for anyone obviously expected to pitch the upcoming season. Further, an individual player can have eligibility in both classes, to be deployed according league rules governing such players.
“Provided your scoring service is set up to score their pitching stats” is included is to cover the pinhead owner wanting to start Chris Gimenez (as an example). In some head-to-head formats, some may opt for no stats from the spot as opposed to risking a pitcher damaging ERA and WHIP.
The common-sense clause covers the Ohtani scenario. There’s also a chance a position player converts to a hurler without having pitched the previous season.
So, no, I haven’t gone crazy, at least not yet. Common sense should prevail, but we also should formally address this new quirk in our constitutions.{jcomments on}