Extra Musings on What Groups Are Paying for a Win in Free Company

Earlier this week, I wrote about the price of a win in free company. I liked seeing the dialogue of that article on-line and within the feedback part, so I believed I’d put aside a while to contemplate just a few of the questions readers had. Listed here are my solutions to these questions.

What if We Used Extra Tiers?
If three tiers is sweet, would 4 be higher? 5? Six? In my preliminary evaluation, I ran all these variations within the background and determined that three was optimum for presentation and readability. I additionally decided that the pattern sizes would get vanishingly small as we expanded to an increasing number of tiers. However as a number of readers requested for extra granular seems, why not? Here’s a four-tier model:

And a five-tier model:

Why didn’t I exploit these? They didn’t add all that a lot info. Per a log probability check, the four-tier mannequin reduces error by round 1-2% relative to the three-tier mannequin, a minor improve. In case you’ll recall from the earlier article, going from one to a few tiers was value a 13% discount in error. By the point I divided issues into 5 tiers, log probability noticed no enchancment relative to the three-tier mannequin. That’s the price of rising complexity with small pattern sizes. The free agent market is cut up into a number of ranges relying on participant caliber. However there are diminishing marginal returns as you slice the information an increasing number of finely. A 3-level mannequin is a big enchancment on a one-level mannequin, however previous that, the information is much less clear.

What About Pitchers Versus Hitters?
I modified my script to run tiers for pitchers and hitters individually. Right here’s how these look:

The variations within the prime two bands aren’t statistically significant. However that 0-1 WAR tier of pitchers is fascinating. Of word, there are much more hitters within the 0-1 WAR group than there are pitchers; since we’ve separated out relievers from our knowledge, the populations don’t fairly match. Nonetheless, it’s a reasonably attention-grabbing impact.

I’ve one predominant concept. That bucket positively has a whole lot of pitchers coming back from damage. Think about a pitcher with a 0.5-WAR projection of their first yr again from elbow surgical procedure signing a two-year deal. My rule-based system for outlining WAR mechanically assigns them 0.5 WAR in yr one and 0.1 WAR in yr two. However that yr one projection was low not due to an absence of expertise, however an absence of availability. While you’re working with massive pattern sizes like this, it’s essential to consider bizarre nook instances your guidelines may create, and this looks as if a superb one to level out.

In any case, there’s one thing attention-grabbing right here: Pitchers don’t have as clear of a talent-based cut up in compensation in comparison with hitters. Groups at all times want extra pitching, and there’s most likely one thing to the truth that pitchers aren’t getting any youthful, which implies that a few of these contracts is perhaps extra about availability than expertise. We discuss in regards to the lack of availability of fine pitching on a regular basis; perhaps that’s resulting in a dislocation within the decrease reaches of the free agent market. It’s one thing to regulate, in any case.

Is Offensive WAR Higher Compensated Than Fielding WAR?
The best way I collected the information means there’s no technique to separate out this explicit aspect of participant worth, however I’ve ideas on it anyway. The reply is a transparent sure. Once I make particular person contract predictions moderately than taking a look at broad league-wide tendencies, I embrace that impact each time. There are any variety of causes this might be, however I’ve just a few favorites.

First, it’s a provide and demand factor. Good fielders aren’t truly that monetarily costly for many groups, as a result of many good fielders are younger and cost-controlled. There are extra plus heart discipline defenders within the minors than plus heart discipline hitters. On condition that, why would groups pay the identical charge for good fielders and good hitters on the open market? WAR is a pleasant abstract statistic given a impartial context, however that is clearly not a impartial context.

May it’s a positional adjustment problem? Positive. The DH and first base changes is perhaps a bit harsh, one thing we’re trying into within the medium time period. However the impact isn’t restricted to these positions, not less than in my expertise in contract predictions. Offense-first gamers are prioritized throughout the board; it’s simply most evident within the two most offensively-focused positions.

May it’s a stability of defensive projections problem? Eh, I’m skeptical. I haven’t seen any proof for it, but it surely’s the form of factor that I don’t know learn how to show or disprove mathematically. For now, I’ll simply say this: As a rule of thumb, bat-first gamers get somewhat greater than their uncooked projected WAR would recommend, and glove-first gamers get rather less. Going into any extra depth is outdoors the confines of such a evaluation.

What if Substitute Stage Is Larger?
This was the principle argument I needed to write down about right now. That is one apparent interpretation of the truth that groups don’t need to pay a lot for “one win above alternative.” If alternative stage is one win greater than we thought, in fact that first “win” isn’t very worthwhile.

Right here’s a easy thought experiment: Think about two full-time gamers. Participant A is projected for 3.0 WAR and receives a one-year, $40 million contract, $13.33 million per win. Participant B is projected for 1.5 WAR and will get a one-year, $15 million deal, $10 million per win. Now, let’s elevate alternative stage by a win and re-evaluate. Now we’ve acquired 2.0 WAR and $40 million, or $20 million per “new win,” for Participant A, and 0.5 WAR and $15 million, or $30 million per “new win,” for Participant B. A better alternative stage makes dollars-per-WAR go up for everybody, but it surely makes that quantity go up essentially the most for the gamers who’re closest to the brand new alternative stage.

Previously, I’ve shied away from this methodology due to one drawback: Groups nonetheless do pay for that first win above the present alternative stage. By transferring the bar greater, we introduce a system the place groups pay for wins beneath alternative. That sounds conceptually bizarre to me. However I’ve spent a while brainstorming this through the years, and I got here up with a workaround that I feel lets me do the maths anyway.

First, I reset alternative stage by lowering the variety of WAR obtainable to the league as an entire. Proper now, we outline alternative stage in order that there’s precisely 1,000 WAR yearly, which suggests {that a} replacement-level crew would play at a .294 profitable share clip. I decreased the quantity of WAR handed out sequentially, anyplace from 50 to 300 wins (a .356 alternative stage). That entails altering the per-PA and per-IP alternative stage after which recalculating every participant’s WAR at every breakpoint. Fortunately, I might simply inform my laptop to try this.

Subsequent, I needed to type out the below-replacement-level pool. If a participant is projected for unfavourable WAR, however a crew indicators him for $2 million, they’re paying $2 million for some base competence stage that they don’t really feel they might get without spending a dime. I outlined this mathematically by taking the sum of money groups assured to below-replacement-level gamers, dividing by their enjoying time, after which including that up into full-time equivalents (160 IP, 600 PA). That gave me the bottom quantity that groups are paying free brokers for his or her abilities. I then subtracted that base quantity from each participant’s contract, and did the identical WAR tiering as earlier than. A methodological word: I excluded 2020 for playing-time-projection causes.

Let’s do a fast instance of how this works, as a result of I do know that’s a whole lot of math phrases all slammed collectively. If I redefine alternative stage in order that the league solely has 750 WAR obtainable, there have been 93 contracts handed out to below-replacement gamers in my pattern set. They acquired a median of $3.9 million per full-season enjoying time equal. In different phrases, the price of discovering a succesful, full-time veteran is $3.9 million, whether or not they clear the alternative stage bar or not.

From right here, I separated the remaining gamers into the identical tiers as earlier than: 0-1, 1-2, and 2-plus WAR. I additionally subtracted out the bottom contract quantity from above, pro-rated by the enjoying time that Steamer projected for every participant. I acquired 377 0-1 WAR gamers, 158 1-2 WAR gamers, and 87 2-plus WAR gamers. Along with the bottom quantity, groups paid $7.7 million per win to the 0-1 WAR group, $11.1 million per win to the 1-2 WAR group, and $13.9 million per win to the 2-plus WAR group. In different phrases, the tiered construction stays a superb description of the market.

That’s the instance, however listed below are all of the numbers:

The upper I set alternative stage, the smaller the hole between the 0-1 WAR and 2-plus WAR tiers acquired. It by no means disappeared, although. Even at greater alternative ranges, groups nonetheless pay up for stars.

For good measure, I attempted one other, less complicated approach of transferring alternative stage. As a substitute of trying on the contracts handed out to below-replacement-level gamers to calculate a base quantity for a free agent contract, I merely threw them out. Then I did my unique tier-by-tier examine the identical approach: calculating {dollars} per WAR for every group individually. Right here’s how that appears:

In different phrases, regardless of the way you slice it, the tiered nature of free agent compensation is about extra than simply the place alternative stage is. Positive, setting the next alternative stage compresses the unfold. It has to, mechanically. However the knowledge nonetheless present that groups are paying one of the best gamers extra per win, even if you happen to assume alternative stage may be very excessive.

I had desires of constructing one other model of this alternative stage examine the place I create a number of alternative ranges for various buckets of groups. The Dodgers and White Sox don’t have the identical alternative stage, in fact. I would nonetheless get that math accomplished sooner or later, in truth. However I wasn’t fairly capable of make it work for this text, and I needed to get some knowledge out, so it should wait. The takeaway right here is that whereas altering alternative stage may clarify a few of this habits, the wage construction stays non-linear. Groups pay extra per win for the perfect free brokers.