Finding True Value in Fantasy Baseball — From Z-Scores to Dollars (4/6)

Part 4: From Z-Scores to Dollars

TRP — True Relative Price: True Value. Market Pricing. No Noise.

Part 3 gave us a common currency: Z-scores that measure each player’s contribution above replacement, comparable across categories and positions. Sum them up and you get total Z — a single number capturing fantasy value.

But Z-scores aren’t actionable. When you’re sitting in an auction and someone nominates Gunnar Henderson, you need a number in dollars. When a trade offer comes in, you need to know if you’re giving up more value than you’re getting. Z-scores don’t answer those questions directly.

This is where TRP converts statistical value into economic value. The framework is simple in concept: take your league’s total auction budget and distribute it proportionally to the Z-scores each player contributes. The execution requires a few deliberate choices about how to slice the budget.

Photo by Eduardo Soares on Unsplash

The Budget Hierarchy

TRP allocates dollars through a hierarchy of splits, each informed by predictability and strategic considerations:

Level 1: Total League Budget

In a standard 12-team auction league, each team has $260 to spend. But $5 is reserved for bench players — replacement-level assets you’ll acquire at minimum cost. That leaves $255 of “real” budget per team, or $3,060 across the league. Every dollar of player value must come from this pool.

Level 2: Hitter/Pitcher Split

The industry standard is 65/35 in favor of hitters. TRP uses a more aggressive 70/30 split.

The baseline comes from roster construction. In a typical 21-slot roster with 9 starting batters, 7 starting pitchers, and 5 bench spots, you’ll usually carry 12–13 hitters (filling 3–4 bench slots with bats). That’s already ~60% hitters by roster share.

The additional weight toward hitters — pushing from 60% to 70% — comes from predictability. Hitting statistics are more stable and projectable than pitching statistics. A hitter’s OBP projection correlates strongly with his actual OBP. A pitcher’s ERA projection is far noisier — ERA depends on sequencing, defense, park factors, and luck in ways that batting stats don’t.

Injury rates compound the problem. Pitchers get hurt more often and more severely than position players. When you invest heavily in pitching, you’re buying more variance.

The 70/30 split reflects both realities: roster slots get you to ~60%, and predictability pushes you to 70%.

Level 3: Category Weights Within Hitting

Not all hitting categories are equally projectable. TRP analyzed projection accuracy across multiple seasons using a Projection Reliability Index (PRI) — a composite measure of correlation, RMSE, and normalized error.

The results show a clear tier break:

Rate stats (OBP, SLG) are dramatically more predictable than counting stats. The gap between SLG (4.88) and R (2.22) is larger than the entire spread among counting stats (2.22 to 1.37).

TRP captures this with a simple 50/50 split:

This means OBP and SLG each get twice the budget weight of R, HR, RBI, or SB. You’re investing more in the categories you can predict.

Level 4: SP/RP Split Within Pitching

Starting pitchers and relief pitchers contribute to different categories and have different risk profiles. TRP splits the pitching budget evenly:

An even split might seem generous to relievers, but it reflects {my} roster construction realities. Most leagues require saves/holds production, and RP represents a distinct strategic asset — not just a lesser version of SP.

Level 5: Category Weights Within Pitching

The same PRI analysis reveals which pitching categories are projectable:

Starting Pitchers:

Relief Pitchers:

One category stands out across both pools: K/9. It’s the most predictable stat for SPs (6.22) and the only reliably predictable stat for RPs (3.61). Strikeout rates are a skill that persists. ERA, by contrast, is nearly random for relievers (0.62 PRI).

TRP weights K/9 at 40% of each pitching pool, with the remaining 60% split evenly among the other four categories:

SP Budget ($459):

RP Budget ($459):

From Category Budgets to Position Budgets

We have category budgets for the entire hitter pool. But catchers and outfielders don’t contribute equally to each category. A position group’s share of each category budget should reflect its actual production share.

Here’s how it works:

Step 1: Calculate each position’s production share per category.

Say the rostered catcher pool (top 12) is projected for 200 HR collectively, while the entire rostered hitter pool is projected for 4,000 HR. Catchers represent 5% of HR production.

Step 2: Allocate that share of the category budget.

The HR category budget is $268 (12.5% of $2,142). Catchers get 5% of that: $13.40.

Step 3: Convert to dollars per Z.

If the rostered catcher pool has a combined +8.5 zHR (sum of all 12 catchers’ HR Z-scores), then:

$13.40 / 8.5 = $1.58 per zHR for catchers

Step 4: Calculate each player’s dollar value from that category.

Will Smith projects for +2.1 zHR. His HR value: 2.1 × $1.58 = $3.32.

Step 5: Repeat for all categories, sum for total player value.

Will Smith’s total value = $3.32 (HR) + $X (R) + $Y (RBI) + $Z (SB) + $A (OBP) + $B (SLG)

Why This Prices Positional Scarcity Automatically

The production-share approach has an elegant property: positional scarcity is baked in without any manual adjustments.

Consider two positions:

Catcher (scarce):

• 12 rostered catchers produce modest counting stats
• Small share of total HR production → small HR budget for position
• But also: lower total zHR across the pool
• Result: $/zHR might be similar to other positions, but elite catchers stand out more because the Z-score spread is compressed

Outfield (deep):

• 36 rostered outfielders produce huge counting stats
• Large share of total HR production → large HR budget for position
• But also: more total zHR to distribute across
• Result: $/zHR gets diluted, but the position absorbs more total dollars

The math self-corrects. You don’t need to manually add “positional adjustment factors.” The production share and Z-score distribution handle it.

A Worked Example: Catcher Valuation

Let’s walk through a complete catcher valuation using hypothetical but realistic numbers.

League Setup:

• 12 teams, $255 budget each = $3,060 total
• 70/30 hitter/pitcher split → $2,142 for hitters
• 50/50 rate/counting split within hitters

Category Budgets:

Catcher Production Shares (hypothetical):

For counting stats, we use actual production totals:

For rate stats, we weight by plate appearances. Catchers average 500 PA vs. 600 PA for other positions. With 12 catchers and varying counts at other positions, catchers represent roughly 7.4% of total weighted PA.

A note on apparent contradiction: Earlier we argued against weighting rate stats by playing time at the individual player level — because counting stats already penalize low-PA players. A catcher’s lower PA already shows up in his R, HR, RBI projections.

But at the position budget level, PA weighting is simply consistent with what we’re already doing for counting stats. If catchers contribute only 5.9% of total HR production, they get 5.9% of the HR budget — not 1/9th (11.1%). The same logic applies to rate stats: if catchers contribute ~7.4% of total weighted PA, they get ~7.4% of the OBP budget — not 1/9th.

Budget allocation is production-based across the board. PA weighting for rate stats isn’t an exception; it’s the rule applied consistently.

Catcher Category Budgets:

Catcher Pool Z-Scores (hypothetical, sum of top 12):

Dollars per Z for Catchers:

Player Valuation: Will Smith

Will Smith’s TRP valuation: $29.

The Rate Stat Premium

Notice something in the Will Smith example: his OBP and SLG contributions ($11.52 + $7.62 = $19.14) account for 66% of his total value, even though they’re only 2 of 6 categories.

This isn’t a bug. It’s the system working as designed.

Rate stats get 50% of the hitter budget (vs. 50% for four counting stats combined). And rate stats are where Smith excels relative to replacement. The budget weighting amplifies his strengths in the categories we can actually predict.

A different player — say, a speed-only catcher with elite SB but replacement-level OBP — would see the opposite effect. His predictable contribution (SB) gets only 12.5% budget weight, while his weakness (OBP) gets 25% weight. The system correctly identifies him as a riskier, less valuable asset.

What About Negative Z-Scores?

Players can have negative Z-scores in categories where they’re below replacement level. How does that affect dollar values?

It subtracts.

If a catcher has zSB of -0.5 and the $/zSB rate is $3.13, his SB contribution is -$1.57. That comes out of his total value.

This is correct and intentional. A player who hurts you in a category — who’s actively dragging down your team’s production below what a replacement player would provide — should be penalized for it.

The sum of all category values can theoretically go negative for a player who’s below replacement across the board. In practice, such players don’t make the rostered tier, so you won’t see many negative total values among draftable players.

Putting It Together: The Full Valuation Pipeline

Here’s the complete TRP valuation flow:

• Set budget parameters
• Total budget: $3,060
• Hitter/pitcher split: 70/30
• Category weights: 50/50 rate/counting for hitters; 40% K/9 + 15% each other for pitchers

2. Calculate category budgets

• Hitter categories: OBP $536, SLG $536, R/HR/RBI/SB $268 each
• SP categories: K/9 $184, others $69 each
• RP categories: K/9 $184, others $69 each

3. Calculate position production shares

• For each position, measure its share of total pool production in each category
• Counting stats: use raw totals
• Rate stats: use PA/IP share

4. Allocate category budgets to positions

• Position category budget = Total category budget × Position share

5. Calculate $/Z rates per position-category

• $/Z = Position category budget / Sum of Z-scores for rostered players at position

6. Value each player

• Player value = Σ (Player Z in category × $/Z for position-category)

7. Validate totals

• Sum of all player values should equal total budget ($3,060)
• If not, check if you normalized proportionally. Also, there may be some slight deviation from perfect re-totaling — these are again not so much rules as they are guidelines.

What We’ve Built

At this point, we have:

• An opinionated, yet principled baseline — the True Replacement Player archetype at each position. You may need to modify budget allocation based on your league’s rules and your desired roster and category compositions.
• A common currency — Z-scores that transform raw stats into comparable units
• A budget architecture — splits that reflect predictability and strategic value
• Dollar values — actionable prices for every player in your league

This is the core of True Relative Pricing. You can now walk into an auction knowing exactly what each player is worth to your team, grounded in production shares and projection confidence rather than gut feel.

Part 5 will give you language-agnostic architectural framework for those looking to compute values for your own league.

TRP is a valuation framework developed within the MTBL (Metaball) ecosystem. It consumes projections from any source and outputs market-calibrated player values for fantasy baseball.