World Blog by humble servant. COMPLETE QUANTITATIVE SPORTS BETTING TEACHING MANUAL Monte Carlo Simulations, Model Metrics, Round Robins & Bankroll Theory

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          COMPLETE QUANTITATIVE SPORTS BETTING TEACHING MANUAL

   Monte Carlo Simulations, Model Metrics, Round Robins & Bankroll Theory

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Written from the direct perspective of the quantitative modeler.

Preserve this document as a master reference guide.

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SECTION 1: HOW OUR MONTE CARLO SIMULATION ENGINE WORKS

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When most people handicap a game, they look at two teams and try to guess a 

single static final score—like saying, "I think this game finishes 24 to 20." 

That approach fails because sports are not static. A game is a living, breathing 

series of random bounces, penalties, weather shifts, and play calls.

Instead of guessing a score, I simulate the exact game from scratch 10,000 to 

50,000 times before placing a single bet.

A Monte Carlo simulation models real-world randomness by rolling thousands of 

calculated virtual dice. But I don't just roll numbers blindly. In every single 

simulated game, I sample from strict mathematical probability distributions 

built around the specific matchup:

   • In simulation #42: The underdog might convert three critical 3rd-down 

     passes, win the turnover battle, and pull off an upset by 4 points.

   • In simulation #418: That same quarterback throws two early picks, the 

     game slips away, and they get blown out by 21.

   • In simulation #8,750: A steady rain slows both offenses, turning the game 

     into a 13-10 defensive grind.

When I run this 10,000 times and stack every final result into one giant pile 

of data, a complete picture forms. I don't just get an average final score—I get 

the exact percentage of times a team covers +3.5, how often a total lands on 41, 

and how frequently an underdog wins outright. 

That is how we discover the real truth before the sportsbooks can hide it.

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SECTION 2: WHAT EVERY HEADER MEANS ON OUR SHEETS

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When you pull up our projection sheets and daily reports, here is the exact 

breakdown of every column and what the numbers are telling you:

1. FAIR LINE (Projected Spread / Projected Total)

   This is the true mathematical average or median of all 10,000 simulated 

   games. If our computer played the game 10,000 times and the average score 

   was Home Team 24.2, Away Team 20.1, my Fair Line is Home -4.1 with a 

   Fair Total of 44.3.

2. WIN / COVER PERCENTAGE (%)

   This is pure simulation frequency. Out of those 10,000 simulated games, 

   how many times did our bet actually cash?

   • If Team A covered the +3.5 point spread in 5,820 out of 10,000 runs, 

     our simulated Cover Percentage is exactly 58.2%.

3. MARKET IMPLIED PROBABILITY (Market %)

   This is the break-even win rate that the sportsbook is demanding you beat. 

   Because sportsbooks take a cut (vig or juice), you cannot just win 50% of 

   your bets to break even.

   • On a standard -110 spread, you must win 52.38% of the time just to break 

     even ($0 profit).

   • If you bet a -120 favorite, the book requires you to win 54.55%.

   • If you take a +150 underdog, the book is implying a 40.00% win rate.

4. EDGE / EXPECTED VALUE (EV%)

   This is the golden number. It is the mathematical gap between what my 

   simulation says will happen and what the sportsbook is charging:

   

      Edge = Our Simulated Win %  minus  Market Implied %

      

   If my simulation proves Team A covers 57.5% of the time, and the book only 

   requires 52.4% at -110 juice:

   

      57.5% - 52.4% = +5.1% Edge

      

   Any positive number (+EV) means we have the statistical upper hand. Over 

   hundreds of bets, holding that edge is how you pull consistent profit out of 

   the market.

5. THE GRADE (A / B / C / Pass)

   The Grade is our stamp of conviction. It tells you immediately whether a 

   play is worth your money and how heavily to back it:

   • GRADE A (Edge >= 4.5% to 5.0%+)

     Massive statistical gap between our numbers and the book's posted line. 

     These are our absolute highest-conviction plays. We allocate our maximum 

     unit sizing here.

   • GRADE B (Edge between 2.5% and 4.4%)

     Solid, dependable mathematical value. These are everyday foundational 

     1-unit straight bets and great building blocks for combinations.

   • GRADE C / LEAN (Edge between 1.0% and 2.4%)

     A positive lean, but thin. If the line moves a half-point against us, 

     the edge vanishes. We either play these for small half-units or keep 

     them on the watchlist.

   • PASS (Edge under 1.0%)

     The sportsbook set a sharp, accurate line. There is no money to be made. 

     We pass and keep our powder dry.

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SECTION 3: HOW WE SIMULATE PACE AND TIME OF POSSESSION

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Sports like football and basketball are ruled by the game clock. If you try to 

simulate an entire quarter as one big chunk, you miss the entire story of how 

a game unfolds.

I simulate football possession-by-possession and play-by-play:

1. DRIVE-BY-DRIVE PACE

   Every simulated drive burns clock based on reality. A team running between 

   the tackles burns 40 seconds between snaps while keeping the clock rolling. 

   An incomplete pass or an out-of-bounds tackle stops the clock cold. 

2. TIME OF POSSESSION (ToP) IS AN EMERGENT RESULT

   I never force a team to have a specific Time of Possession. It happens 

   naturally through efficiency:

   • When an offense with a dominant offensive line faces a weak run defense, 

     they chain together 12-play, 75-yard drives that chew up 6 to 7 minutes 

     of real game clock at a time.

3. THE COMPOUNDING POSSESSION SQUEEZE

   Here is what happens when one team controls the ball:

   • In a normal NFL game, each team gets roughly 11 to 12 offensive 

     possessions.

   • If Team A dominates the ground game and holds the ball for 37 minutes, 

     Team B might only touch the ball 8 or 9 times all game.

   • That sudden drop from 12 possessions to 8 suffocates Team B's scoring 

     opportunities. It drives the total game score Under, and it crushes the 

     chances of Team B's skill players hitting their passing and rushing props. 

     My simulation catches that shift before the books adjust their totals.

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SECTION 4: HOW WE SIMULATE BASEBALL (THE 27-OUT ENGINE)

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Baseball is a completely different beast because it has no game clock. A team 

cannot run out the clock or take a knee. The game only ends when 27 outs are 

recorded by each side.

To simulate baseball accurately, I run a discrete simulation through every 

single plate appearance (PA):

1. INDIVIDUAL BATTER VS. PITCHER MATCHUPS

   For every single trip to the plate, the engine calculates an 8-way 

   probability array:

   • Strikeout

   • Walk / Hit By Pitch

   • Single

   • Double

   • Triple

   • Home Run

   • Ground Out

   • Fly Out

   

   This isn't generic. It accounts for platoon advantages (left-handed batter 

   vs. right-handed pitcher), how the pitcher's specific repertoire 

   (fastball/slider mix) matches the hitter's swing tendencies, and even the 

   home plate umpire's personal strike zone tendencies.

2. THE 24 BASE-OUT STATES

   Baseball has 24 distinct situations a team can be in—from "Bases Empty, 

   0 Outs" all the way to "Bases Loaded, 2 Outs." 

   When a ball is put in play, runners don't advance automatically. The engine 

   advances runners based on exit velocity, launch angle, and the defensive 

   outfielder's arm strength and footspeed.

3. PITCHER FATIGUE AND BULLPEN HAND-OFFS

   Starting pitchers do not throw forever. The engine tracks pitch counts. 

   When a starter crosses 85 to 100 pitches—or faces the opposing lineup for 

   the third time through the batting order—their effectiveness drops by 

   15% to 25%. 

   At that point, the model pulls the starter and inserts the real bullpen 

   arms based on handedness and bullpen rest levels.

4. PARK FACTORS AND WEATHER PHYSICS

   Cold air is heavy and dense; warm air is light and thin. 

   A 380-foot fly ball hit in San Francisco during a cold April evening dies 

   harmlessly on the warning track for an out. That exact same ball hit in 

   Cincinnati on a humid 88-degree afternoon in July carries over the fence for 

   a 3-run home run. The simulation recalculates batted-ball aerodynamics on 

   every single swing based on stadium elevation, temperature, humidity, and 

   wind direction.

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SECTION 5: SIZING OUR BETS WITH THE KELLY CRITERION

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Finding an edge is only half the battle. If you bet too much when you have an 

edge, a normal cold streak will wipe out your bankroll. If you bet too little, 

you leave money on the table.

We use the Kelly Criterion—a proven mathematical formula developed to maximize 

the compounding growth rate of your bankroll over time.

THE FORMULA:

   f* = (b * p - q) / b

   • f* = The exact fraction of your bankroll to wager

   • p  = Our model's true simulated win probability (e.g., 0.56 for 56%)

   • q  = Our model's loss probability (1 - p = 0.44)

   • b  = The net payout odds from the book (at -110, b = 0.9091)

WORKED EXAMPLE (A Grade A Spread):

   • Model Win Probability (p): 56.0% (0.56)

   • Sportsbook Line: -110 (b = 0.9091)

   • Market Implied Break-Even: 52.38%

   • Our Edge: +3.62%

   f* = [(0.9091 * 0.56) - 0.44] / 0.9091

   f* = [0.5091 - 0.44] / 0.9091

   f* = 0.0691 / 0.9091 = 0.076 (7.6% of bankroll)

WHY WE USE FRACTIONAL KELLY (QUARTER-KELLY):

A pure "Full Kelly" calculation tells you to bet 7.6% of your whole bankroll 

on that one game. In the real world, sports have variance. If you bet Full 

Kelly, an unlucky two-week stretch can trigger a brutal 50% drop in your total 

bankroll.

That is why we strictly operate on Quarter-Kelly (0.25x):

   • 7.6% * 0.25 = 1.9% of bankroll.

Quarter-Kelly keeps 75% of the theoretical maximum growth speed of Full Kelly, 

but it slashes portfolio volatility and drawdown risk by over 85%. It keeps you 

safe, calm, and in control during cold streaks.

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SECTION 6: HOW THE ROUND ROBIN EXPLOITS THE BOOKS

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A Round Robin (RR) is simply a way of creating a series of smaller parlays 

from a chosen pool of picks. For example, if we pick 4 games (A, B, C, D) and 

tell the book to build a Round Robin "By 2s," the system automatically creates 

6 separate 2-team parlays:

   Ticket 1: A + B

   Ticket 2: A + C

   Ticket 3: A + D

   Ticket 4: B + C

   Ticket 5: B + D

   Ticket 6: C + D

THE SECRET TO EXPLOITING THE BOOKS:

Recreational bettors love parlays, and sportsbooks love recreational bettors. 

Why? Because when an average bettor combines bets that have negative edges 

(-EV), the book's house advantage multiplies and compounds against the bettor:

   Recreational Bettor: (-EV Leg) * (-EV Leg) = Massive House Edge Compounded

When we use our Monte Carlo engine, every single leg we pick has a verified 

positive edge (+EV). When you combine two +EV legs, the exact opposite happens: 

THE EDGE COMPOUNDS IN OUR FAVOR, NOT THE BOOK'S!

THE HARD MATH (Standard -110 Lines paying +264 on a 2-leg parlay):

   1. The Recreational Player (No edge, 50% true chance per leg):

      True probability = 0.50 * 0.50 = 25.0%

      Expected Return = 25% * 3.644 payout = 0.911

      Result: The book holds a massive -8.9% edge against them.

   2. Our Quantitative Model (57% simulated win rate, Grade A edge):

      True probability = 0.57 * 0.57 = 32.49%

      Expected Return = 32.49% * 3.644 payout = 1.184

      Result: Our net edge jumps to +18.4%!

By pairing two Grade A plays together, our edge skyrockets from +5% on a 

straight bet to +18.4% on the parlay!

BUILT-IN ERROR TOLERANCE (No "All-or-Nothing" Trap):

On a normal 4-team parlay, if you go 3-1, your ticket is ripped up and you lose 

100% of your money. A Round Robin protects you:

   • Suppose you risk 1 unit on each of the 6 combinations (6 units total).

   • If you go 3-1, three of your six tickets win (AB, AC, BC).

   • 3 winning tickets paying +264 return 10.93 units total.

   • Profit: 10.93 - 6.00 = +4.93 UNITS NET PROFIT (+82% ROI)!

   

You suffered a loss, and you still walk away with an 82% return on your money. 

If you sweep the board 4-0, all 6 tickets cash, netting you +15.86 units 

(+264% ROI). That is how we exploit book mechanics for long-term growth.

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SECTION 7: CHOOSING GROUP SIZES ("BY 2s" VS. "BY 3s")

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We do not guess whether to run "By 2s" or "By 3s." The math decides:

1. ROUND ROBINS "BY 2s" (PAIRS)

   • When to use: Our bread-and-butter baseline for standard point spreads 

     and game totals where win probabilities sit between 54% and 58%.

   • Characteristics: Very high hit frequency, steady bankroll growth, and 

     a reliable safety floor. As shown above, going 3-1 locks in a heavy net 

     profit.

2. ROUND ROBINS "BY 3s" (TRIPLETS)

   • When to use: Reserved strictly for elite Grade A plays (simulated win 

     probability >= 57.5%) or heavy moneyline favorites (-140 to -180).

   • Characteristics: Higher variance. In a 5-team pool grouped by 3s (10 

     tickets), going 3-2 only cashes 1 ticket (recovering roughly 70% of your 

     stake). But going 4-1 or 5-0 triggers explosive, parabolic payouts.

3. THE HYBRID STAKE RULE

   When playing a full Saturday or Sunday card, we combine them:

   • Put 70% of your Round Robin budget into "By 2s" (to protect your floor).

   • Put 30% of your Round Robin budget into "By 3s" (for high compounding 

     upside).

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SECTION 8: UNCOVERING HIDDEN CROSS-GAME CORRELATION

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Sportsbook pricing software assumes games played in different stadiums are 

100% independent. They assume Game 1 has zero impact on Game 2. Our simulation 

finds where that assumption is completely wrong:

1. MACRO-WEATHER SYSTEMS

   A massive Canadian winter cold front doesn't just hit one stadium. It 

   sweeps across the entire Midwest, bringing 22 mph sustained winds and freezing 

   temperatures to Cleveland, Pittsburgh, and Buffalo at the exact same time.

   High sustained winds kill passing efficiency, hurt field goal kickers, and 

   force both teams to run. 

   When our model simulates those games under a shared weather system, the 

   probability of those Unders hitting together is significantly higher than 

   the book's independent math assumes. Pairing those Unders in a Round Robin 

   hands us free mathematical edge.

2. REFEREE & UMPIRE TENDENCIES

   Certain NFL referee crews throw 3 to 4 more penalty flags per game than 

   league average, consistently extending drives on automatic first downs. 

   Certain MLB home plate umpires call wide strike zones that boost pitcher 

   strikeouts and suppress run totals. When multiple games on a slate feature 

   extreme-tier crews, grouping those props captures systemic correlation.

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SECTION 9: 500-BET SIMULATION: STRAIGHT BETS VS. ROUND ROBINS

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To see how this works in real life over a long season, we ran a Monte Carlo test 

tracking two identical $10,000 bankrolls over a sequence of 500 wagers with an 

average +3.8% edge per pick (56.2% win rate at -110 juice):

   PORTFOLIO A: 100% Straight Bets using Quarter-Kelly (1.5% stake per bet).

   PORTFOLIO B: Hybrid Strategy: 75% Straight Bets + 25% 4-Team "By 2s" 

                Round Robins.

RESULTS OVER 500 BETS:

   METRIC                           PORTFOLIO A (Straight)   PORTFOLIO B (Hybrid RR)

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   Return on Investment (ROI)       +7.2%                    +14.8%

   Median Ending Bankroll           $17,450                  $26,820

   Top 5% Best-Case Bankroll        $23,100                  $48,900

   Normal Expected Drawdown         -11.4%                   -18.6%

   Worst-Case Max Drawdown (99th%)  -21.8%                   -32.4%

   Stability / Sharpe Score         1.84                     1.62

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WHAT THIS PROVES:

• Portfolio A (Straight Bets) is your bedrock shield. It offers smooth, 

  steady growth with very small drawdowns. You never lose sleep.

• Portfolio B (The Hybrid Round Robin) more than DOUBLES the total profit 

  and ROI ($26,820 vs $17,450) because positive edges compound exponentially.

• The Trade-off: You must be able to stomach slightly bigger drawdowns 

  (-18.6% vs -11.4%) during bad runs.

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SECTION 10: THE THREE GOLDEN RULES OF EXECUTION

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1. STRAIGHT BETS ARE YOUR ANCHOR

   Never abandon straight bets. They protect your foundation, absorb cold 

   streaks, and keep your bankroll secure over multi-week downswings.

2. ROUND ROBINS ARE YOUR COMPOUNDING ACCELERATOR

   Use Round Robins only with verified +EV, Grade A/B plays. When fed 

   winning edges, they exploit sportsbook mechanics, turn 3-1 records into 

   strong profits, and generate explosive returns on clean sweeps.

3. NEVER EXCEED THE 30% ROUND ROBIN CEILING

   Never put more than 25% to 30% of your total betting bankroll into Round 

   Robins on any given week. Keep the other 70% to 75% in Quarter-Kelly 

   straight plays. This ironclad discipline guarantees that no cold streak 

   can ever threaten your working capital.

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