Applied mathematics
Game Theory & Economics Lab
Four models, each built on this season's KBO numbers rather than constants imported from another league. Every assumption is stated where it is made, so you can disagree with a specific one instead of the whole thing.
RE24
Run expectancy
Pick a cell. The bunt and steal models beside it solve for that exact situation.
| Runners | 0 out | 1 out | 2 out |
|---|---|---|---|
| ___Bases empty | |||
| 1__1st | |||
| _2_2nd | |||
| __33rd | |||
| 12_1st, 2nd | |||
| 1_31st, 3rd | |||
| _232nd, 3rd | |||
| 1231st, 2nd, 3rd |
Each cell is the runs a team can expect to score from that situation to the end of the inning, rescaled so the empty-and-nobody-out cell equals the KBO's own 0.56 runs per inning — a factor of 1.17 on the reference grid.
The bunt
1st · 0 outSwing away
1.01
Bunt
0.78
Difference
−0.222
The break-even success rate is 100%. Below that, swinging away scores more runs on average.
The steal
1st · 0 outHold
1.01
Go
0.99
Difference
−0.015
Break-even success rate 72%. A runner who goes at a lower rate than that is costing his team runs, however fast he looks doing it.
Zero-sum game
Nash pitch mix
Why a pitcher does not throw his best pitch every time, expressed as a mixed strategy.
| Batter / Pitcher | Fastball | Offspeed |
|---|---|---|
| Sitting fastball | ||
| Sitting offspeed |
Each cell is the batter's wOBA in that combination. League average wOBA is .346. Change a value and the equilibrium resolves again.
Nash equilibrium
Batter wOBA at equilibrium
.347
Throw the fastball 49% of the time and the batter gains nothing by guessing either way. That is the whole reason a pitcher does not throw his best pitch every time.
Markov chain
Monte Carlo simulator
Two clubs, ten thousand games, one plate appearance at a time, extra innings and walk-offs included.
Win probability
- Away runs / game
- 5.77
- Home runs / game
- 4.25
- Games played
- 10,000
- Went to extras
- 8.9%
- Tied after 11
- 2.7%
- Home W–L–T
- 3,767–5,967–266
Margin of victory, from the home side
Extra innings are played to the KBO's limit of 11, and from the ninth on a game ends the moment the home side leads. Steals, wild pitches, errors, productive outs and sacrifice flies are all in. Win probability splits ties evenly; no home-field edge is added.
Does it work?
The simulator against the season
Each club played 4,000 games against a league-average opponent. If the engine is right, what it scores and allows should land near what the club has actually scored and allowed. Across the ten clubs the typical miss is 0.25 runs a game scored, 0.15 allowed, and 30 points of winning percentage.
| Club | R/G sim | R/G real | RA/G sim | RA/G real | PCT sim | PCT real |
|---|---|---|---|---|---|---|
| KT Wiz | 5.41 | 5.73 | 4.46 | 4.51 | .600 | .647 |
| Samsung Lions | 5.20 | 5.60 | 4.74 | 4.65 | .569 | .589 |
| KIA Tigers | 5.12 | 5.34 | 4.58 | 4.61 | .577 | .556 |
| LG Twins | 4.96 | 5.02 | 5.13 | 5.04 | .506 | .545 |
| Doosan Bears | 4.57 | 4.78 | 4.22 | 4.38 | .559 | .525 |
| SSG Landers | 4.80 | 4.90 | 5.65 | 5.53 | .451 | .468 |
| Lotte Giants | 4.66 | 4.72 | 5.22 | 5.15 | .469 | .454 |
| NC Dinos | 4.87 | 4.99 | 5.42 | 5.36 | .479 | .451 |
| Hanwha Eagles | 5.21 | 5.70 | 6.08 | 5.80 | .453 | .407 |
| Kiwoom Heroes | 4.06 | 3.92 | 5.99 | 5.67 | .355 | .357 |
The engine runs slightly cold — a few tenths of a run below the league — because it has no park effects and treats every out in play alike. Clubs whose real record beats their simulated one have usually won close games the run totals do not explain; the standings page calls that luck.
Marginal value
Contract value
The only comparison that matters in a salary negotiation: what does a win cost from this player against that one?
- WAR so far
- 8.59
- Prorated to 144 games
- 8.59
- Cost per win (₩100M)
- 1.7
KIA Tigers
- WAR so far
- 7.90
- Prorated to 144 games
- 7.90
- Cost per win (₩100M)
- 0.5
LG Twins
WAR is prorated from 144 games to a 144-game schedule, which assumes health and no second-half decline. Salary is yours to enter: the KBO does not publish a complete pay table, and this tool leaves the field blank rather than inventing one.