While thinking about football, I noticed that the geek has the alternate game matrices used for the official WBC tournament.
You are on the one yard line, you need a TD, the clocks about to run out. What play to call (Pro-style offense). What defense? For simplicity, ignore offenses 13-20. [You can't use them inside the 10 yard line anyway]. Let's look at the coach's sheet....
| A | B | C | D | E | F | G | H | I | J | |
| Power Middle | -1,1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 |
| Power Tackle | -1,1 | -1,1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | -1,1 | 1,-1 | 1,-1 |
| QB Keep | -1,1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | -1,1 | 1,-1 | 1,-1 | 1,-1 |
| Slant Run | -1,1 | 1,-1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | -1,1 | 1,-1 | 1,-1 |
| End Run | -1,1 | -1,1 | -1,1 | 0,0 | -1,1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 |
| Reverse | -1,1 | 1,-1 | -1,1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | -1,1 | 1,-1 | 1,-1 |
| Draw | 1,-1 | 1,-1 | -1,1 | 1,-1 | 1,-1 | -1,1 | 1,-1 | -1,1 | 1,-1 | 1,-1 |
| Trap | 1,-1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | -1,1 | -1,1 | 1,-1 | 1,-1 | 1,-1 |
| Option | -1,1 | 1,-1 | 1,-1 | -1,1 | 1,-1 | -1,1 | -1,1 | 1,-1 | 1,-1 | -1,1 |
| Flair Pass | 1,-1 | 1,-1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | -1,1 | -1,1 | 1,-1 | 0,0 |
| Side Line Pass | 1,-1 | -1,1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | 1,-1 | -1,1 | -1,1 | -1,1 |
| Look In Pass | 1,-1 | -1,1 | 1,-1 | -1,1 | -1,1 | -1,1 | 1,-1 | 1,-1 | 1,-1 | -1,1 |
I've flipped the chart around to make offenses run down the side. This is basically taking each chart and answering the game theory question ... does this win me the game? (1,-1) means that the offense (me) wins while (-1,1) means I'm the goat. Note that 5D is (0,0). That's because it's a defensive penalty, and we'll get another play (at the one yard line). Those zeroes should be equal to the value of the rest of the game, but I'm not about to figure that out.
Anything jump out at you?
For this situation, there are some strategies that are Dominated. If you win with Power Tackle, you would have won if you picked Power Middle ... and Power Middle wins a few time that Power Tackle doesn't. With a lot of math (or a computer program) you can solve this exactly. (I did this, but then the file got corrupted and I'm not typing that matrix in again. Maybe I need a better tool). The optimal strategy involves picking three offenses 1/7th of the time, and two others 2/7ths. Ditto for the defenses. (The symmetry of the answer surprised me, which is why I remember it).
Football Strategy is solvable in these "DoOrDie" situations, the real issue is "What do you do on 1st & 10 at your 20 or 25, with the game tied and plenty of time on the clock." How do you value each yard? I could use some ideas that football sabermetricians are using. In fact, I may.
Yes, I have a side project. Right now I'm working on the framework, but I'm also doing this to learn about MFC (which stands for Microsoft's Effin Classes, I believe). Don't expect anything soon, but if anyone has any thoughts about how to place a value on yardage in a "long distance" situation, I'd like to hear it.
Oh, and a good repository of Linear Algebra algorithms would be nice.
Related Posts (on one page):
- Thinking About Football
- Are you ready for some football?