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s12345

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Hello

I am having a hard time understanding which factors should be taken into account and which ones should not be taken into account when calculating probability.

I have the following situation:

Last night I played FIFA12 on xbox live against an unknown opponent. He challenged me to a rematch after the match was over.

I would like to calculate the chance I would have had of winning if I would have said "yes" to the rematch.
However, upon trying to calculate the chance (using Bayes' theorem for example), I quickly gather countless factors such as:

• previous personal win/loss ratio
• the fact he first scored a goal in the first 10 minutes of the first half
• the fact I scored two goals the last 20 minutes of the second half
• his predictability
• my predictability
• my fatigue at that hour; mentally as well as phyiscally
• the knowledge the opponent has about my strategy after having played a match with me
• how tired my opponent is
• the opponent's fatigue; mentally as well as physically
• if he is a night person or not

I keep thinking of factors such as these and I am not sure which ones would be valid factors for probability calculation. I am getting lost.

Does anyone have an idea on this?
Thank you

MrKappa

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If you turn on the air conditioner and cool the room you are in, you'll find yourself a little more alert, thus increasing your odds of predicting the Great Recession and Market collapse of 2008.

StNaive

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Since it's a 101 class I would guess they probably want you to use your personal win/loss ratio, possibly with an adjustment depending on who won the previous game but even then probably not.

Because there are so many things you could consider for this, it might be worth looking to the textbook or professor just to be safe.

s12345

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Yeah I'll ask the professor. I also asked my math major friend and he said: "Not even today's best supercomputer could calculate all the variables one would have to take into account, even if you had a perfect model for this".

gunner21

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I think the most prominent factors to use would be:

Opponent's win/loss ratio
Your team rating vs Opponent's team rating
Hours game played since video games have a learning curve to them.

MrKappa

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Oh sorry this was a serious question...

Look at a baseball card, or horse race statistics, or gambling statistics, and model your stuff based off that, as a starting point.

the fact he first scored a goal in the first 10 minutes of the first half
You might call that "Aggressiveness", or "Intimidation Score" or something else, and simply count or value the number of goals and divide them by the elapsed time from start to give a value.

3 scores early in game.

1rst at 1:23 (83 seconds)
2nd at 2:34 (154 seconds)
3rd at 4:00 (240 seconds)

1 / 83 = 0.01204
1 / 154 = 0.00649
1 / 240 = 0.00416

(0.01204 + 0.00649 + 0.00416) * 100 = 2.27

Bayes' theorem is basically a function used to adjust percentages, as a memory store holder. So you'd need to standardize your final values, and build your functions from that.

If you only have one game on record, and no bets involving the probability of scoring early in the game as being a determining factor of winning the game, then it may be useless.

Statistics are only really only good when you have a good database of previous events to work from. Or unless you have an innate understanding of the mechanics of the game and what it takes to win.

Does scoring early make a difference at all? Maybe you could compare your game with a similar game that has public stats, and look for the possibility. Honestly, seems random though.

Something along the lines of a "home team advantage".

So once you figure out the advantage early scoring makes in the final outcome of the game, you'd take a players "intimidation factor", and value it towards a final probability based on your findings.

Your finding would be one-dimensional or flat, for lacks of better terms, since it's a psychological factor, and individual players with different psychological attributes may skew the value. A veteran player with 2,000 tournament games may feel less disadvantage against early scores, than someone who is playing their 2nd or 3rd tournament game.

the fact I scored two goals the last 20 minutes of the second half
Could call it endurance.

Anyways, baseball cards, normally show stats on batting average, and honestly I can't remember any others...

http://espn.go.com/mlb/statistics

Sure none of those stats take player attributes into consideration. They are politically correct based on game mechanics and do not consider things such as BMI, or IQ, or Weight, or Age.

It's more along the lines of betting on a mechanical roulette wheel, or closer to betting on numbers (odds is probably accurate terminology) rather than player attributes.

Horse betters to my understanding will look at the health of a horse, the skill and weight of a rider, and determine probabilities from there.

Anyways, a good rule of thumb is, "Math abstracts reality, it does not create it". That's how I see things, anyways... it's false in some regards, but more true than false.

In other words, in any system, there are countless unknown variables out of your control, or knowledge. If it were an entirely closed system and every variable was known, then theoretically you could predict things accurately.

So in theory, the more variables known, the higher your accuracy. It's endless in some regards however as to how many variables there are. What happens if your player has a stroke halfway through the game? What happens if your router is more prone to have outages? What happens if your ping time to the server is substantially faster? Odds are totally useless, as the variables are endless.

I am having a hard time understanding which factors should be taken into account and which ones should not be taken into account when calculating probability.
Game stats. If there is only one game on record, perhaps player attributes. That is closer to boxing possibly.

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