Football game - Maximize Talent w/Substitutions

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rlwjr

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Not sure if this is the right area to ask this question. Please guide me to the correct area if it is not.

I play an online fictional football game. Every player has a number of attributes that dictate how well he plays in a position. Each player also has a Stamina attribute. As the game simulation plays out, players are substituted in and out, and the higher a players Stamina, the slower his ratings drop, and he plays longer before being substituted.

The general consensus in the game is to start your best players, regardless of what their Stamina is. My belief, is over the course of a game, this causes your overall talent on the field to spike up and down over time. I believe there is a way to maximize talent over the game, as opposed to riding the up and down rollercoaster. Problem is, I don't know the math to figure out how to go about doing this.

Here is an example with real numbers. I have thought about using an Expected Utility approach, where I multiply their "talent rating" by their stamina. I don't know if that is the right approach, but I will list that number as well.

NAME RATING STAMINA EXPECTED UTILITY/100
Harris 57.52 54 31.06
Johnson 60.68 51 30.95
Smith 57.52 55 31.64
Taylor 60.44 46 27.80
Austin 70.88 49 34.73
Lucas 68.72 57 39.17
Griffin 70.36 48 33.77
Sinclair 69.68 42 29.27
Sweeney 70.80 77 54.52

Don't know if it matters, but their ratings are an average of 3 attributes and are the generally accepted method of judging a players talent. In this case, these are Offensive Linemen. I must start five, and the others substitute in and out over the course of the game, in an order I set before the match. As you can see, the top five according to RATING are different than top 5 by EXPECTED UTILITY. To clarify my question, how do I maximize RATING over time? is EXPECTED UTILITY the right approach?
 
I'm not sure what you're doing with EXPECTED UTILITY. That may not work if you're just grouping all of your terms together.

Here's my take:

If your lineman have given stats like strength (str), speed (spd) or whatever, there is a given function for how these numbers change over time, and you're saying that these numbers reduce slower if the player has a higher stamina. Now, you need to determine what these functions are. The str, spd, whatever numbers may not be governed by the same functions, so grouping them together and multiplying by stamina makes no sense, if that's the case. Here's what I would do to start off. Can you monitor each individual stat over time? If so, using excel (or similar - you can use graph paper if you have to) plot each stat verses time and see what the trend is. It could be linear, it could be something else. You'd have to graph it to see, because these games are usually set up with predetermined "mechanics". graphing them out like this may show you what these mechanics are. In doing this, you will then be able to OPTIMIZE a players performance. If it turns out that all the stats follow the same mechanics, it will be easier. If they are all different, it will take a bit more imagination.

Is that possible to do?

Try to collect as much data as possible.
 
First off... thanks joel for helping me with this... I was about to give up hope!

I'm pretty sure, like 95%, that all stats decline linearly and evenly. The only indication you get during the sim results at the half and the end of the game is an icon next to the player indicating how much he has declined. It goes something like Green=90%+ Green/Yellow=85%-90% Yellow=80%-85% etc etc.

I left this out, and it might be a key, but in my depth charts I can set what % I want the player to come out. Under the method I mentioned in the last post, I have everyone set at 90%. IE, I don't want anyone playing with stats less than 90%.

I used the expected utility method for my first game of a season that just started yesterday. I think it worked okay, but I noticed some problems. Guys with high stamina, that ended up having a higher expected utility and were starters, ended up staying in the game enough that they didn't allow the better "ratings" guys to ever sub in for them. I think at some point, stamina reaches a diminished return.

Don't know if this helps either, but the game developers have made the statement that a player with 50 stamina can play the majority of the game at a substitution setting of 60%. Now, I don't want any of my guys playing under 90%. I know the devs statement should be a big help in solving this, but I 'm not that strong mathematically to figure it out!
 
So, do you assign which bench players replace which starters once they go off or is it first come first serve? It seems to me that your best players at 90% would probably be better than some of your replacements at 100%, is that, at times, the case? Also, once a player goes off, does he come back in after a rest period? There are a lot of things to consider here in order to be able to optimize this process. It seems that the devs statement suggests that the stats are not linear if a player with 50 stamina can stay in all game at 60%. That suggests to me that there's an asymptotic relationship in there (if you know what that means). It is probably linear over a short time duration however (for all intensive purposes) - especially if you're taking players out at 90%. This is a hard problem to analyze with the given information. I have some experience determining stat functions for optimization in other games I've played.

Maybe you can send a link to the game for me to check out.
 
It's a first come first served situation.... I have 9 OL, I list them 1-9...... if #2 comes out first, # 6 replaces him. If #1 comes out next, and #2 hasn't rested enough to return to action, then #7 replaces #1. Yes, they DO rest up and return. I ran across a post on the forums of the game site where the devs said that the decrease is not linear, but close enough to linear to be treated as so. And yes, some of my players at 90% are probably better than some of my worse players. But it's a college game, so after you've been at a school long enough to recruit talent that meets your specs, the drop offs in talent tend to be less of an issue. It's a very competitive game though, and if you can squeeze 2-3 points worth of talent on the field from optimization, it would be worth it!

If you'd like to check out the site, it's WhatifSports.com. The particular game is Gridiron Dynasty, they have several sports games there. you may have a hard time viewing alot of particulars without having an account. If that is the case, let me know what you'd like to see, and I can send you some screen shots or something. Again, I REALLY appreciate your help here!
 
Ah, OK that makes sense. It seems to me that you should probably not set all of your players at 90%. This % setting I think is the key to optimizing your talent level. Your best players should probably be set lower to like 80-85% for example, depending on how long it takes to get there (their stamina), and your worst players should be set to 90% or higher. And, if a player has high stamina, set his % number higher, and if he has low stamina set it lower. Does that make sense?

Once your talent level gets better, then you can level out back to 90% and you'll have less ups and downs. After the simulation runs, does it tell you how long each player was actually on the field? If that's the case, what you can do is average all of their stats and divide by the number of players on the field in order to get an idea of what the average talent level was for the quarter or the half, especially if you can tweak the % numbers during the game as well, that'll help you be more efficient. You can differentiate between OL and recievers for example if you want to focus on specific stats important for that position. I can tell you how to do that if that's the case. It can get very complicated, but that's how you squeeze out every bit - nothing excel can't handle.

Again, I think average value of attributes will tell you what you want to know.
 
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Does this game have an option for firing the coach? (Just curious.) :p
 
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