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Subject: MADBALL Strategy Posted by: Sludge - [1440310] Mon, Mar 26, 10:00 Thought I would start a new thread to discuss strategy for Madman/KKB's Madball game. As usual, my take on the game is statistical in nature. Let P be the probability that a team will win, let W be their winning percentage, and let C be the cost. (C = 1000*W after April 15.) The expected points for picking the team is simply P. (Expected points is the average points you would receive if the game were played over and over and over again.) If you were to go picking the team with the largest expected points, then my guess is you would run out of money in a hurry. So, another thing that may be of value to look at is expected points per dollar. That's just P/C (before April 15) or P/(W*1000) (after April 15). (I would recommend multiplying it by 1000 to get it on a more comfortable scale.) A possible drawback of using this measure to select your team on a daily basis is that you would likely pick mostly sub-par teams who are playing other sub-par teams. In that case, you'd have lots of money you aren't putting to good use. It is obvious that you can quickly rule out teams who's probability of winning is less than their winning percentage. (I.e. those with P/W < 1.) Of those that are left, some things you could try: 1) Rank the teams by each measure. Add up the two ranks for each team. Pick the team with the smallest sum. 2) Assign a score based on the two measures. a*Expected Points + b*P/W is an example, where a and b are constants that reflect how important you think each measure is. 3) Just look at the teams and, based on the expected points and expected points per dollar, go with your gut. Just some thoughts. | ||||||
| 1 | Myboyjack ID: 4443038 Mon, Mar 26, 10:05 | #3 looks like the path for me :) | |||||
| 2 | Guru ID: 330592710 Mon, Mar 26, 10:15 |
I presume the quoted betting lines will be a good source of information that consolidates info including opponent & starting pitchers. Is there a convenient source of betting lines that I could provide a link to? | |||||
| 3 | Sludge ID: 1440310 Mon, Mar 26, 10:23 |
I've found that esportse.com has their lines generally up-to-date, unlike USAToday, which I used to use. I'm sure someone has a better site. I also forgot to mention something about "P". Of course, we don't know exactly what P is, so it has to be estimated somehow. Looking at the sports lines is a good way. One could also look at computer rankings such as Massey or Sagarin, but they don't take into account starting pitchers or injuries. | |||||
| 4 | HooeyPooey ID: 41115208 Mon, Mar 26, 10:44 |
It would be interesting to take a season, such as last years, and do some analysis of frequency of matchups we may expect to see over the course of this year. (i.e. how often a .600 team faced a .500 team with what results. Compare this to a .600 vs .400 or a .500 vs a .400, etc.) This may give some idea as to the optimal way to spend money. Unfortunately, this may be more work than I am up to right now. Of course, I doubt there is any way to really approximate P for all those games at this point in time, though I suppose pitcher stats (or betting lines if you could find such a thing archived somewhere) could be incorporated but that could get involved with perhaps not enough benefit to us now, however I'm sure approximating P is a key aspect to this game. There has to be some formula to maximize expected points utilizing all money, but I haven't found it yet, which is why looking at some history may be helpful. I do think we will have, to some degree, three different games with the three seasons, in which strategy and this formula yet to be found may be slightly different in each case. The post ASB costs are going to be more stable than the two early seasons. I'm thinking that it may be best to choose games earlier in the season (early being after the 4/15 mark) when prices are more likely to be less than P for some teams which didn't fair well early, yet still have fairly high probability of winning, thus producing higher expected points per $. Of course this may also result in extra money which may be (should have been) used to spend on bargains teams before 4/15 which may not be affordable once the new prices are established. Of course, I'm just guessing on all of this. | |||||
| 5 | KrazyKoalaBears ID: 431156218 Mon, Mar 26, 11:23 |
First off, I'm not going to claim to know a single thing about probability, statistics, or anything else with that regard. However, Sludge, I did notice that you didn't take into account who the opposition was and how that effected probability. I did some quick and dirty, though maybe not statistically sound, calculations and came up with an interesting formula that takes into account a team (win %), the opposition (win %) and the price you'll pay for the matchup. Simply put, its: Don't ask how I got there, but here's the results using last years numbers: CLE (556) - TAM (429) SFO (599) - SDG (469) CIN (525) - CHC (401) Now if you look at the Price Differences, they're all within 6 of each other which means the range of difference in win percentages amonst the 4 sets above is .006 (which doesn't even translate to a full game over the course of 162 games). Yet the "Result" ranges .019. Again, it's not a lot, but also look at the fact that SFO (with the best record) has the worst "Result" because of their price. Used accross the board, I think this method could help show which teams have the better win percentage advantage over their opponent for the price they cost. Not sure if this is showing true probability or not, so I'm open for discussion on the matter. | |||||
| 6 | Chris ID: 02372611 Mon, Mar 26, 11:41 |
Most likely I will use a very unscientific method which looks for some of the following factors: - team is at home - team is playing well - team has a favorable opponent - team has a favorable pitcher matchup - so on and so forth Basically, I'll probably pick the team that best satisfies the parameters previously set forth... | |||||
| 8 | HooeyPooey ID: 41115208 Mon, Mar 26, 12:06 |
KKB, I think that Sludge was taking into account the opposition when he stated "The expected points for picking the team is simply P. (Expected points is the average points you would receive if the game were played over and over and over again.)" P in his formula is the probability of team A beating team B, which could only be determined by taking into account who the two teams were. Team B's price or winning percentage does not play a factor in this unless you are using team B's winning percentage to calculate P, which it appears that you are in your calculations. If so, then yes, I believe you are correct in showing that the greater team A's percentage (and price) is the lower their probability of winning is will be (even if the difference in cost of opposition is the same), making the expected points per $ even lower. If one was to only use a teams winning percentage to determine P, I'm not quite sure your formula is correct. Perhaps it should be expressed as P = TeamA%/(TeamA%+TeamB%), though I am not sure at this point. If it is though, I think it would prove your point even better when you factor in price. | |||||
| 9 | JeffG ID: 40451227 Mon, Mar 26, 12:42 |
Vegas money line is a good thing to use since they usually take into account starting pitchers. Otherwise, pick simply based on opponent's winning percentage. You are paying solely based on the team you are selecting. For example, If the Yankees are at a .550 winning percentage, you are better off paying $550 when they play a .400 team than when they are playing a .500 team. In this example, your $550 is much more likely to result in a point for the win. Strategy: Always pick against the worst teams. | |||||
| 10 | KrazyKoalaBears ID: 431156218 Mon, Mar 26, 12:45 |
HooeyPooey, ss, I told you I wasn't a statistics person. ;) I think you're right that P does take into account both teams and it all makes much more sense now. This game is going to get interesting. | |||||
| 11 | HooeyPooey ID: 41115208 Mon, Mar 26, 14:11 |
BTW, just in case anyone wanted to experiment with last years results, I did find an Odds Archive at VegasInsider.com that currently goes back to April 2000. I'd put together a spreadsheet on this, but I haven't learned the art of automatically importing data from web pages yet, of which there is a page for each day, plus it would take some work to get the data in a usable format, but it could be done. I'm still thinking about it... it would be sweet to have something like this for finding an optimal strategy. :) | |||||
| 12 | Madman ID: 29246911 Mon, Mar 26, 14:47 |
Sludge Ever heard of Kuhn-Tucker optimization? That's essentially the problem here, as it is in almost all budget constraint problems, I think. You caught the gist of the fundamental conflict. On the one hand, you need to maximize the number of wins in your limited allotment of 50 selections. On the other hand, you have to maximize wins/$$$$, since you have a budget constraint. And, even if there was no constraint, this is the tie-breaker, so you should try to minimize $$$ to some extent. I should note that this is the fundamental optimization problem that everyone is facing in SW. It's why it makes sense to put a premium on the most productive players. In SW, you have a limited roster of 15 players. Therefore, to maximize points, you should maximize points/roster slot (duh). However, you have limited cash. Therefore, the rate is also important -- i.e., SWP/$$$$. The proper balance between these two objectives is not always clear. And, in SW, you have the extra monkey wrench of changing prices, further complicating the optimization problem. At any rate, my point is to say that you hit the nail on the head. You have to balance the straight expected win total with the cost of a win in terms of $$$. I don't recall anyone trying to fix the proportion of the weight between the two goals before. It's an interesting idea. But I think it's a bit flawed. Going to get a bit technical, but I'll try to still make sense :) . In K-T optimization, the lagrange multipliers on the two constraints (# of picks, $$$) are critical to determining which aspect is more important given the current situation. These multipliers will obviously change depending on the situation your team is in. I think your "a" and "b" may, in effect, be substitutes for these. If not strictly from a mathematical perspective, at least heuristically. For example, if you haven't spent much money, your "a" will become much bigger relative to "b". If you've spent a ton of money, the reverse is true. And thus this could potentially be a very tricky little game. Hopefully, anyway. This is one of the reasons, BTW, that I've always been amazed at the subconscious brain. Experienced and/or smart people tend to naturally gravitate toward solutions that are "somewhat close" to optimal even in these sorts of conflicting objective environments. This has happened throughout human history, despite the fact that no one really knew what many of these optimal solutions were. Very impressive. Kudos to God or evolution or both for that one. Of course, if you can actually calculate something approximating the optimal picks, then you won't just be "somewhat close", anymore, and you'll have a significant advantage . . . :) | |||||
| 13 | Sludge ID: 1440310 Mon, Mar 26, 15:15 |
Madman - Yeah... I know it's a constrained optimization, but I was trying to stay away from those terms as much as possible. And then you go and throw in "lagrange multipliers". :) | |||||
| 14 | Dev ID: 20147416 Mon, Mar 26, 16:32 | Sludge- Your first link in post three doesn't work. Is this what you were trying to do: Massey ? | |||||
| 15 | Sludge ID: 1440310 Mon, Mar 26, 17:15 | Yup... thanks, Dev. Forgot to put the "http://" on the link. | |||||
| 16 | winmiller ID: 107452613 Mon, Mar 26, 21:31 |
After reviewing all of this, I have decided to make all of my picks using the ZZ Top statistical variant. That is, I will review all of the relevant data, then make gut instinct picks from "a shack outside LaGrange." You know what I'm talkin' about. ;-) | |||||
| 17 | Madman ID: 29246911 Mon, Mar 26, 21:37 |
hahaha. Good one, winmiller. sludge I was only trying to discourage people from option (b) by introducing such naughty language as Langrange Multipliers into this thread. If you want a statistical method, perhaps just look at (P - W). Then use your gut instinct to choose. If two teams have very similar (P-W)'s, then go with the cheaper. Or, if you're spending too much money, then start going with cheaper one's even if they don't quite have as high of (P-W)'s... In reality, an optimal strategy would rely on knowing the P's and W's for all the teams for each day of the season, so you could pick the best 50. However, there is obviously great uncertainty with that, since the W's tomorrow rely on outcomes today. I think you could do quite well with my (P-W) method if you had a good method for predicting P. In fact, that's what we all will be doing. But most of us will rely on gut to determine P. In addition, over the course of time, you'd get a feel for what a "good" (P-W) value is -- i.e., one that's sufficiently rare to warrant using one of your limited 50 or 100 or 162 picks on it. | |||||
| 18 | KrazyKoalaBears ID: 51521713 Mon, Mar 26, 21:42 | I think the key is to find the cheap teams with a decent/good pitcher against other bad teams. A good example would be Dempster for FLA against PHI. I know this sounds like the obvious ones, but it's going to pay to know the pitchers on the bad teams that have the best chance of winning. Dempster, Vazquez, Elarton, D'Amico, Wood, Lieber, Eaton, Moehler, Milton, Radke, and Helling are all guys that are somewhat proven, on cheap teams, that have a good chance of winning (relatively, at least). | |||||
| 19 | Sludge ID: 18116195 Mon, Mar 26, 21:57 |
Madman - Fellow threadkiller, not to belabor a point, but P-W is, in fact, the same as P/W. Not in a mathematical sense, mind you, but in a practical/relative sense. Consider: P=0.550 W=0.400 P-W = 0.150 P/W = 1.375 P=0.650 W=0.500 P-W = 0.150 P/W = 1.300 Go with the cheaper team. (If you have plenty of money, go with the more expensive team.) In the end, it's all a gut feeling. To tell the truth, I used mostly my gut during the blind weeks in Pickoff. But, there is something to be said for having an idea of the mechanics to making an "optimal" pick. I have no doubt that understanding the intricacies (sp? my baby is crying at the moment) of the game will help, even if unconcsiously. Rate this thread a 1 all you want, but if you play the game, you will take heed of some of the advice, whether you know it or not. | |||||
| 20 | Madman ID: 29246911 Mon, Mar 26, 22:16 |
Hmmm. They are both ordinally equivalent. But I don't they are equal in practical value. If you look at P/W, also looking at the cheaper team on top of that is a bit weird, I think. After all, the team with the lower W already has some sort of bias in it's favor. By looking at P-W, I'm taking the budget out of the statistic I would look at, and then separate use $$$ to tie break or make judgements on close calls. Consider: P=520 W=400 P-W = 120 P/W = 1.30 Your P/W method will equate this team and your second team -- 400 and 500 winning percentages. But if I have the cash, I might rather go more expensive in this case and get more P (and more P-W). It all depends on how much money I have left. I dunno. This is a matter of individual taste, since some people may find P/W more intuitive. Personally, I think that looking at the gaps makes more sense to me. I understand that occasionally you may not be getting the most P for your W. But the key here is that you need a large amount of P, and the straight P-W helps me to keep that in mind better, I think. | |||||
| 21 | Guru ID: 330592710 Tue, Mar 27, 07:17 | If you need a large amount of P, toss down a few brews before making your picks. | |||||
| 22 | GothWalker ID: 5223144 Tue, Mar 27, 07:36 | Find out all aboot P-W | |||||
| 23 | Sludge ID: 1440310 Tue, Mar 27, 08:50 | But it's still the same, Madman. What are you going to use to break the tie between the 1.3's? Budgetary concerns, of course. | |||||
| 24 | Madman ID: 29246911 Tue, Mar 27, 09:28 |
sludge But the direction of the budgetary concern might very well be reversed -- you can invest more at the solid 1.30 rate, using the P/W terminology. P/W will always reward the cheaper team, but it's not always optimal to go cheaper. As I said, however, it's a matter of taste. You're right that you can get to the same solutions either way. We'll be relying on our subconscious calculations quite a bit, I suspect. | |||||
| 25 | KrazyKoalaBears ID: 431156218 Tue, Mar 27, 11:07 |
Amazing that this is the thread with the highest number of ratings, yet it has such a low rating.... Madman, I do agree that a lot of it's going to come down to subconscious calculations (if I understand what you're saying correctly), at least for the first season. | |||||
| 26 | Sludge ID: 1440310 Tue, Mar 27, 11:11 | I think SZ is trying to kill this thread by rating it low rather than leaving it to the experts. :) | |||||
| 27 | Guru ID: 330592710 Tue, Mar 27, 11:34 | I think the ratings went downhill when Lagrange Multipliers were mentioned... | |||||
| 29 | CanEHdian Pride ID: 426351415 Mon, Apr 02, 13:05 | Uhhhh...I never was to good at figurin' on account of the fact that i didn't get no book learnin' but I's just gonna pick the team who has a good chance of winnin' that won't make me ask pa for a loan....hope this 'un works!!! | |||||
| 30 | Sludge ID: 1440310 Mon, Apr 02, 13:12 | As a child of the south, I demand immediate reperations for your insulting behavior. I figure a cool trillion dollars, to be divided equally among every person south of the Mason Dixon line, would be adequate. | |||||
| 31 | pogophiles ID: 3245839 Mon, Apr 02, 14:06 | Hear Hear Sludge! But given recent migration patterns, I would amend that to read every person born south of the Mason/Dixon line. | |||||
| 32 | Madman ID: 29246911 Mon, Apr 02, 14:17 |
I think we've covered this before. Why is this thread rated poorly? The above link takes you to a filter where you can see all the threads I started. The same phenomenon has occurred with most Madball threads, although the rate of negative ratings has slowed down a bit. So, I bet that 10-20 of these negative ratings can be explained as the anti-Madman factor. Plus, I did the Lagrange Multiplier bit. That probably added in about another 10. Therefore, I take responsibility for ruining not just the content, but also the ratings of sludge's thread. I'll strive to refrain in the future :). | |||||
| 33 | Sludge ID: 1440310 Mon, Apr 02, 14:51 |
pogophiles - I chose my words very carefully. Doesn't matter if you're born in the south or north. All that matters is your current location. I was lampooning some of the proposed reperation plans for black Americans. | |||||
| 34 | James K Polk ID: 32012715 Mon, Apr 02, 16:00 |
Madman, re: link in #32, that's dang impressive!! I just threw off the curve a bit, though, with a quick rating of your Swirve price movers thread :) | |||||
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