I was talking with some co-workers today about the AL Central and one of my friends was adamant that the Cleveland Indians weren't going to win the division. I think that's nuts.
Going back to 2006, an outlier season where three teams in the Central finished with 90 wins or better, this is how many wins the 2nd place team in the AL Central had at the end of the season:
2010 - 88 wins by the Chicago White Sox
2009 - 86 wins by the Detroit Tigers (Minnesota Twins won a 1 game playoff)
2008 - 88 wins by the Minnesota Twins (Chicago White Sox won a 1 game playoff)
2007 - 88 wins by the Detroit Tigers
The winner of the AL Central has needed to win an average of 88.5 games to take home the pennant. Let's call 89 wins the magic number to win the AL Central. The first team past the 89-win post is going to win the AL Central except by fluke.
After 40 games the Indians have banked 26 wins and to get to 89 wins they need 63 wins over their last 122 games. That's only two games above .500 and the Indians are currently playing at a pace 12! games above .500 for the season. They could lose their next ten games and go one for two the rest of the way and still hit 89 wins.
I think the AL Central is over. The Indians would need to collapse in epic fashion and someone else would have to raise their game incredibly to catch them. And that's a problem going forward because this team is built to win for the next handful of years.
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Thursday, May 19, 2011
Thursday, May 20, 2010
It's A Number Game But Shit Don't Add Up Somehow
From the time I got on the bus yesterday morning until when he stopped texting me back seven hours later, Smallz and I exchanged mini-diatribes about the NBA Draft ranging from which player the Wolves should take with the fourth pick to the proper way to evaluate talent and construct a team to the other person's deficiencies at evaluating talent and those of their chosen method to constructing a team. Basically our arguments were this.
Smallz loves efficient players. Thus Kevin Love is his one shining beacon on our entire roster. As such Al Jefferson inspires much hatred in Smallz's gut. Not only does Jefferson play the same position as Love but inefficiently uses the ball in offensive situations Love would efficiently use them. His evidence is statistics and his team-building philosophy is to find other efficient players to pair with Love.
I, on the other hand, believe Jefferson is inefficient because he needs to be. Love is a good player and a compliment to Jefferson. But efficiency statistics don't tell the whole story. As the most offensively-skilled player on the Wolves, a less-than-efficient attempt from Jefferson is still better than passing the ball to a less talented teammate. Being the focus of the offense and the volume of his shots he can't cherry-pick only the best attempts. Basketball is scored as a quantitative game, not an efficiency game, and to remove Jefferson without a suitable replacement will only focus the defense on another lesser player.
(Further reading found HERE.)
This is especially important with the NBA draft coming up. Since the Wolves didn't get one of the surefire guys at the very top of the draft, their path forward is a lot less clear. Smallz wants to trade Jefferson to free playing time for Love and draft Kentucky's DeMarcus Cousins, a freakishly large center who may have character issues. I want to keep both Jefferson and Love while drafting Syracuse small forward Wesley Johnson, a lower risk lower reward player who plays a position of need. We could argue back and forth for hours (and did) about which one would be a better fit for Minnesota. I wanted to model the problem and get some results now.
How I Used Math To "Solve" the Problem
So let's assume three things. First that either Cousins or Johnson could boom or bust with equal likelihood. Let's just say Cousins wider range of possible outcomes averages out to Johnson's thinner range to make things easier. Second, let's assume the pick is an independent outcome. Let's say if Minnesota picked Cousins they wouldn't keep Jefferson and his minutes would go to DeMarcus. Third, the actual outcome will be one of many possible outcomes. When a weatherman says 55% chance of rain and it doesn't, he was right. It just fell in the 45% he didn't mention.
Here's the "game" I developed. Imagine every possible outcome for DeMarcus Cousins' and Wesley Johnson's careers is represented by a playing card. Since they are top draft picks they are more likely to succeed than fail so all face cards represent complete success (being a cornerstone), ten through six represent qualified success (being an NBA starter) and five through two mean they bust. I could look up the real success rate but let's keep it simple. Now draw two cards, one representing Cousins and the other representing Johnson. Reset the deck, reshuffle the cards and repeat the process 100 times.
(Or do like I did and use a random card generator like THIS ONE.)
What I found is Cousins is a cornerstone 37% of the time, a starter 38% of the time and a bust 25% of the time. Likewise Johnson is a cornerstone 38% of the time, a starter 33% of the time and a bust 29% of the time. In 48% of the cases Cousins is the better player while Johnson is the better player 45% of the time. (The remaining 7% is when they're even.) It's also worth noting Cousins is significantly better 27% of the time while Johnson is significantly better 26% of the time.
So what do the results tell us about who the Wolves should take? Nothing. This is a simplified model of an enormously complex system. But within the context of the system it says we should expect any result to be possible. In that way both experience and this simulation align. In the NBA Draft eventually you have to play the odds and hope for the best.
P.S. This is the raw data from my simulation. Cousins is on the left and Johnson on the right. Ignore the symbols. That's just me coding the data.
CJ
A4**
A3**
A9**
88-
610++
610++
Q8**
QK*
63*
32*
5J++
10Q+
9J+
87*
410++
56*
3Q++
34+
5A++
67+
109*
QJ*
4K++
82**
109*
63*
56+
7Q++
86*
J8**
3A++
910+
5K++
J9*
Q4**
103**
KJ*
JQ+
A2**
9Q+
25+
K5**
9Q+
4A++
63*
44-
6K++
6Q++
9K++
K3**
KJ*
8A++
5J++
8Q++
A5**
25++
7Q++
KA+
K8**
A3**
J3**
22-
J3**
37++
24+
76*
9J+
A4**
3K++
QJ*
KA+
88-
53*
A8**
82**
36+
J8*
8Q++
J7**
Q9*
6J++
AA-
6A++
A5**
310++
92**
QQ-
JK+
56+
8Q++
8J+
Q9*
Q6**
Q5**
810+
J2**
33-
104**
A7**
QA+
Smallz loves efficient players. Thus Kevin Love is his one shining beacon on our entire roster. As such Al Jefferson inspires much hatred in Smallz's gut. Not only does Jefferson play the same position as Love but inefficiently uses the ball in offensive situations Love would efficiently use them. His evidence is statistics and his team-building philosophy is to find other efficient players to pair with Love.
I, on the other hand, believe Jefferson is inefficient because he needs to be. Love is a good player and a compliment to Jefferson. But efficiency statistics don't tell the whole story. As the most offensively-skilled player on the Wolves, a less-than-efficient attempt from Jefferson is still better than passing the ball to a less talented teammate. Being the focus of the offense and the volume of his shots he can't cherry-pick only the best attempts. Basketball is scored as a quantitative game, not an efficiency game, and to remove Jefferson without a suitable replacement will only focus the defense on another lesser player.
(Further reading found HERE.)
This is especially important with the NBA draft coming up. Since the Wolves didn't get one of the surefire guys at the very top of the draft, their path forward is a lot less clear. Smallz wants to trade Jefferson to free playing time for Love and draft Kentucky's DeMarcus Cousins, a freakishly large center who may have character issues. I want to keep both Jefferson and Love while drafting Syracuse small forward Wesley Johnson, a lower risk lower reward player who plays a position of need. We could argue back and forth for hours (and did) about which one would be a better fit for Minnesota. I wanted to model the problem and get some results now.
How I Used Math To "Solve" the Problem
So let's assume three things. First that either Cousins or Johnson could boom or bust with equal likelihood. Let's just say Cousins wider range of possible outcomes averages out to Johnson's thinner range to make things easier. Second, let's assume the pick is an independent outcome. Let's say if Minnesota picked Cousins they wouldn't keep Jefferson and his minutes would go to DeMarcus. Third, the actual outcome will be one of many possible outcomes. When a weatherman says 55% chance of rain and it doesn't, he was right. It just fell in the 45% he didn't mention.
Here's the "game" I developed. Imagine every possible outcome for DeMarcus Cousins' and Wesley Johnson's careers is represented by a playing card. Since they are top draft picks they are more likely to succeed than fail so all face cards represent complete success (being a cornerstone), ten through six represent qualified success (being an NBA starter) and five through two mean they bust. I could look up the real success rate but let's keep it simple. Now draw two cards, one representing Cousins and the other representing Johnson. Reset the deck, reshuffle the cards and repeat the process 100 times.
(Or do like I did and use a random card generator like THIS ONE.)
What I found is Cousins is a cornerstone 37% of the time, a starter 38% of the time and a bust 25% of the time. Likewise Johnson is a cornerstone 38% of the time, a starter 33% of the time and a bust 29% of the time. In 48% of the cases Cousins is the better player while Johnson is the better player 45% of the time. (The remaining 7% is when they're even.) It's also worth noting Cousins is significantly better 27% of the time while Johnson is significantly better 26% of the time.
So what do the results tell us about who the Wolves should take? Nothing. This is a simplified model of an enormously complex system. But within the context of the system it says we should expect any result to be possible. In that way both experience and this simulation align. In the NBA Draft eventually you have to play the odds and hope for the best.
P.S. This is the raw data from my simulation. Cousins is on the left and Johnson on the right. Ignore the symbols. That's just me coding the data.
CJ
A4**
A3**
A9**
88-
610++
610++
Q8**
QK*
63*
32*
5J++
10Q+
9J+
87*
410++
56*
3Q++
34+
5A++
67+
109*
QJ*
4K++
82**
109*
63*
56+
7Q++
86*
J8**
3A++
910+
5K++
J9*
Q4**
103**
KJ*
JQ+
A2**
9Q+
25+
K5**
9Q+
4A++
63*
44-
6K++
6Q++
9K++
K3**
KJ*
8A++
5J++
8Q++
A5**
25++
7Q++
KA+
K8**
A3**
J3**
22-
J3**
37++
24+
76*
9J+
A4**
3K++
QJ*
KA+
88-
53*
A8**
82**
36+
J8*
8Q++
J7**
Q9*
6J++
AA-
6A++
A5**
310++
92**
QQ-
JK+
56+
8Q++
8J+
Q9*
Q6**
Q5**
810+
J2**
33-
104**
A7**
QA+
Wednesday, August 6, 2008
Changing Body Math III: The Return of the Update
A little less than three months has passed since I made my last post about the weight I've lost and that means I'm due for another post containing the math of it all.
In the past nine months I've lost 53 pounds dropping my weight from 305 to 252. I've also reduced my body fat composition from 30% to 24%. As I mentioned in the last post about my weight loss, the goals for no longer being obese are 263 pounds and 25% body fat. So you can see that I am healthily under the bar for both metrics.
Multiply those numbers together and I've lost 31 pounds of body fat and 22 pounds of water weight. If 4.5% of the 6% of body mass change is new muscle then I've also added about 11 pound of muscle too. So add 505 calories burned each day just for that new muscle existing meaning I can netting out a pound of fat less every 6.4 days without lifting a weight or spending any time on the elliptical.
Having lost 50 pounds and no longer being obese, I've basically achieved my goals in wanting to lose weight. Now the goal is to maintain my weight, lower my body fat even further and not have to think about the numbers anymore. I'll keep going to the gym three to five times a week and I'm sure I'll keep losing weight for a while. It just won't be as necessary to quantify it which is a good feeling to have.
In the past nine months I've lost 53 pounds dropping my weight from 305 to 252. I've also reduced my body fat composition from 30% to 24%. As I mentioned in the last post about my weight loss, the goals for no longer being obese are 263 pounds and 25% body fat. So you can see that I am healthily under the bar for both metrics.
Multiply those numbers together and I've lost 31 pounds of body fat and 22 pounds of water weight. If 4.5% of the 6% of body mass change is new muscle then I've also added about 11 pound of muscle too. So add 505 calories burned each day just for that new muscle existing meaning I can netting out a pound of fat less every 6.4 days without lifting a weight or spending any time on the elliptical.
Having lost 50 pounds and no longer being obese, I've basically achieved my goals in wanting to lose weight. Now the goal is to maintain my weight, lower my body fat even further and not have to think about the numbers anymore. I'll keep going to the gym three to five times a week and I'm sure I'll keep losing weight for a while. It just won't be as necessary to quantify it which is a good feeling to have.
Thursday, May 29, 2008
While Y'All Were Asking Permission I Just Stepped Up and Took It
Have you heard to the Pythagorean Theorem of Baseball? It’s pretty simple. Basically, it says that your Expected Win-Loss should be equal to the proportion of the runs you score out of all of the runs scored in games you play. (Your Runs) / (Your Runs + Your Runs Allowed) in other words. Normally a team’s record falls within +/- 3 games. There are of course exceptions like last year’s Diamondbacks who “should” have been 79-83 but actually led the NL at 90-72. But it’s a good guideline.
The variation usually comes from games at either end of the spectrum, blowouts and close games. So when the Twins get trounced by the Tigers 19-3 on Saturday it makes the Twins appear worse and the Tigers appear better than they “are.” Additionally when the Twins win one-run games which they’ve done 12 times against 8 loses, they appear better than they “are” and the Royals appear worse.
The cool thing for me as a Twins fan is this. At the beginning of the Twins-Royals series, the Twins record (25-25) was better than their X W-L at (23-27). In both of the Royals games, the Royals led going into the top of the 9th including a blown save by Joe Nathan on Tuesday because of a missed sliding catch by Delmon Young which resulted in an indoor-four for Mark Teahan to tie the game. Each of those nights, the Twins squeaked out extra inning one-run wins alternately by playing small ball on Tuesday and by hitting the long ball last night. There’s no “this game is over” once we reach the late innings with this team. In the end it's the games you do or don't win that count not the ones which you should or shouldn't have.
As a result this morning the Twins record (27-25) is 4 games better than their X W-L (25-27). This makes sense since, as I said before, the Twins have won four more one-run games than they’ve lost.
The variation usually comes from games at either end of the spectrum, blowouts and close games. So when the Twins get trounced by the Tigers 19-3 on Saturday it makes the Twins appear worse and the Tigers appear better than they “are.” Additionally when the Twins win one-run games which they’ve done 12 times against 8 loses, they appear better than they “are” and the Royals appear worse.
The cool thing for me as a Twins fan is this. At the beginning of the Twins-Royals series, the Twins record (25-25) was better than their X W-L at (23-27). In both of the Royals games, the Royals led going into the top of the 9th including a blown save by Joe Nathan on Tuesday because of a missed sliding catch by Delmon Young which resulted in an indoor-four for Mark Teahan to tie the game. Each of those nights, the Twins squeaked out extra inning one-run wins alternately by playing small ball on Tuesday and by hitting the long ball last night. There’s no “this game is over” once we reach the late innings with this team. In the end it's the games you do or don't win that count not the ones which you should or shouldn't have.
As a result this morning the Twins record (27-25) is 4 games better than their X W-L (25-27). This makes sense since, as I said before, the Twins have won four more one-run games than they’ve lost.
Saturday, May 17, 2008
Changing Body Math Update
It's been about four months since I made my first post (I realize I made a math error which I'll point out below but I didn't feel like going back to change.) about working out and losing weight so I figured I was due for an update.
In the last six months, I've dropped my weight from 305 lbs. to 270 lbs for a gross loss of 35 lbs. When I started working out I had 30% body fat and have trimmed that number down to 26%. Multiply all those respective numbers together and I've gone from carrying 91.5 lbs. of fat down to 70.2 lbs. There are 21.3 lbs. of fat (the weight of this 1 year old dog) which *poof* no longer exist.
The other 14 lbs is water weight. Last time I accounted this weight as gaining muscle which is simply not the case. Unless I were losing bone density or giving away internal organs, this is just my body adjusting the amount of water it holds. Think about the blood maintaining the fat which is no longer needed and reabsorbed by the body and it makes sense.
The correct way of figuring out the muscle I've added goes back to the body fat percentage. I've lost 4% of fat which means that a greater proportion is made up of something else now. There are factors like my bones becoming more dense but for the most part it's muscle taking up a greater proportion of my overall weight. Conservatively saying 3% is new muscle growth and 1% other factors that means I've gained 8.1 lbs of muscle in the last six months or about as much as one gallon of water weighs.
1 pound of muscle burns 50 calories at day which means that I'm burning an additional 405 calories per day simply by changing my body makeup. Out of the Bs, that's the same as 2 plain bagels, 4 bananas or light beers, 5.4 oz of blue cheese dressing, about 10 spears of brocolli or 40.5 tbsp. of BBQ sauce. To put it another way, at rate of 405 calories a day, a pound of fat would burn away in about eight and a half days. And that's just existing at rest, not taking into account that muscle actually getting used when I work out.
The thing which I have a greater understanding of since I wrote my last post is that I shouldn't be as concerned with my weight as much as I should be focused on my body fat percentage. According to the BMI scale, I'm obese and will be until I can slide under 263 lbs with a goal of 218 to be on the high end of normal.
Well, if we go back to the top, my baseline weight which includes bones, organs, muscle and water weight but not fat is about 200 lbs. To be 218 pounds, assuming my bones growing more dense and my muscles getting stronger equals my water weight loss, I could carry only 18 lbs. of fat. for a very athletic 8% body fat. For some perspective, Michael Jordan (a world-class athelete) weighed 216 lbs. during his last year in the NBA. And that's the top end of what they consider "normal."
If you focus on body fat percentage instead a different picture emerges. By this metric being over 25% body fat for a male is obese. So let's say I maintain my present weight but lose that 1% body fat. That's only 2.7 lbs. of fat I need to lose. Even if I drop my another 10 pounds to 260, the north end of what I weighed during college and consider a good guideline, I'll need to shed 5.2 lbs of body fat to get to 25%.
There is work yet to be done. Still results are happening and there's no reason why I can't achieve my goals over the next few months. I knew this was going to be at least a year-long process when I started six months ago. With the progress I've made, it looks like I can start setting some goals further out than I expected.
In the last six months, I've dropped my weight from 305 lbs. to 270 lbs for a gross loss of 35 lbs. When I started working out I had 30% body fat and have trimmed that number down to 26%. Multiply all those respective numbers together and I've gone from carrying 91.5 lbs. of fat down to 70.2 lbs. There are 21.3 lbs. of fat (the weight of this 1 year old dog) which *poof* no longer exist.
The other 14 lbs is water weight. Last time I accounted this weight as gaining muscle which is simply not the case. Unless I were losing bone density or giving away internal organs, this is just my body adjusting the amount of water it holds. Think about the blood maintaining the fat which is no longer needed and reabsorbed by the body and it makes sense.
The correct way of figuring out the muscle I've added goes back to the body fat percentage. I've lost 4% of fat which means that a greater proportion is made up of something else now. There are factors like my bones becoming more dense but for the most part it's muscle taking up a greater proportion of my overall weight. Conservatively saying 3% is new muscle growth and 1% other factors that means I've gained 8.1 lbs of muscle in the last six months or about as much as one gallon of water weighs.
1 pound of muscle burns 50 calories at day which means that I'm burning an additional 405 calories per day simply by changing my body makeup. Out of the Bs, that's the same as 2 plain bagels, 4 bananas or light beers, 5.4 oz of blue cheese dressing, about 10 spears of brocolli or 40.5 tbsp. of BBQ sauce. To put it another way, at rate of 405 calories a day, a pound of fat would burn away in about eight and a half days. And that's just existing at rest, not taking into account that muscle actually getting used when I work out.
The thing which I have a greater understanding of since I wrote my last post is that I shouldn't be as concerned with my weight as much as I should be focused on my body fat percentage. According to the BMI scale, I'm obese and will be until I can slide under 263 lbs with a goal of 218 to be on the high end of normal.
Well, if we go back to the top, my baseline weight which includes bones, organs, muscle and water weight but not fat is about 200 lbs. To be 218 pounds, assuming my bones growing more dense and my muscles getting stronger equals my water weight loss, I could carry only 18 lbs. of fat. for a very athletic 8% body fat. For some perspective, Michael Jordan (a world-class athelete) weighed 216 lbs. during his last year in the NBA. And that's the top end of what they consider "normal."
If you focus on body fat percentage instead a different picture emerges. By this metric being over 25% body fat for a male is obese. So let's say I maintain my present weight but lose that 1% body fat. That's only 2.7 lbs. of fat I need to lose. Even if I drop my another 10 pounds to 260, the north end of what I weighed during college and consider a good guideline, I'll need to shed 5.2 lbs of body fat to get to 25%.
There is work yet to be done. Still results are happening and there's no reason why I can't achieve my goals over the next few months. I knew this was going to be at least a year-long process when I started six months ago. With the progress I've made, it looks like I can start setting some goals further out than I expected.
Tuesday, January 29, 2008
Changing Body Math
Was it six or seven weeks ago that I started working out? I don't recall. Let's call it seven.
In those seven weeks, I've dropped my weight from 305 lbs to 285. That's a loss of twenty pounds. Average it out and that's a little under three pounds a week. I pay $140 a month for once a week training sessions and over two months that averages out to $3.50 a pound. One pound of almonds costs $3.50.
When I started I had 30% body fat. That means I was carrying 91.5 pounds of body fat on my frame. I've dropped to 27% body fat meaning I'm carrying 76.95 pounds of body fat. There are 14.55 pounds of fat which used to exist which *poof* don't anymore.
Which means that, not only have I lost 20 pounds, I've gained 5.45 pounds of muscle. An extra pound of muscle burns an extra 50 calories a day. So I've been burning 272.5 extra calories a day.
It would take 21 minutes of chopping wood, 28 minutes of jogging, 36 minutes of caring for a child, 42 minutes of weight-lifting or 97 minutes of taking the lead while doing the deed to burn 272 calories.
I'd need to eat half a Big Mac, a whole croissant, 8.24 tossed salads w/o dressing or drink 272 Diet Cokes extra in order to match the calorie intake - calorie burn ratio I was at before I started working out. Or I can just bank it and every 13 days burn another pound of fat.
If someone had come to 17, 19, 23 or even 26 year-old Mike and explained the math to me, I never would've made it to 305. But, since I did see 305 and someone set me down and ran the math, it's on 28 year-old Mike to pick up the pieces.
It's a long way to go. But the number don't lie. If I keep at it, I will lose the weight my body has been desperately been hoping to shed. Sounds like a fair deal to me.
In those seven weeks, I've dropped my weight from 305 lbs to 285. That's a loss of twenty pounds. Average it out and that's a little under three pounds a week. I pay $140 a month for once a week training sessions and over two months that averages out to $3.50 a pound. One pound of almonds costs $3.50.
When I started I had 30% body fat. That means I was carrying 91.5 pounds of body fat on my frame. I've dropped to 27% body fat meaning I'm carrying 76.95 pounds of body fat. There are 14.55 pounds of fat which used to exist which *poof* don't anymore.
Which means that, not only have I lost 20 pounds, I've gained 5.45 pounds of muscle. An extra pound of muscle burns an extra 50 calories a day. So I've been burning 272.5 extra calories a day.
It would take 21 minutes of chopping wood, 28 minutes of jogging, 36 minutes of caring for a child, 42 minutes of weight-lifting or 97 minutes of taking the lead while doing the deed to burn 272 calories.
I'd need to eat half a Big Mac, a whole croissant, 8.24 tossed salads w/o dressing or drink 272 Diet Cokes extra in order to match the calorie intake - calorie burn ratio I was at before I started working out. Or I can just bank it and every 13 days burn another pound of fat.
If someone had come to 17, 19, 23 or even 26 year-old Mike and explained the math to me, I never would've made it to 305. But, since I did see 305 and someone set me down and ran the math, it's on 28 year-old Mike to pick up the pieces.
It's a long way to go. But the number don't lie. If I keep at it, I will lose the weight my body has been desperately been hoping to shed. Sounds like a fair deal to me.
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