Ranking System - Percentage Theory
Posted: Thu Feb 15, 2007 1:11 pm
I would like some of you to let me know where my new ranking system has flaws. I apologize for the long message. (I apologize if the format is bad, I did a copy paste.)
*******************************
The basic principle of the formula is simple. In order to win, you will need the highest percentage of possible points in your competition. In the NFBC, you will need approximately 84.3% of all available points in order to win. To look at a specific year, we will see more detail.
Last year, the champion, David DiDonato had 85.7% of all available points, the runner up had 79.1% of all available points. To be practical, David would have won with 79.2% of all available points. In 2006, there were 330 teams which means the most points available would be 3,000 (300 points * 10 categories). 79.2% of 3,300 equals 2613. If you break that down into each category, you need 261.5 points from each category. (Sure, you can get more in one and less in another, but I think you see the point.) In 2006, here is the total you would need in each category to have 261.5 points for that category.
Avg - .2843 Run – 1,152 HR – 293 RBI – 1,116 SB – 161
ERA – 4.087 Wins – 103 K – 1,185 Whip – 1.313 SV – 86
(Note, these totals won’t win every year, but they would have in 2006. You should also note the roughly 84.3% of all available points needed will be approximately, but not exactly the same as these totals each year. If that doesn’t make sense, yes, there will be more teams, but with 15 teams in each league, 295 HR will be give you close to 83% of all HR points available. The same will be true in each category. Set your target at about 104 wins to reach 83-85% of all available points. Adding more teams will raise how many points 83% of a category’s available point total, for example, 83% of 300 is 249. 83% of 330 is 274.
If you knew ahead of time what would be needed in each category to win would it affect your draft? Using the numbers above, which are now below:
Avg - .2843 Run – 1,152 HR – 293 RBI – 1,116 SB – 161
ERA – 4.087 Wins – 103 K – 1,185 Whip – 1.313 SV – 86
Each owner will have a target for each category. (For 2007, you can calculate the needed category total at the 83.4% level and find the average. Saves has already been done: 88, 98 and 97 leaves an average of 94.) I provide the rest for each category at the bottom for those interested, but for the example, we will look at last year’s totals.
Players will fall into two categories, pitchers or hitters. Each player can help you in a maximum of 5 categories. Some will help in less, but none will help in more.
Finding the percentage each player provides you towards reaching the target for each category if then broken down into a computable formula. Some categories are easy to find, while others, AVG, WHIP and ERA are a little more detailed because the totals a player provides don’t add to a total, like the other categories. We’ll look at the other categories first. Below the target for each category, you will see a percentage. Each time you add one additional stat for it’s particular target, you are that much closer to the total target. For example, each save is 1.16% of the total you need to get to 86 saves. So, if you have a pitcher who gets 40 saves, those 40 saves will be 46.4% of the total needed towards the saves target. Each run makes up .087% of the target total of 1,152. If you have a hitter who scores 95 runs, he will provide 8.265% of the target total.
Run – 1,152 = 0.087%/per run (towards target total)
HR – 293 0.341%/per HR (towards target total)
RBI – 1,116 0.090%/per run (towards target total)
SB – 161 0.621%/per SB (towards target total)
Wins – 103 = 0.97%/Win (towards target total)
K – 1,185 = 0.084%/K (towards target total)
SV – 86 = 1.16%/SV (towards target total)
You can calculate the total percentage points each player provides for each of the categories, based on your projections. The other 3 categories also have a percentage that a player provides towards getting to the target total. Since the categories are weighted by innings pitched, earned runs, at bats, hits, etc, you must take into account the different weights each player provides.
This is where things can get somewhat tricky, but you need to take a look at the expected at bats and innings pitched a team will provide. The research I have done indicates that an average team will compile 7,413 at bats during the season. In order to achieve a team batting average of .2843, you will need 2,108 hits in those 7,413 at bats. Your pitching staff will have a wider range, depending on your starters to relievers ratio. Your team’s pitchers will average about 1,463 innings. (Again that will change depending on your starters and relievers, but for this example, we will stay with 1,463 IP.) With these baselines, you will be able to weight the numbers both hitters and pitchers will carry based on their AB total and IP total.
To calculate the impact of a pitchers ERA, you need to get the projection for your pitcher. We’ll use a pitcher who pitches 200 innings and an ERA of 2.65. Remember, we are looking for an ERA of 4.087.
Find out the earned run total a pitcher with an ERA of 4.087 and 200IP would have. (200*4.087)/9 = 90.8 runs
Find the earned run total a pitcher with an ERA of 2.65 and 200IP would have. (200*2.65)/9 = 58.9 runs
Determine the difference between the two totals. 90.8 – 58.9 = 31.9
Divide the difference by the average performer’s earned run total to find the percentage earned runs saved. (31.9/90.8 = .351 or 35.1%)
Calculate the percentage of total expected IP this pitcher has provided. (200/1463=13.67%).
200 IP is 13.67% of all IP your team will have.
Take this percentage and divide into 100. (100/13.67=7.315)
Take the total from step 6 and divide it into the percentage from step 4. (7.315/35.1= 4.799)
4.799 is this pitchers ERA point total. It does not mean this pitcher will gain you 4.799 points in that category. It is a total based on the calculation. (All of these totals are referred to as total value points, whether they are a calculation total or an actual percentage. You will be using these total value points later to calculate each players contribution to a category.)
Calculate the total for each pitcher.
Whip is another weighted category. You will also be using a set of steps to come to a Whip category total, as you did with ERA. We’ll use the same 200 IP as our example and assume the pitcher has a whip of 1.05.
1. Find the difference between the target whip total and this pitcher’s whip. (1.313-1.05=.263)
2. Find the percentage difference between the target whip and the subtracted difference from step 1.
(.263/1.313=.2003 or 20.03).
3. Take the percentage from step 2 and multiply by the percentage of IP/100 this pitcher provides.
(Calculated in ERA step 5 above) (20.03*(13.67/100))=2.738
4. This is your Whip Calculation Total.
The last category that we need to calculate a point total for is batting average. We are looking for an average of .2843 We’ll assume we have a hitter with 650 at bats and a .2815 avg.
1. Take the batter’s projected average and subtract it from the Target average and divide by the target avg and multiply this total by 100. (Make sure you place the projected hitter’s avg FIRST, then subtract the target avg. If the projected avg is less than the target, you will have a negative number.) (.2815-.2843)/.2843 *100= -.985)
2. Find the percentage of total at bats this hitter will provide. Leave in decimal form! (650/7,413=.088)
3. Multiply the total from step 1 and the total from step 2. (-.985*.088= -.087) Make sure you have a negative total if the projected average is below the target avg.
Ok, if you are still with me, you know how to get a total for each category scored as it relates to your target score, and is also weighted by the total number of at bats or innings pitched each player provides.
Calculate this total for each player you are doing projections for. After you have each player done, you should have 5 scores for hitters, one for each category, keeping in mind average can be negative. You will also have 5 categories for pitchers. (Starters will have a 0 under saves, so they contribute to 4 categories.)
In order to rank the players, you have to first compare their scored categories. For every hitter, you should have a total for avg, runs, hr, rbi and sb. (Runs, HR, rbi and sb will all be a percentage total, while avg is a calculation total.) Pitchers will have a total for era, wins, whip, K, sv. (Wins, K’s and Saves will be a percentage total; while ERA and Whip are a calculated point total.). Make sure all percentage totals all converted to decimals carried out to the third digit. For example, if a pitcher has 43.2% of your target save total, the column this total is in should show .432. Each column, whether it’s a percentage or a calculation should be multiplied by .2. This is done to represent the 5 different categories a player can contribute to, giving each equal weight of 20%.
Sort the each column to find the highest total for each category. While this player cannot provide you with 100% of any of the stat targets needed, this player’s represents 100% of the highest total available that an individual player can contribute. Let’s take a look at an example of possible total value points for wins:
Player A = 2.106 Player B = 2.054 Player C = 1.136 Player D = 0.227
Granted, it’s a small sample, but you will get the idea from it. The player with the highest total of Total Value Points will be given a Percentage total for that category of 100. After finding the highest total for a category, you take the player’s total value points for the category and divide by the highest total value points for the category and then multiply by 100, just to change the decimal to a whole number. (This is the percentage the player can provide individually compared to the leader in that category.)
Player A (2.106/2.106=1*100=100)
Player B (2.054/2.106=.9753*100=97.53)
Player C (1.136/2.106=.5394*100=53.94)
Player D (.227/2.106=.1078*100=10.78)
You see a percentage total (without the percentage sign) that a player can contribute towards a target as compared to other players also contributing towards the target. The most points a player can have is 500. (They would have to have the highest Total Value Points in all 5 hitting categories.)
Once you have completed finding the percentage total for each category, you can add them all together. You may have pitchers and catchers on separate spreadsheets at this time, so that copying formulas was easier. You can now combine all totals to see who will provide the greatest impact towards reaching the totals needed to win the NFBC.
You can also compare the total value points amongst players at their positions to see a position scarcity total.
When I plugged in last years final stats, it has some surprising results.
Rank Player % Total
1 Santana Johan 400.272
2 Pujols Albert 344.156
3 Jeter Derek 330.433
4 Howard Ryan 322.291
5 HollidayMatt 307.675
6 Cabrera Miguel 305.023
7 Reyes Jose 304.494
8 GuerreroVladimi 300.593
9 CarpenterChris 298.512
10 Atkins Garrett 297.247
11 Webb Brandon 289.767
12 Dye Jermaine288.660
13 Berkman Lance 288.651
14 Utley Chase 288.106
15 Morneau Justin 281.673
16 Soriano Alfonso 280.788
17 Ortiz David 274.913
18 Lee Carlos 272.837
19 CrawfordCarl 272.528
20 Tejada Miguel 272.292
21 Suzuki Ichiro 271.703
22 Oswalt Roy 267.747
23 Wright David 267.090
24 HalladayRoy 265.129
25 Nathan Joe 257.989
[ February 15, 2007, 07:12 PM: Message edited by: poopy tooth ]
*******************************
The basic principle of the formula is simple. In order to win, you will need the highest percentage of possible points in your competition. In the NFBC, you will need approximately 84.3% of all available points in order to win. To look at a specific year, we will see more detail.
Last year, the champion, David DiDonato had 85.7% of all available points, the runner up had 79.1% of all available points. To be practical, David would have won with 79.2% of all available points. In 2006, there were 330 teams which means the most points available would be 3,000 (300 points * 10 categories). 79.2% of 3,300 equals 2613. If you break that down into each category, you need 261.5 points from each category. (Sure, you can get more in one and less in another, but I think you see the point.) In 2006, here is the total you would need in each category to have 261.5 points for that category.
Avg - .2843 Run – 1,152 HR – 293 RBI – 1,116 SB – 161
ERA – 4.087 Wins – 103 K – 1,185 Whip – 1.313 SV – 86
(Note, these totals won’t win every year, but they would have in 2006. You should also note the roughly 84.3% of all available points needed will be approximately, but not exactly the same as these totals each year. If that doesn’t make sense, yes, there will be more teams, but with 15 teams in each league, 295 HR will be give you close to 83% of all HR points available. The same will be true in each category. Set your target at about 104 wins to reach 83-85% of all available points. Adding more teams will raise how many points 83% of a category’s available point total, for example, 83% of 300 is 249. 83% of 330 is 274.
If you knew ahead of time what would be needed in each category to win would it affect your draft? Using the numbers above, which are now below:
Avg - .2843 Run – 1,152 HR – 293 RBI – 1,116 SB – 161
ERA – 4.087 Wins – 103 K – 1,185 Whip – 1.313 SV – 86
Each owner will have a target for each category. (For 2007, you can calculate the needed category total at the 83.4% level and find the average. Saves has already been done: 88, 98 and 97 leaves an average of 94.) I provide the rest for each category at the bottom for those interested, but for the example, we will look at last year’s totals.
Players will fall into two categories, pitchers or hitters. Each player can help you in a maximum of 5 categories. Some will help in less, but none will help in more.
Finding the percentage each player provides you towards reaching the target for each category if then broken down into a computable formula. Some categories are easy to find, while others, AVG, WHIP and ERA are a little more detailed because the totals a player provides don’t add to a total, like the other categories. We’ll look at the other categories first. Below the target for each category, you will see a percentage. Each time you add one additional stat for it’s particular target, you are that much closer to the total target. For example, each save is 1.16% of the total you need to get to 86 saves. So, if you have a pitcher who gets 40 saves, those 40 saves will be 46.4% of the total needed towards the saves target. Each run makes up .087% of the target total of 1,152. If you have a hitter who scores 95 runs, he will provide 8.265% of the target total.
Run – 1,152 = 0.087%/per run (towards target total)
HR – 293 0.341%/per HR (towards target total)
RBI – 1,116 0.090%/per run (towards target total)
SB – 161 0.621%/per SB (towards target total)
Wins – 103 = 0.97%/Win (towards target total)
K – 1,185 = 0.084%/K (towards target total)
SV – 86 = 1.16%/SV (towards target total)
You can calculate the total percentage points each player provides for each of the categories, based on your projections. The other 3 categories also have a percentage that a player provides towards getting to the target total. Since the categories are weighted by innings pitched, earned runs, at bats, hits, etc, you must take into account the different weights each player provides.
This is where things can get somewhat tricky, but you need to take a look at the expected at bats and innings pitched a team will provide. The research I have done indicates that an average team will compile 7,413 at bats during the season. In order to achieve a team batting average of .2843, you will need 2,108 hits in those 7,413 at bats. Your pitching staff will have a wider range, depending on your starters to relievers ratio. Your team’s pitchers will average about 1,463 innings. (Again that will change depending on your starters and relievers, but for this example, we will stay with 1,463 IP.) With these baselines, you will be able to weight the numbers both hitters and pitchers will carry based on their AB total and IP total.
To calculate the impact of a pitchers ERA, you need to get the projection for your pitcher. We’ll use a pitcher who pitches 200 innings and an ERA of 2.65. Remember, we are looking for an ERA of 4.087.
Find out the earned run total a pitcher with an ERA of 4.087 and 200IP would have. (200*4.087)/9 = 90.8 runs
Find the earned run total a pitcher with an ERA of 2.65 and 200IP would have. (200*2.65)/9 = 58.9 runs
Determine the difference between the two totals. 90.8 – 58.9 = 31.9
Divide the difference by the average performer’s earned run total to find the percentage earned runs saved. (31.9/90.8 = .351 or 35.1%)
Calculate the percentage of total expected IP this pitcher has provided. (200/1463=13.67%).
200 IP is 13.67% of all IP your team will have.
Take this percentage and divide into 100. (100/13.67=7.315)
Take the total from step 6 and divide it into the percentage from step 4. (7.315/35.1= 4.799)
4.799 is this pitchers ERA point total. It does not mean this pitcher will gain you 4.799 points in that category. It is a total based on the calculation. (All of these totals are referred to as total value points, whether they are a calculation total or an actual percentage. You will be using these total value points later to calculate each players contribution to a category.)
Calculate the total for each pitcher.
Whip is another weighted category. You will also be using a set of steps to come to a Whip category total, as you did with ERA. We’ll use the same 200 IP as our example and assume the pitcher has a whip of 1.05.
1. Find the difference between the target whip total and this pitcher’s whip. (1.313-1.05=.263)
2. Find the percentage difference between the target whip and the subtracted difference from step 1.
(.263/1.313=.2003 or 20.03).
3. Take the percentage from step 2 and multiply by the percentage of IP/100 this pitcher provides.
(Calculated in ERA step 5 above) (20.03*(13.67/100))=2.738
4. This is your Whip Calculation Total.
The last category that we need to calculate a point total for is batting average. We are looking for an average of .2843 We’ll assume we have a hitter with 650 at bats and a .2815 avg.
1. Take the batter’s projected average and subtract it from the Target average and divide by the target avg and multiply this total by 100. (Make sure you place the projected hitter’s avg FIRST, then subtract the target avg. If the projected avg is less than the target, you will have a negative number.) (.2815-.2843)/.2843 *100= -.985)
2. Find the percentage of total at bats this hitter will provide. Leave in decimal form! (650/7,413=.088)
3. Multiply the total from step 1 and the total from step 2. (-.985*.088= -.087) Make sure you have a negative total if the projected average is below the target avg.
Ok, if you are still with me, you know how to get a total for each category scored as it relates to your target score, and is also weighted by the total number of at bats or innings pitched each player provides.
Calculate this total for each player you are doing projections for. After you have each player done, you should have 5 scores for hitters, one for each category, keeping in mind average can be negative. You will also have 5 categories for pitchers. (Starters will have a 0 under saves, so they contribute to 4 categories.)
In order to rank the players, you have to first compare their scored categories. For every hitter, you should have a total for avg, runs, hr, rbi and sb. (Runs, HR, rbi and sb will all be a percentage total, while avg is a calculation total.) Pitchers will have a total for era, wins, whip, K, sv. (Wins, K’s and Saves will be a percentage total; while ERA and Whip are a calculated point total.). Make sure all percentage totals all converted to decimals carried out to the third digit. For example, if a pitcher has 43.2% of your target save total, the column this total is in should show .432. Each column, whether it’s a percentage or a calculation should be multiplied by .2. This is done to represent the 5 different categories a player can contribute to, giving each equal weight of 20%.
Sort the each column to find the highest total for each category. While this player cannot provide you with 100% of any of the stat targets needed, this player’s represents 100% of the highest total available that an individual player can contribute. Let’s take a look at an example of possible total value points for wins:
Player A = 2.106 Player B = 2.054 Player C = 1.136 Player D = 0.227
Granted, it’s a small sample, but you will get the idea from it. The player with the highest total of Total Value Points will be given a Percentage total for that category of 100. After finding the highest total for a category, you take the player’s total value points for the category and divide by the highest total value points for the category and then multiply by 100, just to change the decimal to a whole number. (This is the percentage the player can provide individually compared to the leader in that category.)
Player A (2.106/2.106=1*100=100)
Player B (2.054/2.106=.9753*100=97.53)
Player C (1.136/2.106=.5394*100=53.94)
Player D (.227/2.106=.1078*100=10.78)
You see a percentage total (without the percentage sign) that a player can contribute towards a target as compared to other players also contributing towards the target. The most points a player can have is 500. (They would have to have the highest Total Value Points in all 5 hitting categories.)
Once you have completed finding the percentage total for each category, you can add them all together. You may have pitchers and catchers on separate spreadsheets at this time, so that copying formulas was easier. You can now combine all totals to see who will provide the greatest impact towards reaching the totals needed to win the NFBC.
You can also compare the total value points amongst players at their positions to see a position scarcity total.
When I plugged in last years final stats, it has some surprising results.
Rank Player % Total
1 Santana Johan 400.272
2 Pujols Albert 344.156
3 Jeter Derek 330.433
4 Howard Ryan 322.291
5 HollidayMatt 307.675
6 Cabrera Miguel 305.023
7 Reyes Jose 304.494
8 GuerreroVladimi 300.593
9 CarpenterChris 298.512
10 Atkins Garrett 297.247
11 Webb Brandon 289.767
12 Dye Jermaine288.660
13 Berkman Lance 288.651
14 Utley Chase 288.106
15 Morneau Justin 281.673
16 Soriano Alfonso 280.788
17 Ortiz David 274.913
18 Lee Carlos 272.837
19 CrawfordCarl 272.528
20 Tejada Miguel 272.292
21 Suzuki Ichiro 271.703
22 Oswalt Roy 267.747
23 Wright David 267.090
24 HalladayRoy 265.129
25 Nathan Joe 257.989
[ February 15, 2007, 07:12 PM: Message edited by: poopy tooth ]
