Thursday, December 31, 2009

Was Ron Santo The Best Player In the National League From 1964-68?

The table below shows how many BFW (batting wins plus fielding wins from Pete Palmer, using the linear weights method) and how many Win Shares (WS), the Bill James stat, various players had in the NL during this period. The two lists are not necessarily the top 25 in either stat. I simply found all the players who had at least 1 season in the top 5 in BFW in these years and at least 1 season in the top 12 in WS, found their total for the 5 years and then ranked them. The BFW totals come from Retrosheet and the WS totals come from the electronic version of the book.

Santo completely dominates in BFW. The age number is given for players who are in the Hall of Fame and it is their age in 1964, with a June 30 cutoff. It may be cherry picking to make these comparisons since I am taking Santo's best 5 year period. But that is why I put the age of the other Hall of Famers in. Many of them were at an age where they could still be performing well. Also, below, I show the best 5 year periods for these other Hall of Famers (except Aaron and Mays) and Santo still does extremely well. I did not include Frank Robinson because he was traded to the AL prior to the 1966 season.

Santo is only 3rd in WS. But he only trails the leader, Mays, by 6. Santo had the following ranks in BFW in these years: 1, 2, 1, 1, 4. For WS, they were 3, 4, 4, 1, 10. Those ranks for both stats are only among position players. I guess not too many people noticed how well he did since his ranks in the MVP voting, among position players, were 8, 13, 9, 4, 17. Maybe he was hurt by the Cubs not winning any pennants.

I also tried to find the leaders in Wins Above Replacement (WAR) during those years from Sean Smith's site. Below are what are probably the top 5. I checked a few other players, but none of them came close to these five.

Mays 40.8
Santo 39.6
Clemente 35.5
Aaron 35.1
Allen 33.1

So only Willie Mays was better. Now the next table shows the best 5 year stretches for what I think are all of the Hall of Famers who played in the NL during these years, not counting Aaron and Mays. This is not limited to the 1964-68 years. It is the highest 5 consecutive years for each one of these players.

Santo is only topped in BFW by Joe Morgan. He is only tied for 3rd in WS. But that still means that he beats 6 Hall of Famers he played with and/or against. Three of them, Willie Stargell, Willie McCovey, and Lou Brock were elected in their first year of eligibility. Clemente would have had he not died and been elected right away under special circumstances.

Sunday, December 27, 2009

Ron Santo vs. Brooks Robinson And Hall Of Fame Voting

How these two players compare in various stats is summarized in the table below. Discussion follows the table.

Robinson was an overwhelming choice to make the Hall in his first year of eligibility while Santo got very little support (normally a player needs 5% to remain on the ballot but somehow Santo returned to the ballot in 1985 after the low vote in 1980, as shown on his Baseball Reference page). And then Santo never got higher than 43.1%.

The predicted 1st year % comes from my model of voting Estimating Hall Of Fame Vote Percentages For The 1980s. Santo was 16.4% below the prediction (20.3 - 3.9 = 16.4). Robinson was 17.4% above the prediction. As much as both of those predictions are off, they both still pretty much predict that Robinson would make it and Santo wouldn't. Since a player needs 75%to get in, Robinson is just about there (according to the model) and very few guys get to the 60% level without eventually making it. For Santo, very few players start out very low and eventually make it. He also got just 13.4% in 1985.

My model is based mainly on how many all-star games and gold gloves a player has gotten, plus MVP awards and milestones like 3000 hits. World Series performance matters, too. Robinson beat Santo in all-star games 18-8 and 15-5 in Gold Gloves. Santo never played in a World Series, while Robinson played in 4. So it is not a surprise that Robinson did so much better in the voting.

The stats WS, BFW and WAR are all composite stats that attempt to value players using all phases of the game. WS is Bill James stat. Robinson beats Santo by 32 here, but that is not alot, actually. James says that a season with 15 WS is an average season. So all that separates the two is a coupld of extra average seasons by Robinson. James says that 20 WS makes an all-star season while 30 is an MVP type season.

Robinson does beat Santo 10-8 in all-star seasons, but it is very close. Then Santo beats him very easily in MVP type seasons and 3 best straight seasons. So he definitely had a higher peak value than Robinson while coming very close to him in career value.

BFW is batting plus fielding wins from Pete Palmer and the data came from Retrosheet. Santo totally outclasses Robinson in both career value and peak value here.

WAR or Wins Above Replacement is from Sean Smith's site and the numbers in parantheses are their respective ranks among position players in career value. Robinson just barely wins the career fight but Santo is way ahead in peak value.

RCAA or runs created above average, which is park adjusted since it is from the Lee Sinins Complete Baseball Encyclopedia. Santo beats Robinson by a wide margin, but Santo's career ended at 34. Robinson played until he was 40. RCAA can be negative so if a player is still active at older ages his career RCAA can go down. But through age 34, to equalize things, Santo is still ahead 253-85. For Robinson to be better, he would have to be ahead in fielding runs by 168. Maybe he was, but that is alot. Then Santo also has a big edge in peak value.

Looking at PAs, we can see that Santo was able to come close to Robinson's career value while having about 2,400 fewer career PAs. It think the sabermetric evidence is in Santo's favor, yet he has gotten much less support. Perhaps my voting model explains the writers's preferences but Santo can still get in by the Veteran's Committee. I hope they look at him again.

Saturday, December 26, 2009

Mark Buehrle Earns Rare Honor For Baseball Player And Becomes A Crossover Star By Appearing On The Cover Of...

It wasn't AROD. Or Albert Pujols. Or Clemens, or Bonds, or Maddux or Pedro Martinez. For the first time in at least 20 years (and maybe the first time ever), a baseball player's picture appears on on the cover of the The World Almanac and Book of Facts. Buehrle not only pitched a perfect game, but he retired 45 straight batters over the course of a 3 games to set a new record.

This will no doubt lead to a huge jolt in his popularity and make him a mega-star. Endorsements and guest appearances will probably come pouring in. People magazine might be next. I checked the covers of past almanacs at and google images and could not find one with a picture of a baseball player on it. It looks like in recent years both Tiger Woods and Michael Phelps have made the cover. I hope scandal is not about to hit Mr. Buehrle anytime soon.

And Buehrle was not the only White Sox left-hander to appear on the cover. Click here to see the other guy. He is even more famous.

Monday, December 21, 2009

Estimating Hall Of Fame Vote Percentages For The 1980s

This is a follow up from on my last post and it is from a suggestion at Baseball Think Factory. You might have to read the previous post to understand this one.

I plugged the values from 1980-89 into the model. There were 115 guys who had their first year on the ballot. The 1990-2009 model (the one without Rose, McGwire and Puckett), predicted 101 of them within .10 of their actual total. So that was 87.8% of them. 89 were predicted to with .05 or 77.4% of them.

In the 1990-2009 group, 88.8% were predicted to within .10 and 74.3% were predicted to within .05. So the 1990-2009 model seems to predict the 1980-1989 results fairly well. The two predictions that are off the most are for Willie McCovey and Willie Stargell. McCovey got 81.4% while the model predicted 38.95, so he got 42.45% more than expected. The difference was even bigger for Stargell. He got 82.4% while the prediction was 23.3. So he got 59.1% more more. But then the next biggest positive differential was Bench who got 96.4% while the prediction said 69.3% for a difference of 27.1%. Then no one else had a positive differential of even 20% (next highest was 17.5%).

The biggest positive differential in the 1990-2009 study was Fisk, who got 35.6% more than expected. Then the next biggest one was about 23%.

Back to the 1980-1989 period, the biggest negative differential belongs to Aaron. The model said he should get 131% but he got "only" 97.8%, for a difference of -32.8%. That is not too much higher than the biggest negative differential from 1990-2009, which belongs to Fred Lynn, of -26.4. Lynn was the only guy to have -20 or bigger (well, bigger in absolute terms among the negative differentials). In the 1980-1989 period, only 2 more guys were -20 or more. I think Aaron's big negative differential is understandable. He scores high on everything or reached almost every milestone. Great world series performer, gold gloves, MVP, 500HR, 3000Hits, 10,000 PAs, etc. All those all-star games. I think some of the voters would give Aaron more than 100% if they could (or the equivalent of more than one vote). I bet most would say that there is alot bigger difference, say, between Aaron and Brooks Robinson, than the 97.8-92=5.8 difference shows. That implies Aaron was only 6.3% better. But I think most people would say it a bigger difference.

The equation for the 1990-2009 period without Rose, McGwire and Puckett was

PCT = -.0165 + .00077*(WSAS/1000) + .04659*(GGAS/1000) + .0475*MVP + .44741*3000HIT + .25953*500HR + .00267*ASSQ10 -.00103*GGSQ7 + .06416*500SB - .0092*(WSIMPSQ50/1000) + .09891*10000PA

Thursday, December 17, 2009

My Predictions For The Hall Of Fame Vote

I base my predictions on regression analysis of the voting from 1990-2009. I looked at voting in the first year of eligibility only. Here is the regression equation:

PCT = .04824*MVP + .45177*3000H + .16754*500HR + .00216*ASSQ10 - .00122*GGSQ7 + .04901*500SB
- .0119*WSIMPSQ50 + .09928*10000PA + .00112*WSAS + .06242*GGAS - .01282

I will explain what the variables mean below. The adjusted r-squared was .923. So 92.3% of the difference across players is explained by the equation. The standard error was .072. There were 181 players, all of those who came up for the first time from 1990-2009, except for Pete Rose. MVP is number of MVP awards won, 3000H is a dummy variable (1 if a player reached it, 0 otherwise). The 500HR is also a dummy variable as it is for 500SB and 10000PA (if you made it to 10,000 career plate appearances, you get a 1, 0 otherwise). I used all the voting data from 1990-2009.

What is ASSQ10? It is the square of the number of All-star games played in squared. But AS games played is maxed out at 10. The assumption here is that being an all-star has a positive exponential effect but only up to a point where no more games helps (I have a graph at a post last summer to help explain this-link below). The GGSQ7 is the same thing for Gold Gloves.

WSIMPSQ50 involves World Series play. First, WSIMP is World Series PAs times OPS. The idea here that the more you play in the World Series the more votes you would get, but by multiplying it by OPS, it also includes how well you played (or just hit). This gets maxed out at 50 and is squared, for the same reason as all-star games (yes, Reggie Jackson is first here and way ahead of everyone else at 141, with Dave Justice and Lonnie Smith tied for 2nd at 101).

The last two variables are interaction variables. GGAS is the gold glove variable multiplied by the all-star variable and WSAS is the world series variable times the all-star game variable. It looks strange that the coefficient values on GGSQ7 and WSIMPSQ50 are negative. But you might notice that they are positive on the interactive variables. I think this is like when a regression uses both X and X-squared in a regression if the phenomena is non-linear (an inverted parabola, for example). The coefficient on X ends up being positive while the x-squared coefficient is negative. The reason I put in these interactive variables was to see if players who were strong in both got an extra boost, as if there was some synergy going on. It seems like they did get an extra boost. My results in terms of r-squared and the standard error are better than what I got without the interaction variables last summer (links below).

All of the variables were significant at the 10% level except for WSIMP, which came close with a p-value of .13. The other variables all had p-values of under .05 with 7 under .01. I also divided the following variables by 1000 since the regression at first gave them a very low coefficient (due to them being very large numbers): WSIMPSQ50, WSAS and GGAS. With WSIMP50 going as high as 50 (then squared to get 2500) and AS going as high as 10 (then squared to get 100), the interaction term could be 250,000. Since the dependent variable can only go from 0 to 100, the coefficient would be very low (even thought the variables were significant). So I divided these three variables by 1000 (my stat package was showing coefficient values of .00000 before I did this).

So, what percentages does this equation predict for the first time eligibles once I plug in their own values? The table below shows this.

Prediction1 is based on the above regression equation. I did another regression with the same variables but I took out Kirby Puckett and Mark McGwire. Puckett retired relatively early due to his eye problems and McGwire has the steroid scandal. Puckett got 82.1% of the vote in his first year of eligibility while the model predicts he would get 63.5%, for positive differential of 18.6%. McGwire got 23.5% of the vote his first time through while the model predicted him to get 40.3%, for a negative differential of -16.8%. Puckett had one of the biggest positive differentials while McGwire had one of the biggest on the negative side. I don't think any of the first-timers for 2010 are like Puckett or McGwire, so it might be reasonable to take them out. The predictions based on the model without those two guys is in the last column of the table above (and the standard error for that regression was .068). Things don't change much. But Alomar does slip below getting in. But that is still a high percentage and if he does not make it in the first time he probably will eventually.

I know that some predictions are negative. That is a drawback of this approach. The intercept is not terriblly negative (just -1.28%). So that is not a big problem. But GGSQ7 and WSIMPSQ50 do both have negative coefficients. So it is possible that a player might have gotten high scores there but if they could not get into any all-star games, those high scores would actually hurt them since the interaction variables would be zero and could not offset the negatives of the straight variables. But anyone with zero all-star games is probably not a Hall-of-Famer.

What Determines Vote Percentage In The First Year Of Hall Of Fame Eligibility? (Part 2)

What Determines Vote Percentage In The First Year Of Hall Of Fame Eligibility?

Saturday, December 12, 2009

Peak Value And Hall Of Fame Worthiness

In my last post, I discussed some eligible players who have not made it in yet who I believe have good sabermetric credentials. I mostly discussed their career rankings by various measures. Here I look at how those players ranked in their best 3-straight seasons by BFW.

Retrosheet has a link with each year called ML Players By Positions. It lists BFW or batting plus fielding wins, which comes from Pete Palmer's linear weights. I took all of that data from Retrosheet then tried to find the best 3-year periods in BFW. This link has the top 500. The Cons3 is their BFW over the 3-year period. The year is the last year in the period. So for Bonds it was 2001-3.

The table below has the highest ranked 3-year period for all the players I looked at in my last post. They are in order starting with the best. So Ron Santo's 1965-67 BFW of 21.1 is tied for the 24th best all-time and is the best among the group I have been looking at. Now Santo's 1964-66 is 37th best, but that is not listed here since it is his 2nd best 3-year period. Players with a * are eligible for the first time in 2010.

I found about 20,000 3-year periods. So anything in the top 200 is in the top 1%. I really don't know how high a player needs to rank here to be considered impressive. There are, of course, overlapping periods for players. So the greatest players often appear several times early on in the rankings. That can push many players down quite a bit. But consider this. The players on the list below are the only players ever to have a better 3-year period than Ron Santo.

Babe Ruth
Barry Bonds
Cal Ripken
Honus Wagner
Joe Morgan
Mickey Mantle
Nap Lajoie
Rogers Hornsby
Ted Williams

So these are the only guys Santo takes a back seat to. Just 9 players.

Three players, Grich, Bell and Dawson all had very good years in 1981, a strike-shortened season when only about 2/3 of the games were played. Here are their BFWs that year:

Andre Dawson 8.4 (T140)
Buddy Bell 5.2 (T69)
Dwight Evans 3.7 (1017)

If you increase each of those by 50%, and then re-calculate their 3-year totals, their ranks would change. Those are the numbers in parantheses. I don't know if that kind of adjustment needs to be done, but some guys might have just been having their best years ever in 1981. Maybe they get short changed (I think that Fred McGriff would have made 500 HRs and Harold Baines might have made 3000 hits without work stoppages and games lost).

One other thing about adjusting for lost time due to strikes. Mike Schmidt had a BFW of 7.2 in 1981. Increasing that to 10.8 would give him 24.2 from 1980-82. Then the only guys better than that are Ruth, Hornsby and Bonds.

I also checked to see how these guys did in Win Shares (WS) during their given 3-year periods. The next table shows this. The numbers in parantheses are their rank in that given year. The players in red were in the top 10 all three years. That seems pretty impressive.

The guys that really stick out are Santo, Dick Allen and Tim Raines. They each had 30+ WS in their years, a level Bill James says is MVP caliber. Raines was clearly the best in the NL for three years running (and I think he has more WS than anyone from the AL, too). Two guys from my last post that I was high on, Barry Larkin and Keith Hernandez just barely miss being in red. They each had two top 10 finishes and an 11th.

But the three guys who were in the top 200 BFW from the first table who also were in the top 10 all three years in WS are Santo, Bobby Grich and Darrell Evans. Both measures, WS and BFW, confirm their elite status for a 3-year period. And this is a very tough test to pass because a player might have had a very high 3-year period in WS that does not match up with their best 3-year BFW. But I required that.

Some additional observations: Roberto Alomar also had a 1st and a 5th in WS in 1992-3, plus a 3rd in 1996. Larkin had a 2nd in 1995. Dick Allen followed his 3-year run with a 7th and then a 4th. Then another number 1 in 1972 as the AL MVP. The players from the early 1900s like Jimmy Sheckard & Sherry Magee also had more pitchers in the top dozen or so than later players. Their ranks could be higher.

I also noticed some guys like Dwight Evans, Reggie Smith and Bill Dahlen who had many seasons well over 20 WS but few, if any, 30+ seasons. Bill James said that 20 is an all-star season. So these guys consistently exceeded that level but maybe really never stood out for very long.

Here are the other top 5 finishes in WS for the players discussed here (outside of their 3-year BFW period)

Magee-1, 3T, 5
Grich-2, 4T
Trammell-2T, 3T
DW Evans-3T
W. Clark-3
McGwire-3, 4, 5T

Now ALL of the top 5 finishes in BFW for this group of players.

Dahlen-1, 2, 2, 4
Leach-3, 3
Magee-3, 3, 4
Sheckard-1, 1
Hack-2, 4, 5
Santo-1, 1, 1, 2, 4, 4
Allen-1, 2, 2, 4
DA Evans-2, 4, 4
Grich-1, 1, 2, 2, 3, 4, 4T
Bell-2, 3
Hernandez-2, 3
Trammell-2, 4,
Raines-2, 3, 3, 4
Larkin-1, 4, 4, 4, 4
W. Clark-2
Martinez-1, 2, 3, 4, 4
McGwire-1, 4, 4
Alomar-1, 1, 3

In some cases my accounting may not be clear. Santo had 3 top 5 finishes in WS and 6 in BFW. Dick Allen had 5 & 4. Grich has 3 & 7. Raines had 4 & 4. Alomar had 5 & 3. McGwire had 4 & 3. Magee had 4 & 3. I think these are all the guys that had at least 3 seasons in the top 5 in both WS and BFW. Seems like they were often among the best playes in their league. Add that to their career values established in the last post, and we have good cases for the Hall of Fame.

Wednesday, December 9, 2009

Some Players With A Good Sabermetric Case For The Hall Of Fame

To come up with this list, I looked for players who were:

1. in the top 150 in wins above replacement (WARP) from Sean Smith's site
2. in the top 120 in MVP win shares as listed at baseball reference
3. in the top 200 in career Win Shares from Bill James' book
4. in the top 150 in batting plus fielding wins or BFW (from Pete Palmer and the Baseball Encyclopedia)

For fans unfamilar with some of these terms, I attempt to explain them at the end of this post. I went with the top 120 for MVP shares because there were not many MVP awards given out before 1931. I went with the top 200 in Win Shares (WS) because about 40 of them are pitchers (through 2001). Some players had some WS after that and their totals were adjusted slightly but I still used the ranks through 2001. I also have only looked at players who are eligible. Pete Rose and Joe Jackson are not included.

The table below shows all the players I could find who fit at least 3 of the 4 criteria (plus the last two guys Tommy Leach & Jimmy Sheckard because they just missed making criteria #1 and did extremely well in WS). You can click on the table to see a larger version. Alomar has a career WARP of 63.6 at Sean Smith's site, ranking him 85th all-time. According to Baseball Reference, he had 1.91 MVP shares, ranking him 98th. He had 375 WS ranking him 53rd. He had 35.8 BFW, ranking him 79th.

The first three players met all 4 criteria. So Alomar will be an interesting case. McGwire has the PED scandal. But Hernandez is surprising. He ranks so highly by different measures including MVP voting. So the voters saw something in him all those years while he was compiling a stellar sabermetric resume. Anyone have an explanation for why he is not in? I think all of the guys who meet 3 or 4 of the criteria deserve serious consideration. The players with a * will be eligible for the first time in this current vote. MVP stands for MVP shares. This list is not meant to be complete-only to show players who pass some major hurdles.

Dick Allen just misses making the top 120 in MVP shares. If he had made that, he would meet all 4 criteria. Andre Dawson looks very good except for his low BFW rating. The only place where Bobby Grich falls down is in MVP shares. Sherry Magee meets 3 of the criteria. The only one missing is MVP shares and they had very little of that in his day. We can say the same thing for Bill Dahlen, whose rankings are very high. Perhaps the most astounding MVP share is for Willie Randolph, .004, for a rank of 1157th yet his rankings in the sabermetric stats are great.

Now alot of career value is all well and good. But what about peak performance? (I tried to bring that in with the MVP shares). The table below shows how many seasons these guys had with 20+ WS, 25+ WS and 30+ WS. Bill James said that 20 WS is an all-star type season while 30 is an MVP type season. So I assume that 25 is an all-star/MVP type season.

I guess everyone will have to judge for themselves if any of these guys had enough all-star or MVP type seasons. But 10 or more all-star type seasons sounds pretty impressive. That helps Hernandez. 10 all-star seasons with his other high ranks should put him in. The following players all had 4 or 5 seasons with 30+ WS

Roberto Alomar*
Dick Allen
Bobby Bonds
Tim Raines
Ron Santo
Jimmy Wynn

Tim Raines should be in. It is a no brainer.

In one way this might not be fair. Players before 1961 or 1962 only played 154 games, so that can knock your WS down 5% (then there were 1900-1903, and 1917-1918 when they played less than 154 games). Then there are strike years. Andre Dawson had 25 WS in 1981. If you play the full season, maybe he gets 37. But I made no adjustment on this account.

I also used BFW to find peak seasons. The table below shows how many seasons each player had a BFW of 2+, 3+, 4+,and 5+. I think a 2+ season is starting to put you into all-star territory while 5+ is MVP territory. This list is in alphabetical order. To see how the table works, look at Dick Allen. He had 10 seasons with 2+ BFW. That ties him for 41st all-time in such seasons (this was through 2005). He had 3 seasons with a BFW of 5+, good for a tie for 33rd.

Many of these players rank very highly here. Look at Bobby Grich. He is tied for 16th in BFW5 seasons. Think about that. Only 15 players ever had more of these kinds of seasons than he did. I think many of these players do well here, showing that they achieved a very high peak value, not just a high career value. Blank spaces means they ranked too low to be worth mentioning. The next table might explain this. I think anyone who had 2 or more BFW5 seasons who also has high career total ranks should be in because only 91 players make this cut.

In many cases, as you might guess, there are many players tied for a certain position. The table above shows how many times each case occurred. For example, there was one player who had 19 seasons with a 2+ in BFW (I think it was Hank Aaron). There is a total of 194 players who had 6+ seasons in BFW2. For BFW5, only 91 players had 2 or more such seasons. If a player in the previous table has a blank, it means that he did not make the minimum number of occurrences in a given case. Norm Cash is blank for BFW3, meaning had fewer than 4 such seasons. Dick Allen is tied with 17 other guys for 41st place in BFW2.

WARP-the idea here is how many more games your team wins with player A as opposed to the next best thing, an easily available or nearly free replacement player. If WARP = 4, then your team won 4 more games with player A than with a replacement. Sean Smith includes hitting, fielding and baserunning in this rating.

Win Shares also includes all phases of the game in its rating. Bill James takes team wins and multiplies it by 3. Then he divides up those WS among the players and pitchers.

BFW rates players compared to the average. So it is like WARP except 0 is average. Usually WARP is -2. BFW also takes all phases of the game into account.

MVP shares-This is a Bill James idea. Players get points in the voting: 14 for a 1st place vote, 9 for a 2nd, 8 for a 3rd. So if there are maximum of 392 points, and a player got 196, he gets a .5 share. If he got 392 points, he gets a 1. Then you add up all those shares from each season to get a career total.

Wednesday, December 2, 2009

Who Was More "Magical" Than Greg Maddux? (Or Pitcher's HR/BB/SO Rating)

Greg Maddux was great at preventing HRs and great at not walking batters. It must be tough for a pitcher to achieve that combination because you are putting the ball in strike zone alot where the batters can hit it. To rate pitchers on this combination, I used data from the Lee Sinins Complete Baseball Encyclopedia which tells us how much better or worse than the league average a pitcher was in various stats.

Maddux, for example, gave up 49% fewer HRs than the league average (what the 1.49 means in the graph below) while walking 86% fewer batters. My HRBB rating multiplies these two numbers together. The table below shows the top 25 among pitchers with 2000+ IP from 1946-2009. Maddux has a pretty clear edge over the competition.

But then I realized that Maddux was not a great strikeout pitcher. He was not preventing batters from hitting HRs by overpowering them. I decided to then multiply each pitcher's HR rate, BB rate and SO rate. But first, I inverted the rate of strikeouts. Maddux struck out 94% as many batters as the average pitcher. Being below average in strikeouts increases the difficulty in achieving a high HRBB rate because there is a positive correlation between not allowing HRs and striking batters out (about .15). So for Maddux, 1/.94 = 1.06, indicating that he was 6% worse at striking out batters than average. So his HRBBSO rating would be 1.49*1.86*1.06 = 2.95.

But notice in the table that he finishes 2nd behind Lew Burdette, who somehow managed to give up 7 fewer HRs than average and walk 76% fewer batters while striking out 61% fewer batters. Pitching the bulk of his career for the Braves in County stadium may have helped. The simple average of the HR park factors from 1952-1962 (which includes the last year the Braves played in Boston) has Burdette with a 75. So he pitched in parks that only allowed about 75% as many HRs as average. For Maddux, from 1987-2003, his parks allowed about 109% of the league average (HR park factors from various Bill James books).

I tried to adjust for this (for these two guys). Assuming that a pitcher pitches half his innings at home, and that he allowed 7% fewer HRs than average (for a rate of 1.07) and that his park has a 75 rating, I thought it best to multiply the 1.07 by .875 (which is half way between 1 and .75). That left Burdette with a HR rate of .936 (which now means he allowed 6.4% more HRs than average). For Maddux, I multipled his 1.49 by 1.045 (half way between 1 and 1.09). That gives him an adjusted HR rate of 1.56. Then recalculating the HRBBSO rate, Burdette ends up with 2.66 while Maddux ends up with 3.09.