How much value does a walk to Barry Bonds have?
by Cyril Morong
Pete Palmer gave the following events run values:
1B = .47
2B = .78
3B = 1.09
HR = 1.40
BB = .33
Out = .25 (this varies)
That is, the average single has a run value of .47. One potential problem in evaluating Barry Bonds is all the walks he gets, whether intentional, semiintentional or otherwise. Should they all get a value of .33 as they do in the linear weights system? Are his walks worth less because the Giant hitters behind him are below average? Does the increased chance of a double play reduce the value of these walks?
The first thing I looked at was the value of a walk in a high slugging percentage (SLG) vs. a low slugging percentage environment. I ran a regression in which team runs was the dependent variable and 1Bs, 2Bs, 3Bs, HRs, BBs, SBs, CSs, and outs were the dependent variables. The first regression in this case included the top 50 NL teams in SLG (average SLG .435) from 19802000 (excluding strike years). The value of a walk was .405 (the linear regression technique determines these values, so, holding all other events constant, a walk increases runs by .405). Then for the lowest 50 teams (.353 SLG), it was .267. When I did this for the top (.272 average AVG) and bottom (.244) 50 in batting average (AVG), the value of a walk was about .33 in each case. So a low AVG environment does not affect walk value.
It looks like going from a high AVG environment to a low one has no impact on the walk value. Going from a high SLG environment to a low one does, by about .14. I doubt that Bonds’s walks would fall this much here, since the Giants have had good team SLGs. Now a lot of that comes from Bonds, but without him they won’t fall to .353 (and he is still part of the environment, if you walk him you raise the chance you might have to face him later slightly).
So if the guys hitting behind Bonds are below average, there might be some diminishing of the value of a walk, but probably not much. But how have Giant hitters been hitting behind Bonds? I looked at how all the Giant hitters hit in each of the next two slots after Bonds for the years 200103. The numbers below include only what the hitters in question hit in the lineup slots behind Bonds, not what they might have hit in other slots.^{1} The Giant hitters easily exceeded the league averages for those seasons. So there is no reason here to think the value of a walk to Bonds is less than .33 based on this.
Year 
Giants AVG 
Giants SLG 
League AVG 
League SLG 
2001 
0.298 
0.507 
0.261 
0.425 
2002 
0.269 
0.440 
0.259 
0.410 
2003 
0.271 
0.426 
0.262 
0.417 
Now turning back to grounding into double plays. Below I show the rate at which the Giants after Bonds grounded into double plays (DPs/(AB+BB)). Then the league rate for each season as well. Considering that Bonds is on first base so much, it is surprising that these hitters’ DP rate is so close to the league average. So it appears that when Bonds walks, very little, if any, value is lost due to DPs.
Year 
Giants DP Rate 
League DP Rate 
2001 
0.014 
0.020 
2002 
0.029 
0.022 
2003 
0.026 
0.021 
Now, we also need to know how the two guys who bat behind Bonds hit with runners on base. Here are their collective AVG and SLG with Runners on Base (ROB).
Year 
Giants/ROB AVG 
Giants/ROB SLG 
2001 
0.280 
0.459 
2002 
0.320 
0.461 
2003 
0.288 
0.447 
So there is no problem here (In all of baseball, from 19912000, both AVG and SLG were .011 higher with (ROB) than with none onI compiled data from STATS, INC Player Profiles books). Now I don’t actually have how these guys hit with Bonds in particular on base and this is not weighted by how often they batted behind Bonds (in general, the guys with the most ROB atbats behind Bonds did well anyway). This is just based on their total atbats with ROB. But it would be very strange if they hit exceedingly well with other runners on base and just happened to not hit well when Bonds was on.
But there is one thing that seems contradictory. The rate at which Bonds scores runs (other than by HRs). I divided his runs minus HRs by the number of times he reached base (not including HRs). Then I did the same for the league. Bonds’ rate is lower.
Year 
League Rate 
Bonds' Rate 
2001 
0.322 
0.215 
2002 
0.307 
0.236 
2003 
0.318 
0.280 
Now if the guys behind Bonds hit well with ROB and don’t ground into an unusual number of double plays, why doesn’t Bonds score at the league rate? The league average for the three years is .316 while for Bonds it is .244. Bonds scores about 23% less often than the average player. I wondered if this was just normal for a middle of the order hitter. So I looked at this same rate for other NL hitters who batted predominantly 4^{th} (at least 3/4ths of the time, as Bonds did) in 2003. Here are their rates and the overall or composite rate for the group.
Player 
Rate 
C. Jones 
0.322 
Lowell 
0.275 
Nevin 
0.239 
Alou 
0.307 
Kent 
0.329 
Kearns 
0.233 
McGriff 
0.207 
Composite 
0.288 
Now the composite rate is very close to what Bonds had in 2003. Since I only included hitters who batted leadoff 3/4ths of the time, there are not more. So Bonds is not that unusual in 2003. But it is probably the case that his rate in 2001 and 2002 are still on the low side. So I looked at how all major league cleanup hitters hit for the two most recent years that Retrosheet has data. The rate in 1992 and 1993 were .290 and .300. Not too much higher than what Bonds had last year. But those were somewhat low scoring seasons. So I looked at 1987 (.314) and 1986 (.303). So again, Bonds’s rate in 2003 is fairly normal. But it was definitely low in 2001 and 2002. So maybe somehow his walks have less value than average.
There is more, however, to this than whether or not Bonds scores. Some of those walks advance runners, who may be more likely to score. With runners on 1^{st} and runners on 1^{st} and 2^{nd}, Bonds had 131 walks from 200103. That was about 25% of his walks. The major league average is about 18%.^{2} So when Bonds walks, he is more likely to push a runner or runners along the bases than other batters will when he walks. This would tend to make his walks a little more valuable than .33. Now I said above that Bonds scored only 77% as often as the average player when he gets on base. So there is no reason for his walks to be worth less than 77% of the value of a normal walk. But this lower scoring rate might be due to Bonds being slow this late in his career or conservative base running. And of course his walks move runners along more than average. But how much value does this have?
So I turned to a run expectancy table from Tangotiger.^{3} Here it is
RE 9902 
0 
1 
2 
Empty 
0.555 
0.297 
0.117 
1st 
0.953 
0.573 
0.251 
2nd 
1.189 
0.725 
0.344 
3rd 
1.482 
0.983 
0.387 
1st_2nd 
1.573 
0.971 
0.466 
1st_3rd 
1.904 
1.243 
0.538 
2nd_3rd 
2.052 
1.467 
0.634 
Loaded 
2.417 
1.650 
0.815 
This says that if you have a runner on 1^{st} and no outs you can expect to score .953 runs. But if you move from that to runners on 1^{st} and 2^{nd} the expected runs rises by about .6. So if Bonds gets a walk with a man on 1^{st}, this should raise run expectancy by .6. If all of Bonds’ walks were such, his walks would have a value of .6. Of course, they are not. He gets walked in all manner of situations. Each time the run expectancy rises by an amount that can be found in the table. So I took all of Bonds’s walks from the various base situations (none on, runners on 1^{st} and 2^{nd}, etc.) and looked at the table to see how much run expectancy increased. I then calculated a weighted average of the value of a walk to Bonds over the years 20013 based on how much it increased run expectancy (if, for example, a walk increased run expectancy by .5 and walks in those situations happened 10% of the time for Bonds, this contributed a value of .05see Appendix for complete details). I came up with .339, very close to the linear weights value of Pete Palmer.^{4} So it appears that his walk value is pretty normal (especially since the following hitters tend to hit at least as well as average). But what about intentional walks?
In the Big Bad Baseball Annual of 1999 Jim Furtado gives an intentional walk a value of .25 (p. 481other walks get a value of .34). In my own regressions, covering the years 19552000, I got about .233 (using data from the Lee Sinins Sabermetric Encyclopedia). About 31% of Bonds’s walks were intentional. A weighted average of his walk value using .24 for intentional walks and .33 for others leaves a value of about .302. Now many of his walks are probably “semiintentional.” But we can’t know for sure how many. The lower bound values of his walks has to be at least .25, probably much closer to .30. Since walks help determine onbase percentage which in turns determines OPS (OBP + SLG), and since a walk to Bonds has pretty close to the normal value, his OPS is still a very good representation of his value.
1. For 2001, I looked at slots 45. For 2002, slots 46 (since Bonds batted quite a bit in both slots 34; Bonds’s numbers for slot 4 are not included, of course). For 2003, I looked at slots 56.
2. From Tom Ruane, for the years 1982, 1983 and 1987 which is at
http://www.baseballthinkfactory.com/btf/scholars/ruane/articles/situational_hitting.htm
3. Sabermetrics 101: Run Expectancy Matrix, 19992002 Which is at
http://www.tangotiger.net/RE9902.html
4. The data on his walks comes from ESPN at
http://sports.espn.go.com/mlb/players/splits3?statsId=3918&type=batting
It does not give the breakdown of how many outs each situation occurred. For example, it just says he had 40 walks with runners on 1^{st} and 2^{nd}. The increase in run expectancy is different if you go from runners on 1^{st} and 2^{nd} to bases loaded depending on how many outs you have (you can see this in the table). I took the simple average in each case of the increase for no outs, one and two outs. Those 3 out situations all occur about onethird of the time. I don’t know if the out percentage varies depending on the base situation.
Back to Cyril Morong's Sabermetric Research
AppendixCalculating the value of a walk to Bonds
Using the values of the run expectancy table from above, here is the increase in expected runs from a walk. In the table below, 1 to 12 means going from having a man on 1^{st} to men on 1^{st} and 2^{nd}. If this change occurs, expected runs increase by .529 if there are no outs. 0 to 1 means going from none on to a man on 1^{st}. 13 to 123 means going from having runners on 1^{st} and 3^{rd} to having bases loaded.

Expected 
Run 
Increase 




Change 
0 Outs 
1 Out 
2 Outs 
AVG 
Walks 
% of total 
Value 
1 to 12 
0.529 
0.410 
0.136 
0.358 
91 
0.174 
0.062 
12 to 123 
0.935 
0.667 
0.428 
0.677 
40 
0.077 
0.052 
0 to 1 
0.398 
0.276 
0.134 
0.269 
210 
0.402 
0.108 
3 to 13 
0.951 
0.670 
0.287 
0.636 
33 
0.063 
0.040 
2 to 12 
0.384 
0.246 
0.122 
0.251 
95 
0.182 
0.046 
23 to 123 
0.365 
0.183 
0.181 
0.243 
32 
0.061 
0.015 
13 to 123 
0.513 
0.407 
0.277 
0.399 
21 
0.04 
0.016 
Sum 




522 

0.339 
The AVG column is the average of the three previous columns. So .358 is
the average of a walk with a man of 1^{st} (.526 + .410 + .136 = 1.075
and that divided by 3 = .358). I took
the average since each out situation comes up about 33% of the time. I don’t
know how many outs there were when Bonds got walks. The walk column just lists
how many walks Bonds got in each of those situations. So he got 91 walks when
there was a runner on 1^{st} only, 210 with none on. The next column
lists what share of the total walks (522) came in that situation. For instance,
17.4% of his walks came with a man on 1^{st}. This is the weight that
the walks from that situation get. The next column is simply the “% of total”
times the AVG column. So .174*.358 = .052. Adding each number from the last
column gets the walk value of .339.
ADDENDUM1
I posted the following to the SABR list on Aug. 27, 2004 to answer
a question:
“To try to answer Larry Grasso's question, I calculated OBP in the
following way
H + BB + HBP  IBB divided by AB +
BB + HBP  IBB
Then I recalculated OPS for the top 10 guys in the NL. Here
they are. Bonds is still ahead by alot. His OBP fell to just .515
B. Bonds, SF 1.318
T. Helton, Col 1.059
A. Pujols, StL 1.047
J. Edmonds, StL 1.043
A. Beltre, LA 1.038
S. Rolen, StL 1.013
J. Thome, Phi 1.007
J. Drew, Atl 1.003
L. Berkman, Hou 0.985
A. Dunn, Cin 0.971
I also
calculated batting runs using the Linear Weights values of 1B = .47, 2B = .78,
3B = 1.09, HR = 1.4, BB = .33 and outs = .25. I counted all walks the same,
intentional or not. HBP were counted as walks. The top 10 guys in OPS in the NL
come out as
B.
Bonds, SF 104.77
T.
Helton, Col 66.11
A.
Pujols, StL 62.8
L.
Berkman, Hou 56.83
J.
Edmonds, StL 56.24
A.
Beltre, LA 55.51
J.
Thome, Phi 54.52
S.
Rolen, StL 53.63
J.
Drew, Atl 51
A.
Dunn, Cin 49.5
Then I
made an IBB worth just .23 runs for everyone. This value was published in the
Big Bad Baseball Annual. Then we get
B.
Bonds, SF 95.37
T.
Helton, Col 64.61
A.
Pujols, StL 61.9
L.
Berkman, Hou 55.63
J.
Edmonds, StL 55.24
A.
Beltre, LA 55.11
S.
Rolen, StL 53.13
J.
Thome, Phi 52.22
J.
Drew, Atl 50.8
A.
Dunn, Cin 48.4
Then I
took into account that the chance for a GDP increases with a man on first. A
couple of weeks ago I determnined that the guys batting in the 2 slots behind
Bonds this year had hit into about 28 more GDPs than the normal rate
would have given (per PA). Let's say it is 30 now. Then let's say
that 15 of them came after regular walks and 15 came after IBBs. Then I
gave those 30 a run value of .25, since Bonds is out on the GDPs and reduced
his BBs and IBBs accordingly. The top 10 would be
B.
Bonds, SF 79.47
T. Helton, Col 64.61
A. Pujols, StL 61.9
L. Berkman, Hou 55.63
J. Edmonds, StL 55.24
A. Beltre, LA 55.11
S. Rolen, StL 53.13
J. Thome, Phi 52.22
J. Drew, Atl 50.8
A. Dunn, Cin 48.4
Now I
did not penalize any other hitter for this. And those GDPs are not really Bonds's
fault. I am just trying to see where this takes us. But Bonds is still way
ahead of everyone. No park adjustments either. My guess is that would only help
Bonds. Unless Bonds is having a horrible year fielding and Rolen is having an
incredible year fielding. Bonds is MVP. I don't see Pujols making up 18 runs
with defense. And Rolen would have to make up 26 runs fielding. Maybe Bonds is
a 10 in fielding runs (which is actually pretty bad for an LFer). Rolen would
still have to be +16. He has reached that 3 times in 7 years. He was 3 last
year.
All of
the assumptions are unlikely to be true at the same time. I think Bonds is the
MVP so far.”
ADDENDUM1
Have the Giants been scoring the expected number of runs in each of the past four years? The first thing I did was run a regression in which team runs per game was the dependent variable and team OPS was the independent variable. The regression equation for runs per game from 200104 is
R/G = 13.266*OPS – 5.29.
Using that to predict Giants’ runs per game in each of the last four years and then seeing how much above or below they are per 162 games, we get the following
2001: –67
2002: –49
2003: –23
2004: –1.5
So they were below expectations in all four years. (A regression without the Giants gave very similar results. I also checked using the simplest Runs Created formula and that shows the Giants falling even more runs short of expectations in each year). Now the last two years are not bad. But 20012 are pretty bad. The Giants scored fewer runs than expected, 67 and 49, respectively, in those two seasons. Now Bonds walked more in 2002 than 2001. So if all those walks to Bonds were holding them down, why did they only fall 49 runs short in 2002 instead of even more than 67 short, as they did the year before? Then this year, with a record number of walks and intentional walks to Bonds, they scored just about what we would expect. Here are his walk totals followed by his intentional walks for the last 4 years.
2001: 17735
2002: 19868
2003: 14861
2004: 232121
I tried a regression that was a little more sophisticated than one with just OPS. I had runs scored as a funtion of 1Bs, 2Bs, 3Bs, HRs, BBs (including HBP) and outs (ABH). The equation was:
Runs = 416 + .597*1B + .773*2B + .806*3B +1.55*HR +.26*BB .222*Outs
The .222 for outs seems high. In other regressions, I have gotten around .09 (which is close to what Jim Furtado has in the 1999 Big Bad Baseball Annual). I checked the data, which I got from ESPN’s site. It seems right. Here is how the Giants actual runs compared to that predicted by the above equation
2001: –63
2002: –46
2003: –28
2004: –9
That is the same pattern as I got from the OPS regession. The Giants generally scored fewer runs than expected. Then I broke down the walks into intentional and nonintentional. The regression equation was
Runs = 567 + .584*1B + .784*2B + .896*3B + 1.51*HR + .342*BB  .26*IBB  .26*Outs
Yes, I got a minus sign on IBBs. In other regressions, it has been positive. Jim Furtado gives IBBs a positive value. One regression I did was on all teams from 19552000 gave IBBs a value of +.23. A regression on all teams from 19972000 gave IBBs a value of .20. If I take the Giants out of the regression which covers 200104, the value of an IBB goes to .38 (it has a tvalue of –2.5 or so in both cases, so it might be statistically significant).
Are teams doing a better job of issuing IBBs the last four years? Does anyone know why this might be if it is true?
Here is how the Giants actual runs compared to that predicted by the last equation
2001: –36
2002: –9
2003: –3
2004: +50
Now, over the four years combined, the Giants scored about as many runs as expected, with only one year being far below expectations. And this is based on an equation that gives intentional walks as negative. Could this mean that the other teams have been giving Bonds intentional walks at the right times, keeping the Giants from scoring as many runs as we might normally expect?
Maybe. But the two years that came in really bad by the OPS regression and the regression with all walks lumped together are 2001 and 2002. In one of those years, 2001, Bonds walked 177 times. In 1923, Ruth walked 170 times and the Yankees scored 823 runs while Runs Created predicted 811 (from Total Baseball, 5^{th} edition). So a team can have a guy with a real high walk total and score the runs we expect. And don’t forget the Giants scored just about the number of runs expected this year while Bonds had an incredible total of 232 walks and 121 IBBs.
If anyone has the time and inclination, take a look at the data. Run the same regressions that I have. I don’t think I did anything wrong and I think the data is correct. I am surprised by the high negative value for batting outs and the negative value for IBBs. I wonder if somenone else will get the same regression results.
Cyril Morong