Monday, July 6, 2026

Last year Grok cited my research on Twitter (X)

Click here to see the thread.

Someone asked Grok: 

 

The reply was

 

The research Grok mentions is called And the Winning Number is…OPS!. Here is that article.

Well, okay, maybe it is not THE WINNING NUMBER, but it is a pretty good one. Here’s why.

Most of you probably know that OPS is on-base percentage (OBP) plus slugging percentage (SLG). OPS is highly correlated with winning. The correlation between team winning percentage OPS differential is .933. OPS differential is the difference between a team’s OPS and the OPS they allow their opponents. A perfect correlation is 1.00. The teams I looked at were from 2001-03 (data from ESPN).

The graph below illustrates the relationship.

 

As you can see, most teams are pretty close to the trend line. As your OPS differential rises, so does your winning percentage.

The correlation is often referred to as r. Another statistic is the r-squared, or square of the correlation. In this case it is .933*.933 or .87. This means that 87% of the difference in winning percentage across teams is explained by the OPS differential. How does this compare to other stats? The r-squared for batting average differential is .738, on-base percentage is .849 and slugging percentage is .786. So OPS tops them all in its ability to explain team winning percentage. This tells us that getting on base and hitting for power (and stopping your opponents from doing so) are very important in baseball.

One problem with OPS, however, is that it adds together two numbers that are highly correlated. In fact, the correlation between OBP and SLG here (only on the hitting side) is .806. So, I looked at an alternative measure. Branch Rickey developed it. It adds OBP plus .75*ISO (Isolated Power, which is slugging percentage minus batting average). The correlation between OBP and ISO was .643, not as high as it is for OBP & SLG. I then found the r-squared between winning percentage and the Rickey stat. It was .863. So again, a measure similar to OPS, which takes into account power hitting and getting on base, does a good job of explaining winning percentage.

Now it is possible that other factors, like stealing, affect a team’s OPS. This is not likely to be true. See “Other Factors” below.

The linear relationship between team winning percentage and OPS differential is 

Pct = .496 + 1.3*OPSDIFF 

Where OPSDIFF is each team’s OPS differential. This formula predicted about two-thirds of the teams to within 5 wins of their actual total. I then looked at which teams won more games than expected according to the formula. Five of the top ten on this list had less than .57 SBs per game, which was the major league average for the three years. I also looked at which teams won fewer games than expected according to the formula Four of the bottom ten had less than .57 SBs per game, almost the same. The top ten averaged .65 SBs per game while the bottom averaged .52. No big difference here. Perhaps some other reason explains why some teams won more than expected while others won less. It might be luck or it might be the bullpen.

            NOTE: THESE NEXT TWO PARAGRAPHS WERE ADDED ON JULY 10, 2005. I also looked at all teams from 1989-2002. The regression formula for that data set was 

Pct = .49996 + 1.26*OPSDIFF 

This is virtually the same as the regression for the 2001-03 period. Then I determined how many more (+) or fewer (-) games each team won for each season. Then all of those plusses and minuses were added up. The A’s won 45 more games than the formula predicted over the 14 year period. That is just a little over 3 a year. All but four of the 30 major league teams won within 2 games a year of what the formula predicted. Only one team was off by more than 4, the Red Sox, who won about 4.06 fewer games a year than predicted.

            If a team happens to win more games one year than expected, then next year they likely win fewer games. The Twins won 13.5 more games than expected in 1994, but won 1.9 FEWER the next (and just 4.6 more games more than predicted in 1993). So one could argue that a team wins more games than OPS would indicate because they play “small ball,” like stealing and moving the runners along through “productive outs.” But this is not likely to be true. If a team is supposedly good at moving runners along one year, it should do so the next. This is not happening. See also Productive Outs Are Not Productive.

            One last thing to remember here. I am basically saying that if you “out-OPS” your opponents, you will do very well. This could be done with better hitting, better pitching, better fielding or some combination of the three. But this analysis shows that comparing two players based on OPS is not a bad way to go. 

Other Factors

Take base stealing for example. If a man is on, this distracts the pitcher. Maybe he throws more fastballs and the batter can be ready for this. Or a hole opens up that makes it easier to get a hit. So some of the 87% I attributed to OPS might, in fact, actually come from another source. So I looked at how both good and bad stealing teams hit with a runner on first base only.

I looked at the top 10 teams in SBs from 1982-92 and the bottom ten. Then I determined how much their AVG, SLG, OBP and OPS differed between having a runner on 1st or no runners on at all. I determined the runner on first data by finding the difference between the runners on base and the runners in scoring position data (from Retrosheet).

The top ten teams in SBs had the following increases when there was a runner on first compared to no runners on (the average across the teams) 

AVG-.025
SLG-.030
OBP-.008
OPS-.038 

That is, with a runner on first, these teams had a .025 higher batting average than they did when there were no runners on base. Slugging went up .030, OBP .008 and OPS .038.

The bottom ten teams in SBs had the following increases 

AVG-.019
SLG-.028
OBP-.011
OPS-.039 

The top ten teams averaged about 240 SBs and the bottom around 40. The one difference that is big is the AVG difference (.025-.019=.006).  But in general, the best stealing teams had little additional benefit over what the worst stealing teams.

The best stealing teams had in the 900 range of ABs with a runner on first. The bottom in the 1100 range. This makes sense because the best steal and they won’t be on first as often. Also, who is most likely to be left on first base on those teams? The few guys who don’t steal, like Jack Clark (5 of the teams were Cards). But those bottom teams must have rarely had a good base stealer on, a lot less often than the best. I think if the runners bother the pitcher, we should see a bigger effect here. After all, we are comparing the best stealing teams to the worst.

The change in OPS for both teams is just about the same. I am still skeptical that having a good stealer on first helps a lot. Maybe the change in AVG is simply a result of the hole opened up at first. There is little change in SLG. Maybe the fast guy bothering the pitcher and making it easier for the hitter is not happening. 

Sources: Retrosheet and ESPN

Sunday, July 5, 2026

Hank Aaron's amazing combination of durability and hitting excellence (part 2)

In Hank Aaron's amazing combination of durability and hitting excellence from January of 2025, I showed that Aaron has the most seasons with at least a 140 OPS+ & 140+ games and the most seasons with at least 150+ games played and at least a 150 OPS+.

Here I look at how he was consistently in the top 10 of 8 different stats for 19 straight years. All data is from Baseball Reference.

The first table has his year by year numbers for the 8 different stats.

Red stats are when he led the league
Blue stats are when he ranked 2nd thru 5th
Green stats are when ranked 6th thru 10th
 
As you can see, he was among the leaders quite often. There will be some summary stats on this after the second table. 
 

Season

H

HR

BA

OBP

SLG

OPS

OPS+

TB

1955

189

27

0.314

0.366

0.540

0.906

141

325

1956

200

26

0.328

0.365

0.558

0.923

151

340

1957

198

44

0.322

0.378

0.600

0.978

166

369

1958

196

30

0.326

0.386

0.546

0.931

153

328

1959

223

39

0.355

0.401

0.636

1.037

183

400

1960

172

40

0.292

0.352

0.566

0.919

156

334

1961

197

34

0.327

0.381

0.594

0.974

163

358

1962

191

45

0.323

0.390

0.618

1.008

170

366

1963

201

44

0.319

0.391

0.586

0.977

179

370

1964

187

24

0.328

0.393

0.514

0.907

153

293

1965

181

32

0.318

0.379

0.560

0.938

161

319

1966

168

44

0.279

0.356

0.539

0.895

142

325

1967

184

39

0.307

0.369

0.573

0.943

168

344

1968

174

29

0.287

0.354

0.498

0.852

153

302

1969

164

44

0.300

0.396

0.607

1.003

177

332

1970

154

38

0.298

0.385

0.574

0.958

149

296

1971

162

47

0.327

0.410

0.669

1.079

194

331

1972

119

34

0.265

0.390

0.514

0.904

147

231

1973

118

40

0.301

0.402

0.643

1.045

177

252

 
This next table shows all the ranks he had in these stats with the same color code.
 

Season

H

HR

BA

OBP

SLG

OPS

OPS+

TB

1955

2

10

5

 

9

9

10

6

1956

1

 

1

 

3

5

3

1

1957

2

1

4

9

3

3

3

1

1958

3

5

4

6

3

4

3

3

1959

1

3

1

2

1

1

1

1

1960

6

2

 

 

2

5

4

1

1961

3

6

5

8

3

3

2

1

1962

6

2

5

5

2

2

2

3

1963

2

1

3

2

1

1

1

1

1964

8

9

3

3

8

6

6

 

1965

10

6

2

5

2

2

2

4

1966

 

1

 

 

6

8

8

4

1967

6

1

 

 

1

3

3

1

1968

10

5

 

 

4

5

5

2

1969

 

2

 

7

2

2

2

1

1970

 

5

 

 

7

6

6

 

1971

 

2

5

3

1

1

1

2

1972

 

4

 

4

5

5

7

 

1973

 

4

 

 

2

2

6

 

 
Aaron had a total of 124  top 10s out of a possible 152 (8*19 = 152). That is about 81.6% of what was possible.  Yes, if a hitter is good at HRs it will help his SLG and OPS. We could say this about a few other stats. But this is still very impressive.
 
He was in the top 10 of all 8 stats in 7 different years and he had 7 top 10s in 2 other years. He was never in fewer than 4 top 10s.
 
He was in the top 5 96 times. That is about 63.2%. He was in the top 5 in at least 1 stat every year and he was in the top 5 in at least 2 stats in 18 of the years.
 
Baseball Reference shows him as 2nd in SLG in 1973. He actually did not qualify for the batting title that year but if we give him an extra 37 ABs to get to 502 PAs without any additional hits, his SLG would still have been .587 and that would have been 2nd in the NL that year.
 
I show him with a 177 OPS+ in 1973 and I rank him 6th. I estimated his OPS+ assuming those additional 37 ABs with no hits and came up with 148. That would tie him for 6th with Ken Singleton. Maybe it would be 7th but I did not redo Singleton's OPS+ to additional decimal points to see who would be ahead. But 7th is still in the top 10.