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No Biggie

September 26, 2021
                                                          No Biggie


I did a little bit of research here, nothing significant; I did this last week and I keep forgetting to write it up and keep forgetting to post it, so I’m going to post it here late on Sunday night, because this is when I am thinking about it.  


          Suppose that all that you know about a team is the percentage margin between their best player and their second-best player.  This is measured by Win Shares.  If the best player on a team is 20% better than the second-best player, that could be 18 and 15, or 24 and 20, or 30 and 25, or 36 and 30, or 42 and 35; we don’t know.   All that we know is that the best player on the team has 20% more Win Shares than the second-best player on the team—or 10% more, or 7% more, or whatever that number is. 

          The issue here is, are you better off if that margin is SMALL, or if that margin is large?  That’s all I’m asking you here.  Are you better off with two good players of roughly the same quality, or with one player who is far better than anybody else on the team?


          I know the answer to that question.  I didn’t know it 10 days ago, but I know it now, and I’m asking you to guess—or rather, I am asking you to figure it out.  Reason it out, and give me your reasons, or just make a wild-ass guess, and give me your wild-ass guess; I don’t care.   I’ll give you the answer tomorrow night.  No, wait a minute; I’ve got something to do tomorrow evening; I’ll give you the answer some time tomorrow.   Thanks.  


COMMENTS (40 Comments, most recent shown first)

I just realized that Bill had already provided his answer below. I gave mine without reading the rest because I wanted it to be my intuition and didn’t want to steal ideas I read on the way. So the fact that I was influenced by the Angels was purely coincidental.
11:10 PM Sep 28th
I’m going to use a one team sample. I’m guessing the Angels have have a pretty big gap from number one to number two over the last few years. So I’m guessing you don’t want a big gap.

My other intuition comes from the fact that offense is a matter of sequences. It takes a few good players to consistently mount rallies and score runs.

If this was the NBA I would guess a big gap, because one player can carry a huge load. But Ozzie Smith can’t field every batted ball. Babe Ruth has to wait through 8 other hitters for his turn. Max Scherzer only takes the ball every fifth day.

You want deep talent, not one standout.
6:08 PM Sep 28th
Ah! I get it now, thanks. . . So the teams with the wider differences between no. 1 & no. 2 players not only have an advantage of having a typically better no. 1 player, but the disadvantage of having a typically worse no. 2 player. Even though the standard deviation of no. 1s is probably greater (which is why I mistakenly thought those teams would be on the average better), the impact of having a worse no. 2 is greater because it means no one else is as good as that inferior no. 2. The differences among no. 1s has no impact on the quality of the rest of the team.
1:10 PM Sep 28th
The "ceiling" I was referring to, we were referring to, is just a mathematical construct. If the two best players on your team have 25 Win Shares each, then other players on the team MAY be as high as 25, or at least 24. But if your two best players are at 30 and 20, then no one else on the team can be higher than 20. That's all we meant by that.
10:45 AM Sep 28th
I think the #2 sets a ceiling if the difference is very large (the only huge negative was when the best was 75%+ better) because outside of a few truly amazing seasons, there's a limit on how good the best player is, because nobody hits close to .500, nobody hits close to 90 home runs, nobody walks close to 200 times.

Still if it were common for a team to have a Babe Ruth, the 75% difference wouldn't be as awful, but few teams have a Babe Ruth.

A more usual "best player," if he's so much better that no one is within 75% of him, it means the doesn't have any other stars.

If Bill feels like it, maybe he can post what an average "best player" would be, the mean or median of Win Shares posted by the best player on a team, and then post some players that typically performed at that level. Then...imagine you have a guy like that and your nest best guy isn't within 75%. it would be obvious you'd have a crappy team then.

The key is that a huge difference says more about the (lack of) quality of the rest of the team than about the greatness of the best player. I'm not sure if I'd have figured it out if I'd read it before the answer was posted; but given the answer that seems to be the explanation.
5:45 AM Sep 28th
How does the no. 2 player set a ceiling? I think there are many possible explanations.

The most plausible to me is that a team with one outstanding player is probably a team in the building phase or deeply in the decline phase.

Once a team gets an outstanding player, then they start signing players to build around him and keep the budding stars they have. As the team improves obviously some of those players will get nearly as good as the star, if not better - and the star will more often then not decline some. A good team will have several really good players. Once they decline, the team will trade or let the pricey free agent go and all they have left is either their youngest star or an untradeable star.

Conjecture, I know. I still think there might be some psychological disadvantage to having one star, too, but a low ceiling no. 2: why?
12:01 AM Sep 28th
I think it's nice that the membership generally found a balanced and correct answer. Strictly speaking, there was a split between large and small gaps. But almost everyone qualified their answers by considering the possible contexts.

11:24 PM Sep 27th
No real idea, but my guess is that it might depend at least as much on the #3 through #9 (or more) as on the difference between #1 and #2. Anyway...Suppose the #1 player has 20 WS and WS fall by 20% as we move down the roster--#2, 16; #3, 12.8, and so on. The top 9 players would have a total of 86.6 WS. If we start at 20 and decrease by 10%, it's 20, 18, 16.2, and so on, with the top 9 amassing 122.5 WS.

It is obvious that, for a given "best" player WS, a smaller drop-off means the sum of #1 and #2 has to be larger than if the drop-off is larger.

But what if we did it in the opposite direction. Start with a #9 player with (say) 3 WS, with a 20% increase, compared with a team with a "worst" player with 5 WS and a 10% increase. Then, the team with the faster "growth" has a larger overall WS, 104 to 68. And that's with a a lower starting point (3, compared with 5) but with a faster rate of increase (20% compared with 10%)

My conclusion is that there's no definitive depends on how you frame the gaps.
11:21 PM Sep 27th
Thanks for the response, Bill.

It was fun that we didn't have a consensus, either in the result or in the reasoning, and then be able to read your answer.
8:03 PM Sep 27th
Bill James here.

I appreciate all of your feedback. The answer is that it makes no difference as long as the difference between your two best players is relatively small, but if the difference is large, then you are significantly better off if the margin between the two is small. Teams which have one player who is 50% better than any other player on the team are NOT successful teams.

I studied this with regard to the California Angels, who have been a one-superstar team for a long time now, but there are many counter-examples, of course. On the 2018 Astros Alex Bregman was 56% more valuable than anyone else on the team (36-23 Win Shares), but the team won 103 games. On the 1962 Giants, Willie Mays was 58% better than anyone else on the team (41-26), but they also won 103 games. On the 2003 Giants, Barry Bonds was 63% better than anyone else on the team (38-24), but they won 100 games. On the 1993 Giants, Bonds was 68% better than anyone else on the team (47-28), but they won 103 games. And there are dozens and dozens of teams that won 95 or more games with one player who was far better than anyone else on the team.

But overall. . . . In my data there are 66 teams on which one player earned 75% more Win Shares than any other player. Their average won-lost record was 73-87. There were 122 teams on which the best player earned 50 to 75% more Win Shares than any other player. Their average record was 78-80.

On the other end, there were 452 teams on which the best player was 10% better than the next-best player, or less. Those teams had an average record of 80-78. Groups 10-25% and 25-50% were also very slightly over .500.

The outlier was "tied". There were 170 teams in the data for which there was a tie for the Team Leadership in Win Shares, and those teams had an average won-lost record of 78-80. The reason for the tie is, it is a lot easier to get a flat-footed tie at a smaller number. As the numbers get larger, the mathematical probability of a tie decreases. You're more likely to get a tie for the league leadership in home runs than in RBI, just because the numbers are larger. You'll rarely get a tie for the league leadership in hits or strikeouts, because the numbers are big, whereas you probably get a tie in Triples maybe half the time, because the numbers are small.

THere are all kinds of different value patterns on teams, and no one value pattern dominates. But the best explanation is the one offered by the second or third reader who posted; sorry I forget your name. The #2 player on the team sets the ceiling for the rest of the team. If the ceiling is low, the total has to be low. That's really what explains the data.

That, and them damned California Angels.

6:11 PM Sep 27th
I will vote for close, but the Yankees in the late 50s and early 60s had Mantle with a lot better than all his teammates except Yogi Berra.
6:06 PM Sep 27th
Typo report: Gehrig was 220 in 1927, not 120.

5:11 PM Sep 27th
I'm going to go with "small gap".

baseball-reference doesn't show Win Shares (that I could see) so I reasoned from OPS+ & picked a couple of extreme cases, the 1933 Phillies and the 1927 Yankees.

1933 Phillies: Best OPS+: Chuck Klein, 176. Second best: Spud Davis, 135 (Wes Schulmerich also had 135, but Davis's other stats looked more valuable than Schulmerich's).
Team: 60-92, 7th place.

1927 Yankees: Best OPS+: Babe Ruth, 225. Second best: Lou Gehrig, 120.
Team: 110/44/1, 1st place.

This is assuming that Win Shares and OPS+ are roughly aligned in their assesment of player value.
5:09 PM Sep 27th
I'm going to guess the imbalanced teams do better, for the simple reason that a true superstar is almost always going to be 20% higher than anyone else on his team. Even on a team as strong top-to-bottom as the Big Red Machine, I suspect that Joe Morgan's 40 Win Shares a year were 20% higher than anyone else's.
5:03 PM Sep 27th
Of course, I thought of a better way to explain my point soon after I posted.

The answer will depend on which teams are being studied. Bill said that the balanced team had two good players but did not say the imbalanced team had two good players. I took this to mean the criteria included a requirement like the top-two players on the team having at least 30 win shares between them. The top player on an imbalanced team might have 30 win shares with the #2 player having zero. This would be a historically bad team with only ten wins. The top two players on a balanced team might have 15 win shares each. This is probably not a good team, but it has at least ten wins and likely has more as other players probably contributed as well.

On the other hand, the criteria could instead include a requirement like each of the top-two players having at least 15 win shares. Then it is possible for the imbalanced team to have one player with 60 win shares and the #2 player with 15 win shares versus the balanced team still having the top two players with 15 win shares each. In this scenario, the first team has at least 25 wins accounted for, whereas the second team still has only ten wins accounted for. Players #3-25 on each team have the same room to contribute further wins, so the first team is likely better.

In short, if two teams have the same number of win shares divided between the top two players, the balanced team is probably better. If the second-best player on each of two teams has the same number of win shares, then the imbalanced team is probably better.
3:44 PM Sep 27th
I'll sit in the two players with a small margin of difference camp. I expect most teams to have at least one "all star caliber" player, so a second player performing at nearly that level would be a good thing.
2:50 PM Sep 27th
I would guess the smaller margin because it may show a more balanced team. I would think teams like the 1969 Orioles and the 1929 Athletics would be in the balanced area. Of course I wonder about teams like the 1923 Yankees where Ruth seemed to be a million miles ahead of number two.
2:35 PM Sep 27th
gonna be boring and guess that a smaller margin between #1 and #2 is better

which would either be a pretty bad team, or a very deep team
1:02 PM Sep 27th
Let me add regarding my last paragraph on the importance of this find: important towards team building and winning, not in terms fun facts, etc. that you give us steadily.
12:34 PM Sep 27th
I feel like many people are implicitly answering the question "If your team has a given talent budget, is it better to have a large or small margin between your top two players?", but that's a very different question from "Which is likely to be better, a random season with a large margin or a random season with a small margin?".
12:31 PM Sep 27th
Interesting question - my initial thought was that teams with a superstar rely too much on that or those couple of obvious top dogs and tend to play worse as a team. Examples already provided by other readers. Don't forget the A-Rod/Griffey Jr. Mariners, although, that's two superstars - three counting Randy Johnson.

Perhaps, it is management's fault - they might get too complacent having the superstar on the team.

But then, many teams with superstars do perfectly well in the post season.

However, looking at it logically, the abilities of every team's no. 2 is going to be closer to each other in abillities than the no. 1 players - the far end of the bell curve. So, any team with a big advantage in the difference between the no. 1 and no. 2 players is more likely to have a superstar of greater magnitude. That's probably an overriding advantage to any psychological disadvantage. Baseball players are professionals after all. My guess is a larger difference is an advantage, but I'm not extremely confident about it.

Bill, this might be your most significant find (that we know about) in a long time, if you have demonstrated otherwise. It's a worthwhile look, though, either way.
12:19 PM Sep 27th
Bill seems to be implying that there is a right answer, or at least that the vast majority of cases allow you to say one or the other with confidence. But there will be many outliers. I'm going to assume the answer is small difference. Looking at 2021 most of the division leaders have very small gaps in WAR (and presumably Win Shares if there was a reasonable way to look up a lot of Win Shares).

But then Mickey Mantle was almost twice as valuable as any other '57 Yankee. Honus Wagner was twice as valuable as anyone else on the '05 and '08 Pirates. Which are similar to the ratios of Cedric Mullins to the other 50-win '21 Orioles.
11:29 AM Sep 27th
My instincts are bigger is better, but looking back on history, a lot of great players on otherwise average teams did quite poorly, especially when it comes to making the post season (Williams, Trout, Banks all come to mind, I am sure there are others).

This gives me 2 ways to be right :)
11:10 AM Sep 27th
I am open to the possibility that the ideal difference between the top-two players is somewhere between the extremes. If I had to pick one extreme, I would go with the balanced team because the quality of the #2 player sets the ceiling for the #3-25 players.

We can take an extreme situation. Suppose that you have a situation in which the star player is Babe Ruth at the plate, Cy Young on the mound, and Ozzie Smith at short in the half of games that he does not pitch. Meanwhile, the #2 player is replacement level. The non-star players will still have eight out of nine plate appearances and will field most of the balls in play, even on the days when the star plays shortstop. I cannot see this team being successful.

Of course, the opposite extreme could be a team with 25 replacement-level players, which would be even worse, but Bill explicitly said "two good players." This could be a team with two 25-win-share players. This leaves plenty of room for the other players to make significant contributions. Theoretically, the #3 player could be replacement level, which would make this team worse that the first team. However, this would not be much more balanced than the first team.

10:49 AM Sep 27th
Having Mike Trout on a lousy team gets you nowhere. The Rays have the right idea; they don't have superstars but, year after year, every single player on their roster is a legitimate major leaguer and that makes them hard as hell to beat. I spend a few months in Florida each year and, while there, I watch all the Rays games. That team never beats itself, never has a losing streak, and never loses in embarrassing fashion because every single player they put on the field actually belongs on the field.
10:10 AM Sep 27th
As long as wild ass guesses are allowed: Intuitively, it seems obvious to me that having a smaller difference is better. Teams with big differences tend to be very bad (1972 Phillies) or underachieving (Barry Bonds Giants.)
8:55 AM Sep 27th
If we're just looking at the extremes, the biggest gaps and the teams with the smallest gaps, I think one wants a large gap. If one is allocating 315 Win Shares versus 120 Win Shares, knowing that Win Share allocations are partially influenced by playing time, I can see the team with the small gap being more likely to be the 120 Win Share team, not the 315 Win Share team.
8:47 AM Sep 27th
Bigger margin is better. Having a forty win share player and a 32 win share player is better than having a 20 and a 16. Unless I misunderstood what you were asking.
8:47 AM Sep 27th
Guessing smaller difference better on a percentage basis because the better the players, the smaller the percentage difference for a given win share difference
8:31 AM Sep 27th
My intuition is that if I'm selecting a random team season from all baseball team seasons in history, I want one with a larger gap; those teams are more likely to have superstars and thus more likely to be good.
8:08 AM Sep 27th
Large, as per wovenstrap.
7:46 AM Sep 27th
Better off if the margin is small.

That means the talent is more evenly spread, and you have more players contributing across more positions, instead of just one or two stars.

The team effort wins out over the individual effort.
3:41 AM Sep 27th
Actually, thinking about it further, I wonder if there’s some sort of weird shape to the curve. For example, I assume you almost never want your best player to be 100% better than your 2nd best. That would give us 40/20, 36/18, 30/15 type pairs. None of those suggest a great team. But you would obviously prefer 30% better in many cases (35/25 beats 25/25, of course). Then again 35/25 seems less desirable than 30/30, since 30/30 means the #3 player might be as high as 30 himself whereas 35/25 means the #3 player is capped at 25.

Faced with the binary question of whether a large or small gap is better, I would still go with large, but I’m on the fence.

- Matthew Namee​
2:47 AM Sep 27th
I think a team is almost certainly worse off if their best player is 20% better than the second best player. That condition would most commonly occur on a bad team, seems to me. Reasons:

1. You may come to overrate the best player as he shines brighter against a weak supporting cast - but he's really not that great
2. If the player is truly a great player, he may disguise the true weak quality of the team, preventing action to improve it

I'll be interested in seeing your reasoning. It seems like a tough nut to crack without knowing how good the theoretical player really is
12:55 AM Sep 27th
My guess is that you want a larger gap. Here’s my reasoning: most teams’ best player will have 18-40 Win Shares. Great teams are more likely to have MVP-level players than bad teams. The gap between a great #1 (say, 35 WS) and an excellent #2 (say, 25 WS) is 29%. I’d say that team is more likely to beat a team whose best player have 25 WS apiece (0% gap).

- Matthew Namee
12:36 AM Sep 27th
I think the smaller gap would be best, because the number 2 guy is the top level for the rest of the team. The number 2 guy being higher leaves room for everyone else on the team to be better. That’s my story, and I’m sticking to it until real information comes along.
12:02 AM Sep 27th
My guess is: better off with larger margin between best and second-best player. My reasoning is interpolating from it’s better if the margin between your best player and worst player is large than small.​
11:53 PM Sep 26th
I'm going to say a larger difference (having one player far better than anyone else) is not as good. It's just a guess but when you have a guy WAY better than the team it is more likely that the rest of the team isn't that good.

No real logical reasoning here. Just a close my eyes and swing choice.

My Best-Carey
11:49 PM Sep 26th
You want the gap to be large. I'm reason it out this way. Let's say the gap is literally as small as it could be. The best player is at 6, #2 is at 5. That means you've got 23 other players milling about and the only fact we know about them is that the #3 best player has 5 win shares (or fewer) and that guy as well as every other player on the team has either 5 win shares or some number lower than that. That does not seem like a good way to gather together some wins. The lower numbers create a kind of ceiling for value and you don't want that.
11:42 PM Sep 26th
My guess is that it is better to have players closer together in value. In your power/speed number, 2 20s are better than a 30 and a 10; I'm guessing that that general principle holds. Mike Trout may also be evidence - great as he is, his teams are not due to lack of supporting cast.
11:32 PM Sep 26th
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