Sports: The Magic Number is Dead

There was a time when smart baseball people, in a not-so-smart way, assigned magic numbers as milestones for Hall of Fame entry.

You collected 3,000 hits? You're in. How about 500 home runs? Money in the bank.

Thanks to the Steroid Era, these same smart baseball people are reevaluating the magic number for home runs. In reality, they should simply get rid of magic numbers altogether.

What do totals really tell us without context? The only total I care about is plate appearances.

Player A collected 2,716 hits
Player B collected 2,654 hits

Which player was the more distinguished hitter?

Of course, Player A was Rusty Staub and Player B was Ted Williams. This is a bit of an extreme example. The number of hits are close while the batting averages (.279 for Staub and .344 for Williams) are not.

However, it helps explains the fundamental problem of relying on totals and assigning arbitrary magic numbers.

Another reason this is problematic is that even if you have two players with identical numbers of hits and plate appearances, the circumstances around the two players may have been different. Let's say, for example, that one of these players was active from 1920 through 1936 while the other was active from 1959 through 1975.

Shouldn't make that big of a difference? Well, the mean batting average from 1920 to 1936 was often between .280 and .295 while the mean batting average between 1959 and 1975 was mostly between .235 and .250. Quite the different circumstances.

While we don't yet have an example of this, a player could collect 3,000 hits with a lifetime batting average of .265. Sound crazy? Cal Ripken has 3,184 career hits with a batting average of .276. Brooks Robinson has 2,848 hits with a career average of .267.

It's time to look at statistics more intelligently. It's time to, for the purposes of analysis, ignore all totals other than plate appearances.

Rely largely on ratios of the player's qualitative stats versus the league average. In other words, what percentage better or worse than the league average was the player in Slugging Percentage during his career?

Consider the same for Batting Average, On Base Percentage and OPS. Of course, you can have great qualitative stats and only play one game, one season, or a small handful of seasons. That's where plate appearances come into play.

It is incredibly difficult for even great players to sustain greatness for the entirety of a long career. Because of that, the perception of the dominance of a long-time player can be diminished.

Similarly, one could dangerously favor a player with slightly better qualitative stats but who played three fewer seasons.

And so, I propose a sliding rule to help evaluate career dominance in offensive statistics. This is not a perfect system. But I find it much more accurate than what we currently have.

To be considered dominant over one's career in Batting Average, On Base Percentage, Slugging Percentage, or OPS, players with the following number of plate appearances must have the corresponding ratio versus the league average in their given qualitative stat.

Ratio	PA
1.00	12,689
1.01	12,450
1.02	12,216
1.03	11,987
1.04	11,762
1.05	11,541
1.06	11,324
1.07	11,112
1.08	10,903
1.09	10,698
1.10	10,497
1.11	10,300
1.12	10,106
1.13	9,915
1.14	9,728
1.15	9,544
1.16	9,363
1.17	9,186
1.18	9,011
1.19	8,840
1.20	8,671
1.21	8,505
1.22	8,341
1.23	8,181
1.24	8,023
1.25	7,867
1.26	7,714
1.27	7,563
1.28	7,415
1.29	7,269
1.30	7,125
1.31	6,984
1.32	6,844
1.33	6,707
1.34	6,572
1.35	6,438
1.36	6,307
1.37	6,178
1.38	6,050

How did I put together these numbers? Lots of trial and error. Essentially, you generally need a minimum of 10 years in the Major Leagues to be considered for the Hall of Fame. And, in most cases, you'd only consider such a player if they performed at the highest level of dominance and played a full 10 seasons. Therefore, about 600 plate appearances per season would be about 6,000 total plate appearances required if someone had a 1.38 ratio (a ratio which is incredibly rare) in a particular qualitative stat.

Knowing that it is impossible to maintain that dominance, I loosened the ratio requirement as plate appearances go up. As a point of reference, there are seven players in the Hall of Fame with greater than 12,689 plate appearances. There are 13 with fewer than 6,050, although many are those who played partially in the Negro Leagues (and therefore have incomplete stats) or played during an era in which fewer games were played.

The result? Following are the players who are considered Hall of Fame quality in regards to dominance of the OPS statistic:

Player	PA	Ratio
Babe Ruth	10,616	1.62
Ted Williams	9,791	1.55
Lou Gehrig	9,660	1.45
Jimmie Foxx	9,670	1.42
Hank Greenberg	6,096	1.41
Dan Brouthers	7,658	1.40
Rogers Hornsby	9,475	1.40
Mickey Mantle	9,909	1.39
Ty Cobb	13,072	1.38
Stan Musial	12,712	1.37
Joe DiMaggio	7,671	1.35
Tris Speaker	11,988	1.35
Willie Mays	12,493	1.34
Frank Robinson	11,743	1.33
Hank Aaron	13,940	1.33
Johnny Mize	7,371	1.33
Ed Delahanty	8,389	1.31
Mel Ott	11,337	1.31
Honus Wagner	11,739	1.30
Roger Connor	8,837	1.30
Harry Heilmann	8,960	1.29
Mike Schmidt	10,062	1.28
Willie Stargell	9,026	1.28
Duke Snider	8,237	1.28
Willie McCovey	9,686	1.28
Nap Lajoie	10,460	1.28
Harmon Killebrew	9,831	1.27
Cap Anson	11,319	1.26
Eddie Mathews	10,101	1.26
Sam Crawford	10,594	1.25
Al Simmons	9,515	1.24
Jesse Burkett	9,605	1.24
Billy Williams	10,519	1.23
Eddie Collins	12,037	1.23
Orlando Cepeda	8,695	1.23
Al Kaline	11,597	1.22
Jim O'Rourke	9,051	1.21
Carl Yastrzemski	13,991	1.21
Paul Waner	10,762	1.21
Reggie Jackson	11,416	1.21
George Brett	11,624	1.21
Jim Rice	9,058	1.20
Fred Clarke	9,819	1.20
Charlie Gehringer	10,237	1.20
Roberto Clemente	10,212	1.20
Goose Goslin	9,822	1.19
Willie Keeler	9,594	1.18
Ernie Banks	10,395	1.18
Joe Morgan	11,329	1.18
Zack Wheat	9,996	1.18
Rod Carew	10,550	1.18
Wade Boggs	10,740	1.18
Jake Beckley	10,470	1.16
Eddie Murray	12,817	1.16
Dave Winfield	12,358	1.16
Tony Gwynn	10,232	1.15
Tony Perez	10,861	1.15
Paul Molitor	12,160	1.13
George Davis	10,151	1.13
Rickey Henderson	13,346	1.12
Andre Dawson	10,769	1.12
Robin Yount	12,249	1.09
Lou Brock	11,235	1.09
Cal Ripken	12,883	1.08

There are a few others I have been able to isolate who are not currently in the Hall of Fame, although it's possible that this is not a complete list:

Player	PA	Ratio
Dick Allen	7,314	1.33
Mark McGwire	7,660	1.33
Bob Johnson	8,047	1.26
Edgar Martinez	8,672	1.26
Sherry Magee	8,546	1.23
Ron Santo	9,396	1.20
Dwight Evans	10,569	1.19
Fred McGriff	10,174	1.19
Dave Parker	10,184	1.14
Rusty Staub	11,229	1.14
Pete Rose	15,861	1.13
Harold Baines	11,092	1.12
Darrell Evans	10,737	1.12
Tim Raines	10,359	1.11

That's right, our buddy Rusty Staub. Also a few surprises of players who are either typically on the edge or no longer considered for enshrinement.

Of course, this is only meant as a guide. My sliding rule still uses some arbitrary numbers, though they aren't round and pretty. Even with the players above (and for those who just missed qualifying), other considerations should be made.

Is Rusty Staub, a player who enjoyed a long though largely unnoticed career be considered in such a positive light? Maybe, maybe not. It's always interesting how perceptions of players can change when you take the names away and look only at the stats.

Also, you may want to require that players are "dominant" in more than one category. And of course you'll also need to consider things like defensive and baserunning prowess.

But this is a start. It's not the be-all-end-all in this type of analysis. But it's the type of analysis that more in baseball need to be making. Why?

Because the magic number is dead.