MASTER NOTES: Arbitrary Endpoints

On Monday of this week, I was watching a Blue Jays telecast on Sportsnet, a national sports network here in Canada. During the game, the producers put an “infographic” on the screen, describing how one of the Jays’ hitters—sorry, I don’t remember who—had a BA above .300 and some other pretty impressive rate stats.

This struck me as odd, since I knew the rate stats of the hitter in question had generally been pretty unimpressive, like the rate stats of almost all the Jays’ hitters, except Justin Smoak and Teoscar Hernandez. The top BA among qualified hitters at the time was Aledmys Diaz’ .254. Five regulars sported OBPs under .300. Nine had ISOs under .200.

Ah, but there’s the fine print: The stats in question were not for the full season. They were for the period that ran from June 3 through July 22, the day before the game being televised. I went and counted, and that was a span of 50 days, during which the team played 42 games.

Now, you might argue that each regular hitter had roughly 150 PA, which seems like a large enough sample. It turns out that 150 PA is well short of sufficient for most rate stats: BA is about 1,000, OBP about 450, and so on.

(Even at that, Russell Carleton, who came up with the stability-point idea, later clarified that "stability" doesn’t mean the metric perfectly describes an established player skill over the period, and certainly does not predict the metric in equal periods to come. It meant only that the metric would be stable if the games in the period were to be replayed—same opponents, same parks, same weather, etc.)

But even if 150 PA were enough, there’s still a question that demands to be answered:

Why those particular 50 days?

This issue is often described as “arbitrary endpoints,” which refers to the likelihood that picking two other endpoints for a fixed length of time can and probably will result in different outcomes. And in the case of a Sportsnet telecast, like many, the producers are employed by the same company that owns the team. So they might have an incentive to carefully choose endpoints that make a player look like he’s better/more productive than he actually is. Or, as my uncle used to say, they’re trying to spitshine a hobo’s gumboot.

Check, please

But I had to admit to myself that I don’t actually know that a sample of 50 days, 42-ish games and 150-ish PA is neither descriptive nor predictive in all those metrics.

So I checked the stats for Jays hitters who had at least 100 PA in two different 50-day periods. One of the periods was the sample whose endpoints were arbitrarily chosen by Sportsnet: June 3 to July 22. The endpoints of the other period were arbitrarily chosen by the RAND function in my trusty Excel workbook, and turned out to be from April 21-June 10. The Jays played 46 games during that span.

I compared the player metrics from the two periods, using four performance metrics—BA, OPS, ISO and HR/600PA (HR600)—and two skills metrics, walk rate and strikeout rate.

The results pretty much confirmed my hypothesis that there wouldn’t be strong similarities between the players’ metrics in the two periods. But in a couple of them, the disparities weren’t especially wide, either.

Here’s the skinny:

ISO: The biggest differences in performance metrics between the two periods were in the players’ ISOs, with only two players coming within 10 percent of their Period 1 marks in Period 2: Teoscar Hernandez (.254/.236) and Aledmys Diaz (.136/.122). The others showed larger differences, some over 50%, in both directions:

ISO              Per 1   Per 2   +/-%
Kendrys Morales   .135    .241   +78%
Russell Martin    .146    .070   -52%
Justin Smoak      .222    .280   +26%
Kevin Pillar      .198    .147   -25%
Yangervis Solarte .167    .136   -19%
Curtis Granderson .190    .214   +12%
Aledmys Diaz      .136    .122   -10%
Teoscar Hernandez .254    .236   - 7%

Walk Rate: This was a surprise. Plate discipline is a skill, right? Once a player displays a skill... you know the rest. And if not, please immediately turn in your Ron Shandler secret decoder ring. But the question is whether "displaying a skill" is possible when the sample is 42-46 games, when swings of 40+ percent occur, and the smallest change is more than 25%:

bb%              Per 1   Per 2   +/-%
Yangervis Solarte   3%      6%   +88%
Kevin Pillar        5%      1%   -84%
Aledmys Diaz        5%      2%   -52%
Teoscar Hernandez   4%      7%   +51%
Kendrys Morales     8%     12%   +46%
Curtis Granderson  14%      8%   -45%
Russell Martin     15%     20%   +35%
Justin Smoak       18%     13%   -27%

Contrast the walk rate with strikeouts, which were much more consistent, with five of the eight hitters within 10% in the two periods:

K%               Per 1   Per 2   +/-%
Teoscar Hernandez  23%     34%   +47%
Curtis Granderson  34%     25%   -26%
Russell Martin     24%     21%   -15%
Kendrys Morales    21%     23%   +10%
Yangervis Solarte  15%     14%   - 6%
Justin Smoak       24%     25%   + 4%
Aledmys Diaz       14%     13%   - 4%
Kevin Pillar       18%     17%   - 2%

The performance metric with the narrowest differences was OPS, where the largest variance was 50% and six of the players were under 10% variance:

BA%              Per 1   Per 2   +/-%
Kendrys Morales   .605    .910   +50%
Kevin Pillar      .721    .607   -16%
Yangervis Solarte .691    .618   -11%
Aledmys Diaz      .673    .716   + 6%
Russell Martin    .653    .623   - 5%
Curtis Granderson .718    .747   + 4%
Teoscar Hernandez .780    .788   + 1%
Justin Smoak      .854    .848   - 1%

What got into Kendrys Morales? Might have been an injury recovery, but we'll leave inventing narratives to Sportsnet's producers. Surprisingly, given the narrow OPS results, HR600 showed a lot of variation between the periods:

HR600            Per 1   Per 2   +/-%
Kendrys Morales     16   32     +100%
Russell Martin      19   11      -42%
Curtis Granderson   19   26      +37%
Justin Smoak        25   31      +24%
Yangervis Solarte   22   17      -23%
Teoscar Hernandez   26   28      + 8%
Aledmys Diaz        14   13      - 7%
Kevin Pillar        19   18      - 5%

Finally, another relatively low-change performance metric was BA, where four of the hitters were again under 10% variance and only one hitter—Morales—showed a variance of more than 17%:

BA               Per 1   Per 2   +/-%
Kendrys Morales   .203    .293   +44%
Aledmys Diaz      .247    .290   +17%
Curtis Granderson .200    .233   +17%
Yangervis Solarte .247    .216   -13%
Kevin Pillar      .244    .225   - 8%
Russell Martin    .184    .198   + 7%
Justin Smoak      .244    .235   - 4%
Teoscar Hernandez .243    .250   +3%%

Last Words

The hitter with the widest discrepancies in all of this was obviously Morales. So I made a spreadsheet of every game in his career through Tuesday, then calculated his rolling 50-day averages in some of these metrics. What they show was very wide variance across the board:

           BA  HR600   bb%    K%
MAX      .361    49    14%   28%
MIN      .184     3     3%   11%
MEDIAN   .271    23     7%   18%
CAREER   .269    24     7%   19%

The 50-day results in this little research effort are also 50-game results, because the baseball-reference database doesn’t put blank lines in for days the player wasn’t in the lineup; it just skips that date entirely for that player.

Also, keep in mind that the career results are based on 1260 games played, while the others are the 50-day rolling averages. Yet it should come as no surprise that the median of all the 50-day results track very closely with the career numbers.

But there’s only one conclusion to be drawn: Looking at outcomes from a 50-ish-game sequence does not result in a truly representative picture of player performance.

So if someone in your league pitches you a questionable player because "he's batting .310 since Bastille Day" or "he has a .781 OPS since my Granny's birthday," or some such other arbitrary period, thank him politely, say you'll think about it, and assess the situation for yourself. Either that or send his resume to your local team's TV broadcaster. Apparently, they like that sort of thinking.

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  For more information about the terms used in this article, see our Glossary Primer.