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# Statistical Contagion of Diamondback Hitters

A way to improve team hitting is explained.

## The Diamondbacks experienced an 8-game losing streak. Does a long losing streak mean anything?

One study showed it means something: “Clearly, better teams will have longer average winning streaks, while lesser teams will have longer average losing streaks. In fact, the correlation between the two entities is −0.5235, which is statistically significant (p = 0.0030).”

The weakness of the study is that better teams were determined by winning percentage. It is likely that the length of streaks was an indirect and imprecise measure of each team’s winning percentage. In other words, it had no added value, so it meant nothing.

## Is there an alternative measure that is not correlated with win percentage?

A smoothness index has been used to study just-in-time scheduling in manufacturing. Patrick R. McMullen wrote a paper that applied smoothness to baseball. After calculating a team’s win percentage for an entire season, his algorithm measures the Euclidean distance between the actual smoothness and optimal smoothness of a team’s pattern of wins and losses. He called the distance the “Gap.”

“It should be noted that there is no significant correlation between a team’s winning percentage and their “Gap” measure―the correlation is −0.2175, with a p-value of 0.2483. As such, the “Gap” measure does provide information beyond a team’s winning percentage.” — Patrick R. McMullen

Because that measure is not correlated with winning percentage, I believe his “Gap” measures a unique characteristic. Potentially, the “Gap” can be changed to make the team better (more on that later).

How to calculate ‘Gap”. Subtract how many games a team has won through game i compared to how many games they were expected to win through game i (equal to season winning percentage multiplied by i). This difference is then squared, and summed for all 162 games. Take the square root of the season total.

## What is the “Gap” of the Diamondbacks?

In the 2016 season, the smooth teams had ‘gaps” less than 20. The Diamondbacks were smooth with a “gap” of 17.35. Similar to the most coarse sandpaper, the most inconsistent team was the Braves with a “Gap” of 76.3.

In 2020, with a 41.67 win % in the 60 game season, the Diamondbacks’ “Gap” was 12.27. When we adjust that to 162 games, the “Gap” was 33.13. Because the “Gap” was above 20, the Diamondbacks were inconsistent, but likely other teams were more inconsistent.

However, in 2020 the “Gap” of 33.13 does not tell the whole story. I am reasonably confident, given the players’ talent and the team’s coaching that the Diamondbacks would be a 500 team in a 162 game season. With a 50 win % instead of a 41.57 win %, their “Gap” would have been 83.98. Given this more accurate perspective of team strength, the team was hugely inconsistent, and even more inconsistent than the 2016 Braves.

## How can the Diamondbacks’ “Gap” be improved?

“Like they say, hitting is contagious.” — Aaron Judge, July 2020. He meant that that one player’s awesome hitting spreads to teammates like an infectious disease. Who said it first is unclear. Maybe it evolved from Vince Lombardi saying, “Confidence is contagious.” Perhaps the general origin of the idea was the French author François de La Rochefoucauld. In 1678, he wrote (translated into English), “Nothing is so contagious as example; never is any considerable good or ill done that does not produce its like.”

A study showed a correlation (existence of statistical contagion) between one player’s positive change in batting average (BA) and his teammates’ BAs.

“Our results show that for the batting average, the null hypothesis of “no difference between groups” is rejected at the alpha =.05 level. We submit that this suggests the existence of a statistical contagion effect for hot hitting. The aggregate BA (n=151) was seen to increase by 1.6 to 20 points (average of percentage points) for the treatment group during a teammate’s hitting streak.” — Joel R. Bock et. al.

## Contagion happens internally.

“If hitting contagion does have a concrete basis, it is likely be motivated internally; some neurobiological or psychological mechanisms then would translate the identification and observation of hot hitting by the streak hitter into an improvement in hitting performance by the observer.” — Joel R. Bock et. al. Bock’s study referenced four studies that could explain the effect.

• Gray and Beilock advanced the idea of the mechanism of “action induction” to explain hot hitting contagious effect. In action induction, observers of the hot hitter tended to imitate performance of others’ actions that were recently observed.
• An experimental study by Cross et al. identified a neurological pathway that associates new action learning from passive observation.
• Rizzolati et al. summarized many studies on mirror neurons that fire in the mind of an observer watching others perform physical activities; these same neurons are associated with limb movements used in actual performance of this activity.
• Lee and co-workers demonstrated a positive contagion effect on golfers who erroneously thought they were using putters belonging to highly skilled golf professionals.

## Implementation details matter.

Bock’s study showed that the hot hitting streak must be noticed within 5 days. If noticed 7 days later there is no significant impact on teammates. What’s up with that?

One possible explanation follows. When teammates notice an emerging hot hitting streak being celebrated, they believe maybe I could start a hot streak, too. However, if they notice a long-standing hot hitting streak without celebration, they believe that player is as good as expected, but not better. Like him, I must be as good as expected, and so I doubt I will start a hot streak.

Could the AZ Snake Pit take action to improve the hitting of the Diamondbacks? Every 5 days, if any hitter has an improved batting average, it could be published on the AZ Snake Pit website. In addition for home games, perhaps Jack Sommers could ask a question about an emerging hot batter in Torey Lovullo’s pregame interview.

## Might there be another measure in addition to batting average?

A study looked separately at two measures: a) batting average and b) batter success calculated by hits+walks+sacrifices / plate appearances. After adding variables to account for impact of home/away, grass/artificial, night/day, lefty/righty pitchers, team ahead/behind, 2outs/<2outs, and 1st 6 innings/later innings, “… the study failed to find convincing evidence in support of wide-scale streakiness [in individual batters over a 4 year period.]”

As much as batting average, maybe their measure of success (hits+walks+sacrifices / plate appearances) indicates a type of hot batting streak and could be infectious to teammates.

I leave it to you the reader to suggest other measures that might be infectious to teammates.