TLDR: "The concept of psychological pricing and our perception of numbers ending in 99 is not unique to the grocery store. Undervaluing a baseball player with a batting average of .299 is consistent with this idea."
"[...] a player going into the final game of the season with a .299 batting average will aggressively chase the goal of hitting .300. [They] swing at 11 percentage points more pitches than the average batter [...] and swing at 63% of pitches on the last day of the season - all for the allure of the ending the season hitting .300"
Aside: In baseball, one of the most common metrics used to discuss the prominence of hitter is the batting average. The batting average is calculated as an individual's number of hits divided by the number of at bats and it is always represented as a three decimal number (e.g. if someone had 5 hits in 20 at bats, we would say he is hitting .250). In 2016 the MLB-wide batting average was .255.
How different is a .299 hitter from a .300 hitter? It turns out about $130 thousand per year. That is how much more money a Major League Baseball (MLB) player would expect to make on their next contract after just one more hit during the regular season.
Valuing .300 significantly more than .299 is consistent with the concept of psychological pricing - the reason why we always see a can of pop selling for $0.99 instead of $1.00. Humans tend to incorrectly perceive prices ending in .99 as meaningfully lower than those ending with one cent more.
In the context of professional baseball, MLB players have to bargain for their wage from prospective teams as part of free agency. Part of the team's due diligence during contract negotiations requires mulling over the player's performance such as their batting average. (For an analogous discussion using the National Football League, see my earlier post). Previous research suggests MLB teams value a .300 hitter much more than .299 hitter (despite the negligible difference) and the former tends to receive a larger contract.
Alternatively, we might say that .300 is a reference point for which baseball players and general managers use as an anchor. The perceived value of a player is now measured against this standard of hitting .300: any player above this number are considered the masters of their craft and should be compensated accordingly.
In either case, we would expect a player sitting just shy of the .300 mark to show more aggression in their at bats to reach this achievement. One place we can look to test this idea is through the number of pitches these players are swinging at. Moreover, when the players know they are near their last chance to improve their batting average we would expect to see their aggression increase. Therefore, I chose to look at the number of pitches a player hitting .299 swings at on the final day of season.
I started by collecting all the pitches thrown on the final day of the regular seasons of 2014 to 2016 from Baseball Savant. Then I used Fan Graphs to identify which players begun the final day of the season hitting .299 and .300. (I term a player who goes into the final game hitting .299 a ".299 hitter", similar with .300 hitters). I then classify the reaction by the batter as either a swing, no swing, or neutral. Swings include putting the ball in play and swinging strikes - this is where the intention is to make contact for a hit. No swings are where the batter does not swing and includes balls and called strikes. Lastly, neutral reactions are when the outcome was already decided: intentional balls, wild pitches, pitch-outs, etc.
I remove the neutral reactions and I calculate the fraction of pitches that resulted in swings. I separate the data into three groups: .299 hitters, .300 hitters, and all hitters (regardless of batting average). The results are as follows:
With just one more hit needed to reach the .300-mark, .299 hitters are significantly more like to swing in their at bats. These .299 hitters swing at 53% of pitches, 11 percentage points more than a .300 hitter.
When we compare these .299 hitters against themselves, their own strategy completely flips on the last day of the season (using the 2016 data). Whereas they were swinging the bat on 38% of pitches for the majority of the season, these .299 hitters swing 63% of the time on the final day of the season.
The concept of psychological pricing and our perception of numbers ending in 99 is not unique to the grocery store. Undervaluing a baseball player with a batting average of .299 is consistent with this idea. Here I have demonstrated that a player going into the final game of the season with a .299 batting average will aggressively chase the somewhat arbitrary goal of hitting .300.
Whether they are aware of the financial payoffs or they have set an internal reference point, .299 hitters swing at 11 percentage points more pitches than the average batter on the final day of the season. Moreover, while .299 hitters do not swing at 62% of pitches for the majority of the season, they swing at 63% of pitches on the last day of the season - all for the allure of the ending the season hitting .300!
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