2008 Topps Allen & Ginter – A Statistical Approach

This summer I took a statistics course at my college.  In fact, when this blog gets posted I will be in the middle of my final exam.  For this class I had to do a project that involved testing something with what we have learned.  I decided to test whether or not 2008 Topps Allen & Ginter baseball boxes really contain more than two “hits” per box on average.  Below you will find my paper that I wrote.  Right now I have a B+ in the class.  I might squeeze out a low A if I do really well with this project and final exam.




Sports card collecting is a major hobby in today’s society.  Even in this high tech world of gadgets and video games people still have the urge to crack open a pack of baseball cards hoping to find one of their favorite players.  Overtime the hobby has changed very much.  Today you can open up a pack and find cards that contain actual pieces of memorabilia (bat, jersey, pants) that a player used in a major league game.  In addition to memorabilia you can also pull out autographs, original vintage cards, and the actual printing plates that are used to make the cards.  The Topps Company is one of the biggest suppliers of baseball cards in the industry and in recent years they have introduced a product called Allen & Ginter.  This product is modeled after the 1887 set that was the first set of cards actually created for collecting instead of just finding them inserted into packs of cigarettes.  This year, Topps released its 2008 version of this specific product.  On the side of the product, the Topps Company states that you will receive two “hits” per box on average.  A “hit” can be defined as an autograph, memorabilia, printing plate, rip card, or any serial numbered cards that are numbered to only one in the entire world.  Topps introduced the world to the “rip card” back in 2006, which is a card that you tear open and inside there will be a special mini card.  Rip cards come one in every twelve box case.  Another potential hit would be what Topps calls a silk card.  These are small baseball cards made of silk and there are only ten of those per player.  Since this product has been released, many people have said that their boxes have contained more than two hits.  In this study, I will attempt to figure out if the average is really more than two per box. 




             This study consisted of 33 random samples ranging from long time collectors all the way to fairly new collectors that were trying out this product for the first time.  After witnessing a number of these boxes opened and seeing that collectors were receiving more than two “hits” per box, a survey was conducted to see if two “hits” per box was incorrect.  Along with asking how many “hits” they received, they were also asked what kind of “hits” they got.  The “hits” were broken down into six different categories: memorabilia, autograph, printing plate, rip card, 1/1, and silk insert. 


Statistical Analysis:

            The statistical analysis will be using a t-distribution test because this is a real life situation in which we do not know what the actual standard deviation will be without calculation.  The 33 random samples contained a mean of 3.091 “hits” per box, and a standard deviation of 1.071.  The Topps Company states that there is an average of “two” hits per box.  As you can see from the 33 random samples the mean is higher.

Descriptive Statistics: Hits Per Box


Variable       N  N*   Mean  SE Mean  StDev  Minimum     Q1  Median     Q3

Hits Per Box  33   0  3.091    0.186  1.071    1.000  2.000   3.000  4.000


Variable      Maximum

Hits Per Box    5.000


            Using Minitab, and running a t-distribution with a 99% confidence interval, you can see that the Ho = 2.  The distribution provides me with a p-value of 0.0000008.



One-Sample T: Hits Per Box


Test of mu = 2 vs > 2



                                         99% Lower

Variable       N   Mean  StDev  SE Mean      Bound     T      P

Hits Per Box  33  3.091  1.071    0.186      2.634  5.85  0.000

The above histogram shows you were the mu is in relation with the rest of the sample based on the 99% t-confidence interval for the mean.  When comparing the p-value to the alpha (0.0000008 < .01), you can see that the p-value is much lower.  Since the p-value is lower than the alpha, I can reject the Ho hypothesis and say that there is good evidence that the average is more than two “hits” per box.  To support my claim that the average is not two, below you will find Minitab output that produced a t-distribution asking whether or not the mu was two or not.



One-Sample T: Hits Per Box


Test of mu = 2 vs not = 2



Variable       N   Mean  StDev  SE Mean      99% CI         T      P

Hits Per Box  33  3.091  1.071    0.186  (2.580, 3.602)  5.85  0.000


As you can see, the 99% confidence interval ranges from (2.580 – 3.602).  Since zero is not between those two numbers, that gives me another reason to reject the Ho.

            Out of the 33 random samples, there was a total of 102 “hits”.  Most of the “hits” that collectors were pulling were additional memorabilia cards.  87 of the 102 “hits” were memorabilia cards. That is 85% of the “hits” pulled from their boxes.  Autographed cards came is second, with 9%.   



            After obtaining data from the 33 samples, I statistically found evidence that The Topps Company has inserted more than two “hits” per box.  It seems that the average collector is pulling three “hits” per box.  Due to the p-value being smaller than the alpha you can reject Ho.  When doing another t-distribution to see if two was equal to the mu or not, I obtained an interval that did not contain zero.  That is another reason to reject Ho = 2.  In my research, I believe that the average is not two “hits” per box, but three.  Most of the time, that extra “hit” will be a memorabilia card.

7 Responses

  1. Because my degree is in English, I can only really comment on the mechanics of the writing itself, which is unfortunately just average. Your introduction, while serviceable and informative, doesn’t really capture the attention of your reader. Mainly you have too many very short sentences in a very long paragraph, this gives your reader a sense of a lot of information being conveyed in a short amount of time. I realize that the intended audience is not necessarily a hobby collector and that certain information is key to the understanding of the paper, however, that doesn’t mitigate the importance for good writing.

    I also found a typo that you should fix before turning in the paper. (You have “silk” as “sik” at one point).

    The statistical data seems fine however, and I was very, very interested to see that your results confirm that Topps was heavy with the “hits”. However, I wonder if 33 samples is quite enough to make any serious correlations, Were you able to discern how many total boxes of cards exist in the hobby channel? If so, what percentage of the entire run does 33 samples represent?

    All-in-all, writing quality aside, a very interesting paper, and good luck. I realize it’s for a statistics class so the mechanics of the writing is probably not as important as it would be in an English class, but I would feel remiss if I didn’t try to help you a little.

  2. William,

    Thanks for the comments. In my coarse we were taught about the birthday probability problem. Have you heard of it? It states, “How many people in a room does it take for there to be two birthdays that are the same?” The answer is 23. 25 – 30 samples is a good way to get a feel for the whole population. This was the first time I ever wrote a statistics paper, hopefully it will get better over time. Thanks.

  3. Yes, I have heard of the birthday probability, but that only takes into account that there are only 365 different birthdays, and each day of the year doesn’t have the total number of people born on that day. IN the western hemisphere September – December birthdays are far more common than other months due to parents cuddling during Winter. Spring has a similar effect.

    It just seems to me that less than a 10% (23 out of 265) correlation isn’t much to go on. I seriously doubt that 33 boxes is 10% of the entire box run of A&G, which is why I asked if you found out the total box run of A&G.

  4. No, I did not find out how many total boxes and/or cases they made. I looked, but did not find anything. Sometimes companies release how many cases they made and other times not.

  5. I too thought the sample was small, but you would certainly know better than I. Can’t you figure out an approimate print run by figuring out the 1/case odds etc? I’ve seen it done for other products. By the way, assuming Topps is correct (and that is a big assumption) I will most certainly purchase the “one hit” or less boxes out there, if past history serves as proof.

  6. I’ve busted two boxes of A&G.

    My results:

    BOX #1- 4 hits (all memorabilia)
    BOX #2- 5 hits (all memorabilia)

    I did pull a Stevie Williams skateboard piece. I thought that was pretty cool. I really like A&G, I think the variations of the hits is a cool concept.

    In addition, I really enjoyed your paper.

  7. As a part time statistician (stats minor), I enjoyed the paper. I would have loved to have seen a larger sample, but n=30 is the magic number…

    Your results mirror what I have seen in my own experiences…this is the ONLY trading card product that has yielded the odds or better for me…

    I hope you got that A…

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