Whoops, messed up the title.

Hello everyone, I'm currently taking a course designed around writing research papers and for the most recent project I got to choose something related to my major (Math). Being a huge baseball fan, I decided to make a model of expected performance of MLB players for various batted ball velocities. If you want to read the whole paper, I uploaded it to imgur HERE, but it's a bit messed up since imgur made it one big picture instead of a picture per page. The large white spaces are page breaks.

I used the Baseball Savant database to find the batted ball data for 10 "league average" players (10 players with about 100 wRC and combined BSR of about 0). I then tallied whether it was an out, single, double, triple, or home run for each of the 3300 data points, sorted by batted ball velocity, and then calculated the average batting average and OPS for ranges of batted ball velocity. Then I made two scatter plots, one for batting average and one for OPS, using that calculated data.

I then found a polynomial trendline that matched the data by seeing which line of degree up to 6 fit the data best while also staying positive for the entire range (since no player is bad enough to have a negative AVG!)

Lastly I took the equation of that trendline and plugged it into Wolfram Alpha along with any hitter's average batted ball velocity to find the "expected" performance. Strangely, I originally thought that the results would be similar to BABIP/OBP (since no walks is mitigated by no strikeouts) and OPS, but it actually ended up being closer to AVG and AVG SLG. So to calculate expected OBP and OPS I ended up taking the calculated values and adding in career walk rate.

Anyway, enough with the wall of text, let's get to numbers! It's what you all actually care about. For the project I only analyzed 10 players originally, so if you want me to look at someone else, just comment and I'll get back to you as soon as I can (probably).

Note: I make no promises on the accuracy. Take it with a grain of salt.

*I think his low contact tool and high power tool broke it. It would be more realistic as 0.222/0.362/0.970 (His career OBP is 0.140 higher than his AVG) and 0.124/0.264/0.639

So there you have it, from this data it seems like Cespedes and Desmond should improve greatly next year while Harper, Gordon, Zobrist, and Wieters should decline.

Now, I know what you're about to say, "Batted ball velocity isn't the whole picture, the angle and direction also affects performance". My response to that is that I personally think that it is the largest piece of the puzzle, and the OPS predictions for Donaldson, Davis, Heyward, and Upton being practically the same seems to agree. Maybe Harper and the others have the ability to consistently put the ball exactly where they want it.

Either way, I'm open to criticism and other comments. I also posted it here because I think you guys will provide better comments about this post.

From this data, I would love it if we signed Cespedes, but we don't have room for much more salary growth. In a game where hitting the ball hard is important, Cespedes hits the ball much harder than average.

Also, if we can dump Elvis' salary, I would love to sign Desmond for a 1-2 year bounceback contract. If he puts up something close to a 0.777 OPS next year he's easily worth 20 million a year but I don't see him getting that this year due to his stats. He could potentially be THE hidden bargain of this offseason.

Let me know if there's another player you want me to analyze.

Thank you for your time.

EDIT: Forgot to mention, I have no idea if this will work for pitchers (using the against velocity). It should since Baseball Savant has that option but I don't know about the accuracy.